Giant dipoles and superfluorescence in perovskite superlattices for optical transistors under ambient conditions

Abstract

The giant dipole, a collective state of coherent dipole coupling, offers significant potential for quantum computing applications. An example method for detecting a giant dipole in a material can include applying, to a material comprising dipoles configured to couple to one another via dipole-dipole coupling, an optical pulse having a polarization; and detecting the giant dipole in the material based on one or more of: a time evolution of an excited energy state associated with a population of the dipoles, an emission signal in measured photoluminescence data of the material, or one or more temporal correlations between a first photoemission data obtained from the material and a second photoemission data obtained from the material.

Description

GIANT DIPOLES AND SUPERFLUORESCENCE IN PEROVSKITE SUPERLATTICES FOR OPTICAL TRANSISTORS UNDER AMBIENT CONDITIONS CROSS-REFERENCE TO RELATED APPLICATION

[0001] This patent document claims priority to and benefits of U.S. Provisional Application 63 / 705,739, entitled “GIANT DIPOLES AND SUPERFLUORESCENCE IN PEROVSKITE SUPERLATTICES FOR OPTICAL TRANSISTORS UNDER AMBIENT CONDITIONS,” and filed on October 10th, 2024. The entire content of the above noted patent application is incorporated by reference as part of the disclosure of this patent document. TECHNICAL FIELD

[0002] The present patent document relates to methods, systems, materials, devices and applications pertaining to giant dipoles created under ambient conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0003] FIGS.1A-1C show example structural properties of perovskite superlattices according to some disclosed embodiments.

[0004] FIGS.2A-2F show example data plots describing superfluorescence characteristics of some disclosed embodiments.

[0005] FIGS.3A-3G show example data plots to describe formation dynamics of a giant dipole that can be obtained in accordance with some disclosed embodiments.

[0006] FIGS.4A-4G show example data plots illustrating performance of some embodiments of superfluorescence-based optical transistors based on the disclosed technology.

[0007] FIGS.5A-5C show results of an example material characterization for PEA2MAPb2I7single-crystal flakes and its epitaxial superlattices.

[0008] FIGS.6A-6C show images of example PEA2MAn-1PbnI3n+1single crystal flakes.

[0009] FIGS.7A-7B show scanning electron microscopy images of example PEA2MAPb2I7single crystal flakes.

[0010] FIGS.8A-8B show top-view scanning electron microscopy images of example morphologies of disclosed epitaxial perovskite superlattices.

[0011] FIGS.9A-9D show schematics illustrating examples of different epitaxial growth models.

[0012] FIGS.10A-10I show example synchrotron-based grazing incidence wide- angle X-ray scattering (GIWAXS) mappings of different incidence angles that were obtained in accordance with some disclosed embodiments.

[0013] FIGS.11A-11B show example X-ray diffraction patterns extracted from GIWAXS mappings for disclosed epitaxial PEA2MAPb2I7superlattices grown on a single-crystal MAPbBr3 substrate.

[0014] FIGS.12A-12C show top-view scanning electron microscopy images of example morphologies of disclosed epitaxial PEA2MAPb2I7superlattices processed at various spin-coating speeds.

[0015] FIGS.13A-13C show top-view scanning electron microscopy images of example morphologies of disclosed epitaxial superlattices on MAPbBr3 single-crystal substrates grown with different PEA2MAPb2I7precursor concentrations.

[0016] FIGS.14A-14B show examples of calculated optical properties of a disclosed perovskite superlattice under polarized excitations.

[0017] FIG.15 shows example band structures with the density of states of different elements for a disclosed PEA2MAPb2I7superlattice.

[0018] FIGS.16A-16B show example plots of charge density of a disclosed PEA2MAPb2I7superlattice at low photoexcited dipole densities.

[0019] FIGS.17A-17B show example plots of charge density of some disclosed PEA2MAPb2I7superlattices at high photoexcited dipole densities.

[0020] FIG.18 shows an example of phonon dispersion of different elements in a disclosed PEA2MAPb2I7superlattice.

[0021] FIGS.19A-19B show examples of photoexcited dipoles with anisotropic behaviors in some disclosed PEA2MAPb2I7superlattices.

[0022] FIG.20 shows a schematic to explain an example timeline for the formation of a giant dipole based on the disclosed technology.

[0023] FIGS.21A-21B show schematics illustrating an example of bandgap renormalization during the formation of a giant dipole.

[0024] FIGS.22A-22E show schematics to explain an example mechanism related to obtaining a transient absorption spectrum (TAS).

[0025] FIG.23 shows example transient absorption mappings under p-polarized light.

[0026] FIGS.24A-24B show example schematic energy diagrams and associated transient absorption spectra of a disclosed giant dipole.

[0027] FIG.25 shows an example plot illustrating detailed delays in the formation of a disclosed giant dipole.

[0028] FIGS.26A-26B show example plots of photoluminescence at different p- polarized excitation fluences.

[0029] FIGS.27A-27G show an example series of streak camera images of an emission from a disclosed superlattice.

[0030] FIG.28 shows an example superfluorescence decay time as a function of excitation fluence from time-resolved photoluminescence.

[0031] FIG.29 shows an example emission spectra of a disclosed PEA2MAPb2I7superlattice under s-polarized excitation of 26 μJ·cm-2fluence.

[0032] FIG.30 shows an example of peak wavelength variations at different excitation fluences.

[0033] FIGS.31A-31B show example emission intensity at 720 nm plotted as a function of the IN1 / IN2 fluences for different intensities of IN2 / IN1 fluences.

[0034] FIG.32 shows an example air stability test of the superfluorescence from a disclosed PEA2MAPb2I7superlattice.

[0035] FIG.33 shows an example schematic optical path for pump-probe measurements.

[0036] FIG.34 shows an example schematic optical path for polarization- dependent superfluorescence emission measurements.

[0037] FIG.35 shows an example schematic optical path for streak camera- based time-resolved emission measurements.

[0038] FIG.36 shows an example schematic optical path for testing a disclosed optical transistor.

[0039] FIG.37 shows a flow chart of an example method based on the disclosed technology.

[0040] FIG. 38 shows a flow chart of another example method based on the disclosed technology. DETAILED DESCRIPTION

[0041] Section headings are used in the present document only for ease of understanding and do not limit the scope of the embodiments to the section in which they are described.

[0042] Disclosed are methods, materials, designs, devices and applications that pertain to giant dipoles created under ambient conditions. Some disclosed embodiments use an epitaxial two-dimensional halide perovskite superlattice, which confines photoexcited carriers and enhances the formation of a giant dipole. In some embodiments, superfluorescence bursts from the giant dipole, exhibiting distinct Rabi oscillations. In some disclosed embodiments, a dependence of the superfluorescence on photoexcitation polarization is demonstrated, leading to the design of an innovative optical transistor. The disclosed embodiments relate to giant dipoles. Embodiments of the disclosed technology can be implemented in quantum systems, development of high-precision quantum logic gates, and novel optical devices, among other possibilities.

[0043] In one aspect, a method for detecting a giant dipole in a material is disclosed. The method comprising: applying, to a material comprising dipoles configured to couple to one another via dipole-dipole coupling, an optical pulse having a polarization, wherein the optical pulse having the polarization causes a population ofthe dipoles to synchronize with one another forming the giant dipole in the material that exhibits one or more correlated behaviors; and detecting the giant dipole in the material based on one or more of: a time evolution of an excited energy state associated with the population, wherein the time evolution is detected based on measured absorption data of the material, an emission signal in measured photoluminescence data of the material, wherein the emission signal is indicative of a superfluorescence emission by the population, or one or more temporal correlations between a first photoemission data obtained from the material at a first time and a second photoemission data obtained from the material at a second time, wherein the first time is different from the second time.

[0044] In another aspect, a method of controlling a giant dipole is disclosed. The method comprising: providing a material comprising dipoles configured to couple to one another via dipole-dipole coupling; applying, to the material, a first optical pulse to cause the giant dipole to form in the material, wherein the giant dipole is formed from a population of the dipoles that is excited by the first optical pulse into an excited energy state, wherein the population is excited into the excited energy state based on a polarization of the first optical pulse; and applying, to the material, a second optical pulse configured to cause the population to transition from the excited energy state to another energy state, wherein the second optical pulse is configured to cause decay of the giant dipole in the material.

[0045] In yet another aspect, a device based on giant dipole superfluorescence is disclosed. The device comprises: a substrate; a material, disposed on the substrate, comprising dipoles configured to couple to one another via dipole-dipole coupling, wherein the material is configured to receive a first optical pulse and a second optical pulse, the first optical pulse and the second optical pulse each having a polarization selected to control the dipole-dipole coupling to cause a giant dipole to form in the material, wherein the giant dipole is formed from a population of the dipoles that is excited by the first optical pulse and the second optical pulse; and a logic system comprising the substrate and the material, wherein: the polarization of the first optical pulse defines a binary input of the logic system, the polarization of a second optical pulse defines a second binary input of the logic system, a superfluorescence emission detected from the material in response to the first optical pulse and the second opticalpulse defines a first binary output of the logic system, and absence of the superfluorescence emission defines a second binary output of the logic system.

[0046] The giant dipole, a collective state of coherent dipole coupling, plays a pivotal role in understanding macroscopic quantum transitions and offers significant potential for quantum computing. Traditionally, realizing giant dipoles has required extreme conditions, and their detailed behavior remains underexplored. The technology disclosed herein presents the formation of a giant dipole under ambient conditions for the first time and techniques to investigate its ultrafast formation dynamics and energy transfer mechanisms.

[0047] Dipoles comprising photo-excited electron-hole pairs can reconfigure collectively at high density, with the wavefunctions of individual dipoles sharing spatially and temporally synchronized phases, to form a giant dipole (FIG.1A). Its macroscopic quantum behaviors with particular interest, such as collective transitions and resonant response, endow it with intrinsic robustness and feasibility for quantum information processing.

[0048] The formation of giant dipoles requires a sufficiently large and close- packed dipole population to ensure overlapping electromagnetic fields, which increase the likelihood of interactions and thus facilitate the reconfiguration of many individual dipoles to the collective state. People conventionally inferred giant dipole through its coherent emission, known as superfluorescence, which often requires low temperatures or strong magnetic fields for spontaneously correlations. Recently, halide perovskites have attracted considerable interest because they exhibit superfluorescence under relaxed conditions, even at room temperature. Nevertheless, the direct evolution of the giant dipole lacks description. Dipole motions and disturbances in surrounding electromagnetic fields inducing random phase variations, blur thorough observations, and superfluorescence alone reveals only the emission, not the underlying collective state. As a result, these encouraging superfluorescence findings have yet to translate to quantum information technologies as promised, because emitted photons do not interact directly and the inaccessible giant dipole cannot be prepared or switched on demand. To overcome this limitation, a major challenge is to move beyond emission and resolve the origin of superfluorescence— giant dipole—by tracking its formation, evolution, and controlling the emission.

[0049] Some disclosed techniques enable study of the collective behaviors of giant dipoles under ambient conditions. Some embodiments relate to epitaxial growth of halide perovskite superlattices with vertically aligned multi-quantum wells, which create natural cavities facilitating giant dipole formation by effective dipole confinements. In some embodiments, the formation dynamics of the giant dipole is described through transient absorption mappings, where the coherent-state bleaching band emerges as an energy fingerprint with excitation dependency, appearing separately from the primary excited state. In some embodiments, the collective recombination of carriers within the giant dipole results in superfluorescence, characterized by Burnham-Chiao ringing, extension coherence time, and coherent multi-photon emission burst. With a unified understanding of superfluorescence origin, some embodiments exploit the controllable dynamics of the giant dipole to realize an optical transistor with quantum logic operations. In some embodiments, by tuning the carrier coupling to modulate superfluorescence emission of the giant dipole, an equivalent controlled-NOT gate can be provided, where the presence of control enables or suppresses the coupling, thereby gating the transition pathway of the target state. Some embodiments relate to a device that introduces a macroscopic quantum control based on giant dipole formation and superfluorescence emission, paving the way for optical qubit processing through collective transitions. In some embodiments, the epitaxially grown superlattice ensures the long-term stability of both the material and device under ambient conditions. In some embodiments, an optical pulse having a polarization causes a population of dipoles to synchronize with one another forming a giant dipole, in a material, that exhibits one or more correlated behaviors.

[0050] Example anisotropic structure of an epitaxial superlattice

[0051] In an example embodiment, a quasi-two-dimensional perovskite PEA2MAPb2I7(PEA = phenethylamine; MA = methylamine) was chosen as raw material for chemistry stability; the PEA has better moisture resistance than other organic spacers and Pb is more stable than Sn in air. The as-dissolved PEA2MAPb2I7precursor was then used for epitaxially grown on a single-crystal MAPbBr3substrate to form the superlattices (FIGS.5A-5C, FIGS.6A-6C, FIGS.7A-7B, FIGS.8A-8B, FIGS.9A-9D and Section S2). In some embodiments, bonding selectivity at the epitaxial single-crystal interface drives vertically aligned multi-quantum wells with long-range order and uniformity. Cryogenic transmission electron microscopy images in an example analysis revealed superlattices of periodic Pb-I slabs separated by PEA spacers in the xz plane and homogeneous Pb-I slabs in the xy plane (FIG.1B and FIGS.10A-10I). Long-range order within the superlattice was evidenced by synchrotron-based grazing incidence wide-angle X-ray scattering, which revealed spot patterns with directional anisotropy (FIGS.11A-11B and FIGS.12A-12C).

[0052] In some embodiments, this vertical aligned multi-quantum wells consistently confine dipole motion along the z-direction across the entire superlattice, substantially reducing random distributions and promoting dipole–dipole coupling (FIG.1C, left and Section S3). In some embodiments, the homogeneous Pb-I slabs in the xy plane offer dipoles a high degree of freedom (FIG.1C, right). In some embodiments, the cavity qualities (e.g., continuity, uniformity, and purity) can be optimized by tuning the superlattice growth parameters (FIGS.13A-13C, FIGS.14A- 14B, FIG.15, and FIGS.16A-16B). In some embodiments, the thin organic spacer enables interlayer dipole coupling between adjacent inorganic layers, further fostering superfluorescence (Section S3).

[0053] Example superfluorescence from a superlattice

[0054] Superfluorescence is the coherent emission of the giant dipole when it undergoes synchronized recombination, releasing its energy in a collective photon burst that represented the macroscopic quantum nature of the ensemble (Section S4). In some embodiments, a streak camera can be used under ambient conditions to capture its ultrafast recombination character. In an example study performed in accordance with disclosed techniques, under low excitation fluence, only fluorescence was observed at ~705 nm, associated with nanosecond-scale intensity decay (FIG.2A and FIG.2B). This fluorescence corresponded to the original bandgap of the superlattice and random dipole recombination. At higher excitation fluences (e.g., >16 μJ⋅cm-), superfluorescence emission was observed. This threshold was markedly lower than previously reported (Table 1). The superfluorescence showed differences from normal fluorescence in intensity, wavelength, and decay behavior (FIGS.2A-2B and FIGS.17A-17B). Specifically, stronger superfluorescence intensities were detected at ~720 nm. The peak intensities followed the superlinear power-law dependence of superfluorescence (FIG.2C). The intensity decayed on a picosecondscale, three orders of magnitude faster than fluorescence, reflecting the collective emission of the giant dipole (FIG.18). The superfluorescence exhibited distinct intensity oscillations during decay (FIGS.2A-2B and FIGS.17A-17B), because it interacts coherently and exchanges energy periodically with the giant dipole. This process is known as Burnham-Chiao ringing, an intrinsic property of superfluorescence (Section S4). Notably, excitation-dependent measurements showed that the oscillation period remains unchanged as the pump fluence increases (FIG.2D). In an amplified-spontaneous-emission propagation effect, although similar oscillations occur, the period would shorten with stronger optical field, because the spatial beating length contracts as gain and group velocity vary. The observed fluence-invariant period in superfluorescence decay therefore rules out propagation-induced modulation and firmly attributes the oscillations to intrinsic coherence of giant dipole.

[0055] In some embodiments, superfluorescence is accompanied by fluorescence. In the example study, superfluorescence was always accompanied by fluorescence (FIG.2E), indicating remnant random dipoles even after giant dipole formation. The Lorentzian-fitted 720-nm peak suggested a superfluorescence resonance mechanism, whereas the Gaussian-fitted 705-nm peak corresponded to fluorescence (FIGS.19A-19B). As the excitation fluence increased, redshifts were observed in the superfluorescence peak from ~718 to ~720 nm and in the fluorescence peak from ~706 to ~708 nm (FIG.20), probably due to energy dissipation via lattice vibrations at elevated temperatures under high excitation fluences. The normalized superfluorescence intensity demonstrated a 180° periodicity in its emission polarization angle because it originated from the giant dipole (FIG.2E, inset and Section S4), whereas the fluorescence remained isotropic because it originated from random dipoles.

[0056] In some embodiments, besides the emission dynamics, first- / second- order correlation measurements for the coherence time are conducted. In some embodiments, first-order correlation measurements can be used to determine the phase coherence time of emissions (FIG.2F). In some embodiments, the normal fluorescence exhibits a short coherence time with Gaussian decay, similar with incoherent light sources. In some embodiments, the superfluorescence exhibits a much longer coherence time with an exponential decay, indicating the macroscopicphase coherence in the emission process (Section S4). In some embodiments, second-order coherence reveals the photon-number statistics and temporal correlations of emissions. In some embodiments, for typical lasing, the photon-arrivals follow Poissonian distribution, leading to photon antibunching over time. In contrast, in some embodiments, superfluorescence arises from coherent recombination of the giant dipole, leading to correlated multi-photon emitting (Section S4). In someembodiments, as a result, photon bunching is observed (e.g., with ^^^^(2)(0) > 1 ) as acharacteristic signature of its coherence before (FIG.2G). In some embodiments, the exponential decay time of the second-order correlation is of the order of the radiative decay time of the superfluorescence emission for low excitation densities.

[0057] Example formation dynamics of a giant dipole

[0058] Superfluorescence is not an isolated optical effect but is the photon burst that accompanies the radiative recombination of giant dipoles. Only by following how this collective state forms can we understand the origin of superfluorescence. In some embodiments, the formation of a giant dipole is from a confined, high-density dipole ensemble developing strong dipole–dipole coupling, inducing excited-state energy evolution. In some embodiments, as individual dipoles synchronize into a giant dipole, these interactions drive their collective transition to a new coherent state with new energy level (FIGS.21A-21B and FIGS.22A-22E). In some embodiments, such dynamics and energy distribution are absent for thermodynamic processes, where no collective interactions are involved to support the formation of the coherent state (Section S5). In an example study performed in accordance with disclosed techniques, to investigate this collective process, pump-probe transient absorption mapping was applied, which achieved high temporal and energetic resolution (FIG. 23). All measurements were conducted under ambient conditions.

[0059] In some embodiments, a superlattice shows ground state bleaching (GSB). In the example study described above, the superlattice showed ground state bleaching (GSB) of 600~682 nm, corresponding to its original bandgap (FIG.3A). Compared with its raw flake materials, the redshifted bandgap is because epitaxy introduces lattice compression for both organic spacer and Pb-I slabs, whose strain decreases the bandgap of the superlattice. At a low fluence of 3 μJ⋅cm-2, the dipole population was insufficient to establish strong dipole–dipole interactions. Under thiscondition, the transient absorption mapping displays conventional features of the GSB and the following excited state absorption (ESA) at 695~710 nm (FIG.3A and Section S5). Raising the fluence to 16 μJ⋅cm-2, the dipole population enlarged, enhancing GSB signals as expected. However, a new coherent-state bleaching (CSB) appeared at 717~734 nm among ESA (FIG.3A). This bleaching indicates a much faster population-depletion channel that is absent from the low-fluence spectra. At 43 μJ⋅cm-2, the new bleaching evolves into a pronounced stripe, suggesting a distinct population that decays far rapidly than normal excited carriers within that specific energy window (FIG.3A).

[0060] In some embodiments, to understand the origin of this new bleaching, the evolution of the ESA and its excitation dependency are studied, because the CSB appears within that band. In some embodiments, the ESA represents the excited dipole population, so its spectral behaviors reveal excited-state interaction through energy transition (Section S5). In some embodiments, when strong dipole–dipole interactions lead to the formation of a giant dipole, the excited-state energy levels undergo polarization because of their collective arrangement. In some embodiments, the long-range ordered moments of giant dipole are parallel with the internal collective field, thereby reducing the higher-excited-state energy (Section S5). As a result, in some embodiments, when excitation fluence increases, intense dipole density brings stronger interactions, and the ESA peak shifts toward longer wavelengths, e.g., from ~700 nm to ~720 nm (FIG.3B), corresponding to the superfluorescence peak at 720 nm (FIG.2E). In some embodiments, this shift represents giant dipole formation and brings a modulation of the excited-state energy structure (Section S5). In some embodiments, the new bleaching appears exactly within this shifted ESA window, indicating that giant dipole undergoes a synchronized ultrafast decay (FIGS.24A-24B and Section S5). In some embodiments, this selective bleaching indicates that the giant dipole possesses independent energy levels generated by collective coherence and distinguished from uncoupled dipoles, providing basis for tracing and controlling this collective state. In some embodiments, the population depletion cannot be filled by surrounding individual dipoles within the ultrafast timescale, as vibrational relaxation is comparatively slow (Section S5). In some embodiments, the shifted ESA and following bleaching provide energy-resolved signatures of the giant dipole formation in a material.

[0061] Some disclosed embodiments relate to analyzing collective dynamics of giant dipoles. In some embodiments, after clarifying the formation energy associated with giant dipole formation, its collective dynamics can be examined with temporal resolution. In some embodiments, when the giant dipole decays, its collective polarization generates a transient electromagnetic field that modulates the optical response of surrounding media (Section S5). In some embodiments, this interaction leads to periodic photon exchange between the collective state and the ground state and induces oscillations in the giant dipole population. In some embodiments, beats are experimentally observed within the ESA, corresponding to the population oscillation of the giant dipole (FIG.3C). In some embodiments, similar with the Burnham-Chiao ringing (FIG.2B), these beats arising from the same dipole–dipole coherence and collective dipole coupling to the optical field. In some embodiments, the decay rate of the giant dipole is highly dependent on excitation fluence. In some embodiments, a giant dipole exhibited a decay of picosecond-scale due to strong synchronization (FIG.3D) at high excitation fluence, as opposed to nanoseconds for random dipoles at 3 μJ⋅cm-2. In some embodiments, it takes time to synchronize the random dipoles before the collective decay (FIGS.21A-21B), which introduces a characteristic delay (e.g., ~4 ps at 7 μJ⋅cm-2excitation fluence) following excitation (FIG.3D, FIG.25, and Section S5). In some embodiments, compared to the tens of picoseconds of delay in polycrystalline perovskites, the ultrashort delay in the superlattice makes it less likely that coherence will dephase due to quantum fluctuations, facilitating superfluorescence. In some embodiments, at high excitation fluence (e.g., 43 μJ⋅cm-2), the delay is reduced further (e.g., to less than 1 ps) before it decays, indicating that a larger dipole population expedites the synchronization (FIG. 3E, top). In some embodiments, this is because larger dipole populations enhance dipole interactions and generate a stronger collective electromagnetic field, promoting synchronization. For the same reason, in some embodiments, the decay time of the giant dipole can also be reduced (FIG.3E, bottom). In some embodiments, this rapid decay, similar to the superfluorescence decay (FIG.3B and FIG.18), is even faster at higher excitation fluences. In some embodiments, these distinct decay dynamics further reveal the collective behaviors of giant dipoles.

[0062] Some disclosed embodiments relate to the coherent response of giant dipole under external driving fields. In some embodiments, under strong excitation, thepopulation of the collective excited-state exhibits a sine-squared oscillation as function of the pulse area (Section S5). In some embodiments, the experimental feature for the giant dipole accords with the function, as shown in FIG.2F. In some embodiments, as pulse area increases (from 0 to π to 2π), the complete oscillating period of the intensity indicates the system undergoes population inversion, such as a π-pulse pumps the state entirely from the ground to the giant dipole, which is brought back to ground by a 2π-pulse. In an example, after estimating the electric field amplitude at the superlattice that corresponds to the 2π pulse, a dipole moment of ~6 Debye was extracted. In some embodiments, when the pulse area exceeds π to 2π, the collective decay begins, where the maximum population was excited and then immediately switched back down. Some disclosed embodiments enable the giant dipole state to be precisely manipulated for macroscopic quantum control through pulse area.

[0063] Example optical transistors

[0064] Some disclosed embodiments relate to optical transistors. Artificial cavities with complicated fabrications are typically required to construct optical transistors (Section S6). In some embodiments, the natural cavities in the perovskite superlattice address this issue. In some embodiments, the superfluorescence emitted from the giant dipole reveals the underlying coherent coupling. In some embodiments,, its superlinear evolution of intensity ensures the fidelity that coupling is amplified when pump exceeds a certain threshold, similar to the transfer curve of electrical transistors. In some embodiments, beyond classical logics, the manipulability of the giant dipole (FIG.3F) provides an equivalent control-NOT quantum-logic gate, while the target bit flips (i.e., couples to the giant dipole or vice versa) only if the control bit is active (Section S6). In some embodiments, a two-qubit optical transistor based on superfluorescence and a giant dipole is provided.

[0065] In some embodiments, for excited states, one approach to encode qubits relies on polarization, which promotes or isolates coupling by applying the same or orthogonal polarizations. In some embodiments, this maintains the independence and high fidelity of the qubits. In some embodiments, polarization-selective coupling is supported by the anisotropic structure of perovskite superlattices. In an example study performed in accordance with disclosed techniques, ab initio calculations revealed that a perovskite superlattice had anisotropic reflectivity, absorbance, and thusefficiency of photo-excitation, resulting in a polarization-dependent dipole population (FIG.4A, FIGS.26A-26B, and Section S7). In some embodiments, under s-polarized excitation along the z-direction, the perovskite superlattice reflects less and absorbs more light, generating a larger dipole population compared to p-polarized excitation at the same fluence in the x-direction (FIGS.26A-26B). In some embodiments, a perovskite superlattice exhibits dipole-population-dependent electronic behavior. In some embodiments, I pxyorbitals were dominant at the valence band maximum, whereas deeper valance states (e.g., from ~0.4 eV below the valence band maximum) were dominated by I pzorbitals (FIG.4B). In some embodiments, this variation in orbital occupation implies that larger photo-excited carrier populations change electron-hole occupancy in different anisotropic orbitals. In some embodiments, in small dipole populations, holes are mostly found at the valence band maximum of the I pxyorbitals, whereas electrons were found at the conduction band minimum of the Pb pxyorbitals (FIGS.27A-27G). In some embodiments, this indicates that most dipole movements were in the xy plane with a high degree of freedom (FIG.28), resulting in large quantum fluctuations and thus no giant dipole formation. In contrast, in some embodiments, in large dipole populations, electrons are excited from deeper valence states to higher conduction states. In some embodiments, although the conduction band is dominated by the same Pb pxyorbitals, the I pzorbital became dominant in the deeper valence band (FIG.4B, FIG.29, and FIG.30). In some embodiments, dipole movements are primarily distributed along the z-direction (FIG.29), confined by the superlattice cavities, thereby facilitating giant dipole formation (FIGS.31A-31B).

[0066] Some disclosed embodiments relate to manipulating dipole coupling. In some embodiments, to manipulate dipole coupling, a superlattice is pumped with collinear polarization. In an example, two s-polarized lasers with tunable power, aligned in the same incident xy plane, are used to excite the superlattice (FIG.4C, FIG.32, and FIG.33). With one beam (IN1) maintaining a certain power, the other beam (IN2) modulates the superlinearity of superfluorescence (FIG.2C), and vice versa, demonstrating collaborative regulation of dipole coupling (FIGS.31A-31B). In an example study, in contrast to superlinear intensity-growth of superfluorescence under s-polarization, only fluorescence was detected under p-polarized excitation, with peak intensity increasing linearly with excitation fluence, representing the dipoles of high degree of freedom without coupling (FIG.4D and FIG.34). Correspondingly, onlyground-state absorption was observed, even at high fluences under p-polarized light (FIG.35).

[0067] In some embodiments, this polarization-dependent dipole coupling enables gate operations. In some embodiments, first, IN1 produces a pre-pulse that drives the system from the ground state (|00^) to excited states. In some embodiments, when IN1 is s-polarization, it initializes the system to z-direction dipoles (|10^) or giant dipole state (|11^). In contrast, in some embodiments, p-polarization pre-pulse maintains an uncoupled state of dipoles in the xy plane (|01^). In some embodiments , building on this initialization, a control-NOT gate is here using IN2 as the operational pulse, whose intensity is adjusted to π-pulse-area that tunes the transition between |10^ and |11^ (Section S6). In some embodiments, when the initial state is |10^, IN2 promotes it to the |11^ because the confined z-direction dipoles facilitate coupling and thus the giant dipole formation (FIG.4E). In some embodiments, if the system is already initiated to |11^, IN2 then stimulates superfluorescence and triggers collective decay of the giant dipole, bringing the state back to |10^ (FIG.4E). In some embodiments, this corresponds to the reduced giant dipole population at 2π-pulse-area in FIG.2F. In some embodiments, if the input is |01^, the wrong coupling will not induce giant dipole formation. In some embodiments, another probe is used to obtain the results as done in ESA detection (FIG.3B). In some embodiments, the substantial differences in wavelength, intensity, and decay time between the giant dipole and random dipole ensure their isolation. In some embodiments, the truth table of this control-NOT gate is mapped out experimentally (FIG.4F). In one example demonstration of the disclosed embodiments, the rotation of the |10^ state to |11^ state was calculated to be 0.80, in excellent agreement with the measured value of 0.77 ± 0.06. In some embodiments, the inherent binary nature of excitation polarization remains reliable during operation, thus mitigating the loss- dependent issues of logic operations commonly encountered in other optical transistors (Section S6).

[0068] In some embodiments, given the strong ionic bonds between the substrate and epitaxial superlattice, the material structure remain intact even under continuous exposure to high-intensity (e.g., 40 μJ⋅cm-2) laser excitation. In some embodiments, the superfluorescence also remains stable under ambient conditionswithout any encapsulation (FIG.36). Consequently, in some embodiments, the logic gates are stable. In an example demonstration, logic gates were stable at a high extinction ratio (i.e., the ratio between the [1] and [0] levels) after at least 1.8 million test cycles (FIG.4G and Section S6).

[0069] Example Methods

[0070] Example materials and solvents

[0071] Some disclosed embodiments use lead (II) bromide (PbBr2, 98%+). Some disclosed embodiments use lead (II) oxide (PbO, 99.9%). Some disclosed embodiments use Methylammonium bromide (MABr, 99.99%), methylammonium iodide (MAI, 99.99%), and phenethylammonium iodide (PEAI, 99.99%). Some disclosed embodiments use Gamma butyrolactone (GBL, 98%). Some disclosed embodiments use Methanol (MeOH, 99.8%), isopropanol (IPA, 99.5%), propylene carbonate (PC, 99%), acetone (99.5%), dimethylformamide (DMF, 99.8%), hydriodic acid (HI, 57 wt.% in H2O, 99.95%), and hypophosphorous acid (H3PO2, 50 wt.% in H2O). In some embodiments, all reagents were used as received without further purification.

[0072] Example synthesis of PEA2MAPb2I7single-crystal flakes

[0073] In an example synthesis, 7.4 mmol of PbO was added to 10 ml of pre- heated HI (57 wt.% in H2O) at 180 ℃, mixed with 1 ml of H3PO2 (50 wt.% in H2O), and stirred until the precursor solution became transparent yellow. A solution of MAI (4.2 mmol) / PEAI (4.2 mmol) in MeOH was then injected into the precursor solution and stirred for 2 min. Subsequently, the beaker was transferred into a vacuum chamber for 15 s to remove dissolved air, before being returned to ambient atmosphere for crystallization. The flakes nucleated, grew, and filled the beaker within ~2 h. After precipitation, the crystal flakes were filtered and sequentially washed with IPA, PC, and acetone using a vacuum funnel. Each washing step consisted of a 5‑second suction‑filtration rinse with 20^mL of the respective solvent, followed by drying under vacuum.

[0074] Example preparation of bulk MAPbBr3 single crystals

[0075] In an example preparation, bulk MAPbBr3 single crystals were grown by slow solution evaporation. MABr and PbBr2were dissolved in a 1:1 stoichiometric ratioin DMF at a concentration of 1.67 M. The solution was kept at room temperature to allow the solvent to evaporate slowly for growing MAPbBr3 single crystals. The as- grown single crystals were collected and used as substrates for superlattice growth without any further treatment.

[0076] Example fabrication of perovskite superlattices

[0077] In an example fabrication, the PEA2MAPb2I7single-crystal flakes were redissolved in GBL to prepare a 1 M growth solution. This growth solution was spin- coated onto the bulk MAPbBr3 single crystal substrate at 4,000 revolutions per minute (r.p.m.) for 30 s. The coated substrate was then annealed at 180 ℃ for 2 min to form the superlattices.

[0078] Example Ab initio calculations

[0079] In an example analysis performed in accordance with disclosed techniques, first-principles density functional theory calculations were performed using the Vienna ab initio Simulation Package. Projector-augmented wave potentials were employed with the generalized gradient approximation in the Perdew-Burke-Ernzerhof parametrizations for the exchange-correlation functional. Van der Waals interactions were described using the DFT-D3 method of Grimme with a zero-damping function, properly describing the long-range dispersion interactions between the organic molecules in the hybrid materials. Based on convergence tests, a plane-wave basis set with a kinetic energy cutoff of 800 eV and a Brillouin zone grid of 5×5×2 Γ- centered k-points were employed. Relaxation was carried out until the energy differences were converged within 10-6eV, with a Hellman-Feynman force convergence threshold of 10-2eV / Å. Spin-orbit coupling was included throughout all electronic structures and optical properties calculations. To calculate the bandgap of the perovskite superlattices, hybrid functionals within the Heyd–Scuseria–Ernzerhof HSE06 formalism were used. On top of the HSE06 band structures, the excitonic effects are computed from time-dependent Hartree−Fock calculations using the Casida equation with a total of 24 valence and 24 conduction bands.

[0080] Example structure and morphology characterizations

[0081] In an example structural and morphological characterization of an embodiment based on the disclosed technology, X-ray diffraction (XRD) was takenusing an Anton Paar XRDynamic 500 diffractometers. Scanning electron microscopy images were captured using a Zeiss Sigma 500. Cryo-transmission electron microscope (cryo-TEM) samples were prepared with an FEI Scios DualBeam cryo- FIB / scanning electron microscope (cryo-FIB / SEM). Cryo-TEM images were acquired on a Thermofisher Talos F200X G2 cryo-S / TEM with a Gatan Elsa cryo-transfer holder. Cross-sectional electron energy loss spectroscopy mapping was performed using a Gatan Enfinium ER (977) spectrometer. Synchrotron-based grazing incidence wide-angle X-ray scattering was measured on beamline 7.3.3 at the Advanced Light Source, Lawrence Berkeley National Laboratory. The X-ray wavelength was 1.240^Å, with various grazing incident angles and scattering intensity was detected using a PILATUS 2M detector. The exposure time was 5^s per frame in single mode, with a total measurement time of 2 min. The images were sector-averaged using the Nika software package.

[0082] Example ultrafast pump-probe measurements

[0083] Some disclosed embodiments involve ultrafast pump-probe measurements. In one example ultrafast pump-probe measurement, reflection mode was used for transient absorption measurements because the superlattices were epitaxially grown on a thick, non-transparent single-crystal MAPbBr3 substrate. Pump- probe absorption was measured using a Helios system from Ultrafast Systems (FIG. 33). The excitation source was generated by an Astrella-F-1K femtosecond amplifier with an 800 nm, 1 kHz fundamental beam. This beam was directly applied to produce the probe beam by passing through a crystal for continuum generation in the Helios system. The 515 nm pump beam was produced by an optical parametric amplifier system from Coherent. The sample was positioned on a reflection sample holder, and the chopper-modulated pump light was directed onto the sample. The detector was triggered to record every probe pulse and calculate the reflection spectrum. From the chopper sync out, the Helios software determined the chopper state (pump-on or pump-off) for each measured probe spectrum, allowing for the calculation of the differential reflection spectrum by taking the difference between pump-on and pump- off states. All measurements were conducted at room temperature in ambient air.

[0084] Example time-resolved photoluminescence spectra

[0085] Some disclosed embodiments involve obtaining time-resolved photoluminescence spectra. In one example study, a femtosecond laser used to excite the sample was generated by a regenerative amplifier (400 nm wavelength, 100 fs pulse width, and 1 kHz repetition, Coherent Legend) seeded by a Ti: sapphire oscillator (100 fs, 80 MHz, Coherent Vitesse) (FIG.34). The pump laser wavelength was controlled at 515 nm by an optical parametric amplifier. Emission from the sample was collected in a backscattered geometry with a pair of lenses and directed to a monochromator (Acton, Spectra Pro 2500i) coupled to a streak camera (Hamamatsu, ultimate temporal resolution of ~1 ps). Superfluorescence peak intensities were extracted from the streak camera images. All measurements were performed at room temperature in ambient air.

[0086] Example polarization-dependent emission spectra

[0087] Some disclosed embodiments involve obtaining polarization-dependent emission spectra. In some one example study, a high-repetition-rate femtosecond laser system (Pharos, 100 kHz, Light Conversion) in a reflection geometry was used for a customized superfluorescence spectra measurement (FIG.35). The Pharos laser generated pulses with a center wavelength of 1030 nm and a pulse width of 160 fs, delivering a pulse energy of 100 μJ. In this example study, the 1030 nm pulses were directed through a beta barium borate crystal to generate a 515 nm second harmonic excitation beam. This excitation beam was then directed through a 515 nm λ / 2 waveplate to control polarization and a continuous neutral density filter to achieve tunable pulse energy. The beam was focused onto the sample surface using an NBK- 7 lens with a 12.5 cm focal length. The incident angle was set at 15°. To prevent burning damage to the sample, a repetition rate of 100 Hz was used. The superfluorescence signals were dispersed by a spectrograph (Shamrock, Andor) and detected by a charge-coupled device (Newton idus, Andor). All measurements were performed at room temperature in ambient air.

[0088] Example optical transistors

[0089] In an example demonstration of the performance of an optical transistor based on the disclosed technology, a 1030 nm femtosecond pulse (Pharos, 100 kHz, Light Conversion) was filtered through an etalon (SLS optics) to create an up- conversion pulse with a narrow bandwidth of 4 cm-1full width at half maximum (FIG.36). This pulse was then directed through a beta barium borate crystal to generate a 515 nm beam, referred to as IN1. Simultaneously, the reflection of the 1030 nm pulse from the etalon was directed through another beta barium borate crystal to generate a second 515 nm beam, referred to as IN2. Beam IN1 was focused onto the sample surface using a 10 cm focal length parabolic mirror, spatially overlapping with beam IN2, which was focused by a 12.5 cm focal length NBK-7 convex lens. The staggered distances between the lenses facilitated easier adjustment and alignment in the optical path. The incident angles were set at 15° for beam IN1 and 20° for beam IN2. The generated superfluorescence signals were collected by a 5 cm focal length NBK- 7 convex lens, then dispersed by a spectrograph (Shamrock, Andor), and detected by a charge-coupled device (Newton idus, Andor). NOR and NAND gates were realized by employing inverse polarizers before the superlattices. Inverse polarizers, such as a λ / 2 waveplate, invert the polarization of the light, serving as a NOT gate. For example, s-polarized light representing [1] becomes [0] after passing through the inverse polarizer. Combining a NOT gate with AND / OR gates created NAND / NOR gates. All measurements were performed at room temperature in ambient air.

[0090] Various aspects related to the disclosed embodiments are described in further detail below.

[0091] S1: Example superfluorescence and the role of collective states

[0092] The nature of superfluorescence is the collective radiative decay of a macroscopic quantum coherent state, namely the giant dipole. Although emission exhibits strong directionality and coherence, photons suffer from inherent limitations due to the absence of direct photon-photon interactions, thereby preventing the formation of nonlinear couplings or conditional operations between photonic qubits, which are essential for scalable quantum information processing. Without such interactions, photonic qubit systems rely predominantly on external optical setups, such as artificial cavities or nonlinear media, to mediate effective coupling. However, similar functions can often be realized using conventional coherent sources, such as lasers, without necessitating the involvement of macroscopic quantum coherence inherent in superfluorescence. As a result, the quantum advantage offered by superfluorescence becomes diminished in these configurations, limiting its “super” for practical quantum information applications. Despite the remarkable environmentaltolerance demonstrated by halide perovskite superfluorescence, its application in quantum technologies remains hindered by the lack of photon-photon interactions and the limited precision in manipulating collective states. Overcoming these challenges requires the research of giant dipole behaviors, such as dipole confinement by multi- quantum wells that enhances dipole-dipole interactions to trigger nonlinear effects. Accordingly, it is important to directly resolve the formation dynamics of the giant dipole, extract its transient absorption signatures, and employ polarization encoding to enable quantum gate operations.

[0093] S2: Example two-dimensional (2D) / quasi-2D halide perovskite superlattices

[0094] S2.1 Example structure of 2D / quasi-2D halide perovskites

[0095] Some disclosed low-dimensional perovskites comprise two components: the inorganic slab and the organic spacer. The inorganic slab retains the structural integrity of conventional three-dimensional (3D) perovskites, which include metal- halide frameworks and organic cations. However, the continuous crystal structure of 3D perovskites is divided by organic spacers, forming periodic 2D layered structures. This key difference defines low-dimensional perovskites, where the layered organic spacers determine the ‘n’ value—the number of inorganic slab layers—in the chemical formula B2An−1MnX3n+1, where:

[0096] · B represents organic spacer cations like R-NH3+.

[0097] · A includes cations such as CH3NH3+, HC(NH2)2+, and Cs+.

[0098] · M represents metal ions like Pb2+and Sn2+.

[0099] · X stands for halide anions such as Cl−, Br−, and I−.

[0100] S2.2 Example synthesis principles of 2D / quasi-2D halide perovskite flakes

[0101] During an example synthesis, excessive hydroiodic acid was utilized to maintain an acidic environment, which prevents the decomposition of 2D / quasi-2D perovskite structure by water, because protons in acid combine with the halide anions, inhibiting their interaction with water, which helps maintain the integrity of the perovskite lattice and avoid unwanted side reactions. The selected precursor molar ratios (PbO: MAI: PEAI = 1.76: 1: 1) yielded pure PEA2MAPb2I7 (n = 2) single crystalflakes, confirmed by X-ray diffraction and UV-vis spectroscopy (FIGS.5A-5B). Redissolving these flakes and subsequent growth of PEA2MAPb2I7 superlattices on MAPbBr3single-crystal substrates showed a clear elemental boundary between iodine and bromine, confirmed by electron energy loss spectroscopy (FIG.5C).

[0102] Optical images of the 2D / quasi-2D perovskite flakes are presented in FIGS.6A-6C. An appropriate amount of hypophosphorous acid (every 10 ml of HI, 57 wt.% in H2O, was matched with 1 ml of H3PO2, 50 wt.% in H2O) was added to reduce iodine (I) into iodide anions (I-) in the precursor solution, turning the solution transparent yellow; otherwise, iodine would adhere to the quasi-2D perovskite flakes, introducing impurities.

[0103] Given that the quasi-2D flakes were prepared for redissolving, the washing process is important to remove all reaction residues. Initially, isopropanol was used to eliminate hydroiodic acid, which also dissolved the organic spacers (phenethylammonium) on the flakes' surface, causing them to turn black. Hence, the redissolved solution would become muddy, resulting in disordered superlattices (FIGS.7A-7B and FIGS.8A-8B). Therefore, propylene carbonate was used for a 5- second suction-filtration wash, selectively dissolving the Pb-I slabs on the surface without affecting the organic spacers. This step restored the flakes to their original color. Finally, acetone does not dissolve the organic spacers in 2D / quasi-2D perovskites and was employed to wash away the propylene carbonate, ensuring a quick drying process in a vacuum. Moreover, acetone also removes residual MA⁺ and organic precursors from the crystal surface without inducing impurities.

[0104] S2.3 Example epitaxy mechanism for perovskite superlattices on 3D perovskite substrates

[0105] In some embodiments, the vertical alignment of quantum wells in the epitaxial perovskite superlattice is not a consequence of annealing alone but results from the interfacial chemistry during growth, and is directly confirmed by structural characterization at both local and macroscopic scales. In some embodiments, cryogenic transmission electron microscopy images (FIG.1B) clearly reveal the periodic stacking of inorganic Pb–I layers separated by organic spacers, oriented perpendicular to the substrate to form a vertically aligned multi-quantum-well structure.. In some embodiments, , this is further proved by synchrotron-based grazing incidence wide-angle X-ray scattering, which exhibits discrete, spot-likediffraction features.. In some embodiments, such patterns are indicative of long-range directional order and confirm that the vertical alignment is a macroscopic feature of the superlattice rather than a grain phenomenon.

[0106] The top view of example epitaxial perovskite superlattices is presented in FIGS.9A-9D. In some embodiments, during growth, the substrate, also halide perovskites, forms strong metal-halide ionic bonds with the inorganic slabs (Pb-I) while weak Van der Waals forces with the organic spacers (PEA) in low-dimensional perovskites. In some embodiments, these ionic bonds are stronger than the Van der Waals forces. In some embodiments, this strong bonding enables the selective anchoring of different facets of the low-dimensional perovskites, achieving precise quantum-well alignment and orientation control.

[0107] In some embodiments, growth along horizontal orientations is unstable due to its energetic unfavourability. Initiating horizontal epitaxial layers would require forming a complete organic or inorganic layer as the first layer on the substrate, akin to a perovskite layer with an infinite ‘n’ value, which is thermodynamically unstable1. Consequently, in some embodiments, the epitaxial layers predominantly form a vertically aligned structure rather than a horizontal one (FIGS.10A-10I).

[0108] In some embodiments, in the superlattice, compressive strain reduces the bandgap relative to the unstrained raw material. In some embodiments, low-dimensional perovskites comprise alternating inorganic slabs and organic spacers, whose dielectric constants differ. In some embodiments, the inorganic slabs have a much higher dielectric constant than the organic spacers, leading to strong dielectric confinement in the unstrained state. In some embodiments, under large compressive strain, the dielectric constant of the organic spacers increases, reducing the dielectric contrast between the two components, thus narrowing the bandgap compared with the raw material. In some embodiments, the compressive strain reduces the thickness of the organic spacers, thereby decreasing the barrier width in the multi-quantum-well structure, which also contributes to the redshift of the emission peak.

[0109] S2.4 Example selection of the precursor solvent for epitaxial growth

[0110] In some embodiments, non-volatile GBL was employed as the solvent to prepare the precursor solution for epitaxial growth, for its insolubility of the MAPbBr3substrate. In some embodiments, after spin coating, the surface remained wet with a clear precursor solution. In some embodiments, high-temperature annealing typically at 180 ˚C initiated the crystallization from the precursor solution, by slowly evaporating the solvent. In an example study, cross-sectional electron energy loss spectroscopy mapping showed a clear boundary between iodine and bromine, where iodine corresponds to the PEA2MAPb2I7superlattice and bromine to the MAPbBr3substrate (FIG.5C).

[0111] S2.5 Example synchrotron-based grazing incidence wide-angle X-ray scattering

[0112] In some embodiments, the spin-coating speed of the growth precursors on the MAPbBr3 substrate is important for the superlattice crystallization. In an example study, synchrotron-based grazing incidence wide-angle X-ray scattering (GIWAXS) was used to assess the orientation of samples prepared at different spin speeds. GIWAXS, which requires a monochromatic and high-flux (beam “brilliance”) X-ray source, is typically conducted at synchrotron facilities.

[0113] Comparing the GIWAXS results in the example study with spin speeds of 2000 r.p.m., 3000 r.p.m., and 4000 r.p.m. (FIGS.11A-11B), it was evident that increasing the spin speed leads to more ordered orientations in the superlattice. This transition was observed as the Bragg peaks in the GIWAXS patterns evolve from rings to center-dotted streaks, indicating better alignment of the superlattice structure. Given the millimeter-thick MAPbBr3 single-crystal substrate for epitaxial growth, the incidence angle of the X-ray beam is crucial, influencing the beam's footprint and penetration depth. Generally, the incidence angle should be < 0.5° for optimal results. We adjusted the incidence angles at 0.1°, 0.3°, and 0.5° (FIGS.11A-11B), with 0.5° providing the clearest streak pattern for superlattice.

[0114] In the example study, the extracted small-angle (< 1 Å-1) streaks from GIWAXS observed in both qyz(refers to the surface plane of the substrate) and qxy(refers to the plane perpendicular to the surface of the substrate) directions indicate a long-range ordered superlattice structure (FIGS.12A-12C). The qyzsignal, with a relatively uniform intensity distribution in the (002), (040), (004), and (060) directions at small angles, are typically from regularly spaced scattering centers (i.e., crystalline planes), suggesting a layered structure of multi-quantum wells oriented perpendicularto the substrate surface. Conversely, the qxy signal predominantly exhibits a (060) peak with minimal reflections at other angles, indicating a high degree of order and periodicity along this axis, which suggests a homogeneous and highly oriented crystalline structure within the plane. This contrast underscores the anisotropic structure of the quantum wells relative to the substrate orientation.

[0115] In some embodiments, the "criss-cross" morphology arises from the symmetric cubic substrate (MAPbBr3). In some embodiments, the substrate has two equivalent in-plane crystallographic axes, which results in a roughly equal probability for vertically aligned crystal plates to extend along either in-plane direction during growth. In some embodiments, it is critical that within this criss-cross network, the quantum wells maintain their vertical orientation relative to the substrate. In some embodiments, since the superlattices are epitaxially grown on the substrate, this extension cannot go horizontally due to the same thermodynamic chemical principle. In some embodiments, the structure is therefore not a random mix of horizontal and vertical plates, but an ordered array of vertical quantum wells that are organized perpendicularly in the xy-plane.

[0116] S2.6 Example morphology control of perovskite superlattices

[0117] In some embodiments, in addition to crystallinity, the cavity qualities, including continuity, uniformity, and purity are important because they directly influence the cavity performance to closely pack dipoles. In some embodiments, continuity ensures defect-free cavities, uniformity guarantees consistent structural properties across the entire material, and purity minimizes foreign ions / molecules that can introduce unwanted scattering, potentially disrupting the formation and coherence of the giant dipoles. In some embodiments, the cavity qualities can be precisely controlled by adjusting the concentration of the PEA2MAPb2I7 flake-redissolved solution.

[0118] In some embodiments, for optimal morphology, a concentration of 1 M was preferable when spin-coating at 4000 r.p.m., because it ensured the appropriate superlattice height. If the spin speed was too low, the precursor solution heaped on the substrate, disrupting the evaporation process necessary for crystallization and resulting in random growth (FIGS.13A-13C). If the spin speed was too high, the precursor may spread too thin, leading to incomplete coverage and poorcrystallization. If the concentration was too low, the superlattice may grow discontinuously on the substrate, disrupting long-range order (FIGS.14A-14B). If the concentration was too high, the volume of the superlattice became too large for coherent light-matter interactions. Thus, balancing the concentration is crucial to ensure both the continuity and uniformity in the superlattice thin film. In some embodiments, the sample was annealed at 180 ℃ for 1 min, which slowly evaporated the solvent and started the epitaxial growth.

[0119] S2.7 Materials selection for superfluorescence

[0120] In some embodiments, the selection of the quasi-2D halide perovskite raw material with layer number n = 2 was guided by the practical need to balance between growth strain, quantum confinement, and interlayer coupling, thereby enabling phase synchronization and macroscopic coherence. In principle, perovskite structures with n = 1 provide stronger out-of-plane quantum confinement. However, this structure comes at the cost of excessive lattice strain during epitaxial growth (more than 10%), which leads to poor structural stability and film quality. In addition, the thick insulating organic spacers in n = 1 systems suppress vertical dipole–dipole coupling by spatially isolating the layers.

[0121] In some embodiments, systems with higher layer numbers (e.g., n = 3) begin to approach bulk-like three-dimensional behavior. The inorganic quantum wells become thicker, and the effective confinement along the z-direction weakens. This allows greater freedom of dipole movement within the inorganic framework, leading to increased thermal and spatial fluctuations. These fluctuations disrupt phase synchronization and degrade the conditions needed for collective behavior. As a result, high-n perovskites exhibit neither giant dipole formation nor superfluorescence, even under excitation fluence near the material damage threshold.

[0122] In some embodiments, the n = 2 perovskite thus represents an optimized structural compromise. In some embodiments, it maintains strong quantum confinement while avoiding the excessive strain associated with n^=^1, enabling stable high-quality epitaxial growth and supporting superfluorescence. Comparing with extreme strain that compromises stability, moderate strain preserves strong ionic bonds between the substrate and epitaxial superlattice, stabling the superlattice. In one example demonsration, only the n^=^2 superlattice in the epitaxial systemexhibited clear signatures of superfluorescence, whereas both n^=^1 and n^=^3 showed only normal fluorescence, even under high-power excitation below the burning threshold (FIG.15).

[0123] In some embodiments, the vertical epitaxial configuration was selected over a classical horizontal quantum-well orientation to optimize material quality, maintain strong optical confinement, and ensure experimental feasibility for superfluorescence studies. In some embodiments, epitaxial growth enables precise control over crystal orientation, uniform thickness (~1^µm), and large-area morphological homogeneity. In contrast, horizontally oriented perovskites are typically obtained as synthesized single-crystal flakes, which show large variations in thickness, lateral shape, and surface quality. In some embodiments, such inhomogeneity reduces stability and reproducibility in ultrafast optical measurements, where superfluorescence dynamics are highly sensitive to sample morphology.

[0124] In some embodiments, physically, horizontal crystals with tens of microns to millimeters thickness create large, inhomogeneous excitation volumes when pumped, generating spatially varying carrier densities and uncontrolled quantum fluctuations that hinder dipole–dipole coupling and dipole phase synchronization. In an example demonstration, measurements confirmed that horizontally oriented single-crystal flakes produced only fluorescence, even under high excitation fluence, whereas the vertical superlattice with its confined geometry readily supported giant dipole formation and superfluorescence emission.

[0125] In some embodiments, the vertical geometry is also better suited to our transient absorption and time-resolved emission setups, both of which are designed for normal-incidence excitation and detection. In some embodiments, a horizontal configuration involves side-collection optics.

[0126] S3 Example giant dipole formation

[0127] S3.1 Example dipole-dipole interactions

[0128] In some embodiments, when at low populations, dipoles, also known as excitons in optics, return to the ground state independently. In some embodiments, the energy is released in a series of weak, random, unstable, and incoherent emissions. In some embodiments, when at high populations (e.g., through intenseexcitation), dipoles are densely packed and are in proximity to one another. In some embodiments, this proximity means that the electromagnetic fields of individual dipoles effectively overlap, which facilitates frequent and strong interactions between dipoles, necessary for achieving phase synchronization (i.e., the dipoles' wavefunctions retain a fixed phase spatially and temporally). In some embodiments, when dipoles interact effectively, they can align their oscillations more easily, leading to a coherent collective state.

[0129] In some embodiments, under high dipole populations, the material's ability to polarize in response to the electric fields created by the dipoles increases, enhancing dielectric screening, and thus the Coulombic interactions within individual dipoles (between electron and hole) are strongly screened, reducing the exciton binding energy to nearly zero. In some embodiments, as a result, the photoexcited dipoles transition from discrete individuals to a dense electron-hole plasma. In quantum physics, this plasma undergoes a phase transition from many random ground states to a single collective state, known as a "giant dipole" quasi-particle, distinguishing it from normal photoexcited dipoles. In some embodiments, with established coherence, its internal dipoles cannot always be treated as independent units. The enhanced dipole ensemble shows collective properties.

[0130] In some embodiments, besides high dipole populations, confinement is important because without confinement, the dipoles would undergo more quantum fluctuations, such as random phase variations, random emission events, and disturbances in surrounding electromagnetic fields, disrupting their coherent interactions and thus causing dipoles to return to the ground state before forming a giant dipole. Therefore, confinement allows light to interact coherently with the entire dipole ensemble, enabling cooperative behaviors.

[0131] In some embodiments, the dipole-dipole interactions always consume energy. In some embodiments, because after photoexcitation this is a closed system, such interactions result in an overall reduction in energy. This process, also known as bandgap renormalization, shifts the bandgap below the energy of initial exciton, which is a crucial feature in the giant dipole formation. The overall bandgap shift Δ^^^^^^^^in the renormalization can be represented as:

[0133] where ^^^^ is the momentum, ^^^^^^^^(^^^^) and ^^^^(^^^^) are Fourier transforms of the screened and unscreened Coulombic potentials, and ^^^^^^^^(^^^^) and ^^^ℎ^ (^^^^) are the electron and hole occupation probabilities of the states with ^^^^. The first term of the equation represents the screened exchange of electron-hole pairs, while the second term represents the potential energy from light-dipole interaction. Together, these terms reduce the total energy of the system and renormalize the giant dipole's bandgap.

[0134] In some embodiments, dipole-dipole interactions are highly distance- dependent. The normal coupling distance for these interactions is often a few nanometers in solid-state materials. In some embodiments of the halide perovskite superlattice, the thin organic spacer layers had a thickness that is comparable to or even less than this normal coupling distance (FIG.1B), which effectively brings the adjacent inorganic layers—and thus the dipoles within them—within close proximity. In some embodiments, this minimal separation allows for strong interlayer dipole-dipole interactions. In some embodiments, this enhanced interlayer coupling accelerates the formation of giant dipoles by allowing dipoles in adjacent layers to align cooperatively.

[0135] S3.2 Example quantum fluctuations

[0136] Quantum fluctuations refer to temporary changes in the amount of energy at a point in space due to the uncertainty principle. These fluctuations influence phase transitions in matter. In some embodiments, in formation of a giant dipole, the transition of the dipole system from random states to a collective state induces quantum fluctuations in both energy and electromagnetic fields, leading to random disruptions to the delicate balance of dipole coherence.

[0137] In some embodiments, coherence in a giant dipole refers to the property of the dipole ensemble where the electron and hole states have a well-defined synchronized phase. In some embodiments, this coherence is crucial for applications in quantum computing and optoelectronics. In some embodiments, dephasing is the process by which this coherent phase is lost over time. In some embodiments, dephasing is driven by electromagnetic field fluctuations, carrier fluctuations, and phonon interactions, which are all manifestations of quantum fluctuations.

[0138] In some embodiments, electromagnetic field fluctuations arise from the quantum nature of the electromagnetic field, interacting with dipoles and inducing transitions between different states, causing variations in the potential energylandscape.. In some embodiments, these variations lead to time-dependent phase shifts in the dipole's wavefunction, contributing to dephasing. In some embodiments, carrier fluctuations occur when the density of free carriers fluctuates due to thermal excitation, impurity states, and external influences such as light or electrical fields. In some embodiments, shifting carrier density weakens the condition for giant dipole formation. In some embodiments, dipoles interact and exchange energy with phonons through scattering events, where each scattering event changes the momentum and energy of the dipole, resulting in phase shifts and contributing to dephasing.

[0139] S3.3 Example delays and dephasing time

[0140] In some embodiments, the randomly distributed dipole moments in the ground state undergo screening and alignment to form the giant dipole in the collective state (FIGS.21A-21B and FIGS.22A-22E). In some embodiments, this transition is driven by electromagnetic waves and requires time, resulting in delays between photoexcitation and giant dipole formation, also known as the self- organization time of random dipoles.

[0141] In some embodiments, these delays are relatively long because the system must undergo coherent light-matter interactions before spontaneous synchronization. In some embodiments, the delayed formation process is highly susceptible to quantum fluctuations, causing the giant dipole to revert to random dipoles and lose coherence, which makes it challenging to investigate the giant dipole. In some embodiments, to mitigate quantum fluctuations, cryogenic or strong magnetic environments are typically necessitated to maintain coherence and extend dephasing times (the duration over which coherence between dipoles is preserved before the phases of individual dipoles start to randomize again). In some embodiments, strong magnetic fields align the electrons and holes due to their spin, facilitating their confinement and interactions. In some embodiments, cryogenic temperatures reduce dipole activities and energies, allowing them to be confined and aligned, making the dipole-dipole interactions more manageable. In some embodiments, in nanocrystal assemblies, the long ligands on nanocrystal surfaces weaken dipole-dipole interactions, requiring cryogenic conditions to observe the collective state. Systems without superlattice confinement easily undergo dephasing.

[0142] In some embodiments, the dipoles are confined within anisotropic superlattices, exhibiting enhanced interactions and coherence. In some embodiments, this confinement shortened the delay and lengthened the dephasing times during giant dipole formation. In some embodiments, these enhanced interactions enable a rapid transition to the collective state, as the system quickly achieves the necessary coherence and efficient interactions among dipoles. Consequently, a lower threshold for the giant dipole and superfluorescence can be achieved compared to studies in the literature (Table 1), which allowed observation of these phenomena, in an example study, with high data quality and under ambient conditions. In some embodiments, this confinement reduces the susceptibility of the system to quantum fluctuations, because disturbances are more uniformly absorbed and averaged across the entire ensemble.

[0143] S4. Example Burnham-Chiao ringing and superfluorescence

[0144] S4.1 Example Burnham-Chiao ringing

[0145] In some embodiments, Burnham-Chiao ringing is a fundamental property observed in the generation of superfluorescence within quantum optical systems. It plays a crucial role in understanding the dynamics of superfluorescence generation and propagation.

[0146] In some embodiments, the Burnham-Chiao ringing originates from the Rabi oscillation. In a single two-level system (a system that can exist in two distinct energy states, typically referred to as a ground state and an excited state), a periodic exchange of energy between light (electromagnetic field) and matter (a two-level system) occurs when light comprises a coherent beam of photons. This periodic exchange of energy is known as Rabi oscillation. The electromagnetic field drives the transition between the ground and excited states, causing oscillations in the population of the two states. The frequency Ω for the Rabi oscillation characterizes the strength of the coupling between light and matter, which is described as:where d is the dipole moment, E0is the amplitude of the electromagnetic field in light, and ℏ is the reduced Planck constant. This process involves the system cyclically absorbing and re-emitting photons, similar to an echo where energy bounces back and forth between light and matter.

[0147] Burnham and Chiao applied the model of Rabi oscillations to their research on superfluorescence, leading to the discovery of what is now known as Burnham-Chiao ringing. In some embodiments, Burnham-Chiao ringing represents macroscopic Rabi oscillations in the superfluorescence emitted by the giant dipole. In some embodiments, a collectively enhanced ensemble of dipoles behaves like a single giant dipole.

[0148] Burnham-Chiao ringing is a striking manifestation of quantum mechanics on the macroscopic scale and has been extensively studied since 1969. In some embodiments, it provides evidence of the collective behaviors within the giant dipole because the periodic energy exchange of the Rabi oscillation occurs only in strongly coupled systems. Numerous studies have shown that the superfluorescence pulse undergoes nonlinear interactions with the giant dipole or other coherent systems during propagation.

[0149] In some embodiments, Burnham-Chiao ringing can be observed as the oscillating population of charged carriers. In some embodiments, to model this characteristic ringing behavior, a bi-exponential decay function multiplied by a damped oscillating term was used, represented as:where ^^^^ is the initial amplitude of the oscillation, ^^^^Dampis the damping constant, t is the time, ω is the angular frequency, and ^^^^0is the initial phase. In some embodiments, a complete fit function is given by:where ^^^^ is the quantum number, ^^^^^^^^is the amplitude of the exponential decay, ^^^^^^^^is the corresponding decay time of the superfluorescence, ^^^^riseis the rising time of the superfluorescence, ^^^^Dis the delay time for the giant dipole to build up, and erf is the error function. In some embodiments, this model captures the important features of Burnham-Chiao ringing by combining exponential decay terms with a damped oscillatory component, reflecting both the decay dynamics and the coherent interactions in the system.

[0150] S4.2 Example superfluorescence and its characteristics

[0151] In some embodiments, superfluorescence occurs when giant dipoles release energy in the form of photons simultaneously, resulting in an intense burst of coherent radiation.

[0152] It is crucial to distinguish between superfluorescence and superradiance. Superradiance occurs when coherent polarization is generated by an external laser field, whereas superfluorescence arises only when the atomic / molecular system is initially incoherent, and then absorbs and emits photons, with coherent macroscopic polarization developed spontaneously from internal dipole-dipole interactions.

[0153] Superfluorescence should also be distinguished from lasing and amplified spontaneous emission. Even though they have similar photoluminescence spectra, each of them has different mechanisms and coherence properties. Superfluorescence is a cooperative phenomenon where a large ensemble of excited dipoles collectively emits an intense, highly coherent burst of light after a characteristic delay. This coherence arises from the synchronization of the emitters themselves—they spontaneously align their phases through interactions, forming a macroscopic dipole moment. Because the entire ensemble acts as a single quantum system, superfluorescence exhibits exceptionally high temporal and spatial coherence. It involves the collective, in-phase transition of the entire ensemble without reliance on optical feedback mechanisms.

[0154] In contrast, lasing emission involves intense light generation through stimulated emission within a gain medium, sustained by an optical cavity that provides feedback and mode selection. In lasing, coherence is primarily about the coherence of photons. When an excited atom / molecule undergoes stimulated emission, it emits a photon that is identical in phase, frequency, and direction to the stimulating photon. The optical structure reinforces this process by selecting specific photon modes. This photon-phase coherence depends on spontaneous emission events and may introduce phase noise. Therefore, the coherence in lasing is achieved and maintained through the stimulated emission of the photons and feedback of the optical cavity rather than the collective synchronization of the emitters.

[0155] Amplified spontaneous emission occurs when spontaneous emission from excited particles is amplified as it passes through a gain medium with populationinversion. This produces directional light with partial coherence by stimulating additional emissions along the path of the initial spontaneous photons. Compared to lasing, which generates coherent, narrowband light through stimulated emission with optical feedback in a resonant cavity, amplified spontaneous emission only amplifies spontaneous emission without feedback and stimulation, resulting in partially coherent, broadband light.

[0156] In some embodiments, to distinguish superfluorescence from lasing and amplified spontaneous emission, coherence properties and temporal dynamics are key. In some embodiments, superfluorescence exhibits a characteristic delay before emission, followed by a sharp, intense pulse, due to the cooperative synchronization of emitters. In some embodiments, a hallmark of superfluorescence is Burnham-Chiao ringing—oscillations in the temporal profile of the emitted light, resulting from the coherent synchronization and subsequent dephasing of the macroscopic dipole moment. In contrast, lasing and amplified spontaneous emission emit light without significant delay or ringing patterns, with emission beginning immediately upon reaching the threshold conditions for population inversion. In some embodiments, transient absorption measurements reveal signatures of a new energy state indicative of collective synchronization, such as accelerated decay rates and spectral shifts. In lasing or amplified spontaneous emission, coherence is totally or partially maintained among photons but not the emitters themselves, so that their transient absorption signals reflect population dynamics without signatures of collective synchronization.

[0157] In some embodiments, compared to fluorescence, superfluorescence is characterized by a narrow linewidth (reduced full width at half maximum) and relatively long-wavelength emission, which can be observed from photoluminescence emission spectra. This phenomenon applies to a general N-body system, where oscillating dipoles couple through interactions with a common external light field, accelerating the radiative decay of the entire system. In an incoherently prepared system of N-excited atoms, macroscopic coherence of giant dipole is spontaneously developed, resulting in a delayed pulse of coherent light with peak intensity proportional to N2. This behavior is characterized by a superlinear increase in intensity compared with the linear increase of individual emitters in fluorescence. The emitted photons in superfluorescence have a fixed phase. Additionally, the superfluorescence decay timeis shortened by the number of coupled emitters N, compared to the longer decay time of fluorescence from uncoupled dipoles.

[0158] In some embodiments, superfluorescence arises from the spontaneous emission of photons driven by coherent coupling among N identical two-level systems interacting through coherent electromagnetic waves. This coherent coupling consolidates the N two-level systems into a single, macroscopic two-level system (i.e., the giant dipole). In this collective state, the excited atoms, molecules, or dipoles become phase-locked, causing the entire ensemble to act as a giant dipole with strength N times that of a single emitter. Consequently, the transition rate of this system to emit photons is enhanced by a factor of N, leading to a radiated intensity that scales with N2, illustrating the profound impact of collective quantum effects on superfluorescence. Hence, in some embodiments, the superfluorescence is uniquely characterized by: • The pulse peak intensity depends quadratically (~N2) on the number of emitters N and its duration is inversely proportional to N. • The delay time required for giant dipole formation scales with ~1 / N. • Superfluorescence can be distinguished by coherent oscillations (Burnham- Chiao ringing) due to strong light-matter interactions.

[0159] In some embodiments, considering an incoherent ensemble of N-excited two-level atoms, at low populations, the spontaneous emission intensity is proportional to N, with a decay rate of T1−1, where T1is the radiative decay time of an isolated dipole. In some embodiments, at high populations, a giant dipole P ∼ Nd forms via dipole-dipole interactions, where d is the dipole moment of a single emitter. In some embdoiments, the P decays at an accelerated rate ΓSF ∼ NT1−1by emitting a pulse with a peak intensity Imax proportional to N2. In some embodiments, this basic physical picture suggests that during the giant dipole formation, initial microscopic dipole interactions are exponentially amplified, leading to a delay time τdthat dictates the giant dipole formation, followed by collective light emission.

[0160] In some embodiments, because superfluorescence originates from the giant dipole, which exhibits 180-degree symmetry in pzorbitals in one example study, the superfluorescence emission, which is the resonance of the giant dipole, alsodemonstrates 180-degree symmetry as a function of the emission polarization angle (FIG.3C, inset).

[0161] In addition to the power dependence of superfluorescence intensities, coherent superfluorescence emission is well-reported to exhibit a redshift compared to the inherent emission of individual emitters. In some embodiments, after the giant dipole formation, radiative recombination occurs from the coherent state to the random incoherent ground states. In some embodiments, the energy difference between the coherent state and ground states is lower than the energy differences between incoherent excited states and ground states.

[0162] S4.3 Example emission peaks of superfluorescnence

[0163] In some embodiments, in photoluminescence spectra, two distinct emission peaks can be observed: a high-energy peak corresponding to the central energy of fluorescence and a narrow, redshifted peak corresponding to superfluorescence. In some embodiments, the superfluorescence peak was best fitted with a Lorentzian shape function, while the fluorescence peak was best fitted with a Gaussian shape function (FIGS.19A-19B). In some embodiments, the difference in shape functions aligned with the distinct physical mechanisms underlying both emission processes.

[0164] In some embodiments, in fluorescence, the random energy distribution of incoherent dipoles leads to a broad, Gaussian-shaped emission peak. In some embodiments, this distribution results from the independent emission of photons by randomly oriented dipoles, producing a wide range of emission energies centered around the emission wavelength. In contrast, in some embodiments, superfluorescence arises from the coherent coupling of dipoles within the giant dipole, leading to a more concentrated energy emission. In some embodiments, this coherence results in a Lorentzian-shaped emission peak, reflecting the strong correlations and resonant behavior among the coupled dipoles in the giant dipole.

[0165] S4.4 Example direct coherence measurements of superfluorescence

[0166] In some embodiments, to provide direct coherence measurement of superfluorescence, first- and second-order optical coherence measurements were performed. In some embodiments, first-order coherence, quantified by the degree offirst-order temporal coherence ^^^^(1)(^^^^), measures the correlation of a light field's phase with itself at a later time ^^^^. In practical terms, it determines the timescale over which the phase of the light remains predictable, a property often measured by the visibility of interference fringes in a Michelson interferometer. In some embodiments, the decayas the delay ^^^^ increases defines the coherence time. The shape of this decay is also informative: a Gaussian decay is typical of inhomogeneously broadened, incoherent sources where many independent emitters contribute with a distribution of frequencies, while an exponential decay is characteristic of a homogeneously broadened, coherent emission process. In some embodiments, it was observed that the normal fluorescence at ~705 nm exhibits a very short coherence time with a Gaussian decay profile. In some embodiments, this is the expected behavior for an incoherent ensemble of randomly oriented, independently emitting dipoles. In some embodiments, in contrast, the superfluorescence at ~720 nm shows a much longer coherence time with an exponential decay. In some embodiments, this extended, exponential coherence is direct evidence of macroscopic phase coherence. In some embodiments, it signifies that the individual dipoles are no longer emitting independently but are synchronized and acting as a giant dipole.

[0167] In some embodiments, second-order coherence, quantified by the second-order correlation function, describes the photon statistics of a light source. In some embodiments, it measures the conditional probability of detecting a second photon at a time ^^^^ after detecting a first one, typically using a Hanbury Brown and Twiss interferometer. In some embodiments, the value at zero time delay,(0), identifying the nature of the emission process: •^^^^(2)(0) < 1 (photon antibunching): Photons tend to arrive one by one. This is anon-classical effect and the signature of a single-photon emitter. •^^^^(2)(0) = 1 (no correlation): Photon arrivals are random and follow Poissonianstatistics. This is characteristic of a classical coherent state, such as the light from an ideal laser. •^^^^(2)(0) > 1 (photon bunching): Photons have a higher-than-random probabilityof arriving close together in bunches. Notably, the photon bunching of superfluorescence is different from both lasing and thermal / amplified spontaneous emission statistics. A lasing field exhibits ^^^^(2)(^^^^) = 1at all time. A continuous thermal source (like a lamp) or amplified spontaneous can show photon bunching (^^^^(2)(^^^^) > 1), but the bunching persists over a broad timerange because fluctuations are sustained by ongoing spontaneous processes. In contrast, in some embodiments, superfluorescence is a collective emission of transient phenomenon. In some embodiments, the entire ensemble emits collectively in a time window much shorter than any single-dipole lifetime, so photons arrive in correlated groups rather than independently. In some embodiments, after the giant dipole emits its burst of photons, the system returns to the ground state. In some embodiments, the second-order coherence of superfluorescence therefore exhibits a sharp peak followed by rapid relaxation to unity. In some embodiments, under those conditions, the second-order coherence function of superfluorescence is written as: cosh 2( ^^^^^^^^(2)(^^^^) = 1 + ^^^^D) cosh2(0)exp (−2 ∣ ^^^^ ∣ / ^^^^D)where ^^^^Dis the decay time of second-order coherence. In this equation,(0) reaches its maximum at the intensity peak, and then decays exponentially on the same order ofmagnitudes as the burst itself, which finally returns to ^^^^(2)(^^^^) = 1. In someembodiments, this peak-decay process distinguishes superfluorescence thoroughly from thermal / amplified spontaneous emission statistics and is consistent with collective photon emission from a synchronized giant dipole. In some embodiments, measurement of photon bunching represents that the emission is not a stream of independent photons but occurs as correlated, multi-photon bursts.

[0168] S5. Example transient absorption to discover giant dipole in perovskite superlattice

[0169] S5.1 Example excitation-fluence-dependent transient absorption spectroscopy

[0170] In some embodiments, the formation of giant dipoles involves bandgap renormalization (Δ^^^^^^^^), where an additional absorption band representing the collective state appears alongside the original absorption band associated with the ground state (FIGS.21A-21B and FIGS.22A-22E). In some embodiments, there is a delay time for the bandgap renormalization during the giant dipole formation (FIGS.21A-21B and FIGS.22A-22E). In some embodiments, excitation-fluence-dependent transientabsorption spectroscopy (TAS) provides a powerful tool for studying the distinctive features of the formation of giant dipoles due to its high temporal resolution and spectral precision. In some embodiments, by varying the excitation fluence, TAS enables detailed insights into the underlying mechanisms and dynamics in quantum optics. In some embodiments, the pump-probe setup allows selective excitation, isolating effects only to those contributing to bandgap renormalization.

[0171] In some embodiments, in TAS measurements, quantifying carrier dynamics and lifetimes generally involves analyzing the rapid decay of excited states or transient absorption signals immediately following excitation. In some embodiments, this approach enables direct observation of excited state populations and their evolution. In some embodiments, a short femtosecond laser pulse (the pump pulse) excited the sample, creating excited states and transient species. In some embodiments, then, another laser pulse (the probe pulse) was used to measure the absorption of the sample at different probe-time delays after the excitation (FIG.23).

[0172] In some embodiments, the temporal resolution of TAS is primarily governed by the probe delay time and the laser pulse width. In some embodiments, utilizing a femtosecond-laser pulse allows resolution on the picosecond or even the femtosecond timescale. In some embodiments, the probe delay time between the pump and probe is controlled by a motorized stage. In some embodiments, by progressive scanning (i.e., recording the spectrum in temporal sequence) the transmission (ΔT) and reflection (ΔR) spectra, which are converted to absorption (ΔA) at each probe-time delay, ΔT, ΔR, and ΔA spectra as a function of probe delay time can be mapped. In some embodiments, the recorded TAS signals typically decay over time, which provides information about the lifetime of the excited state, transient species, and thus energy transfer dynamics, crucial for understanding bandgap renormalization.

[0173] S5.2 Example absorption bands and their degradation through TAS mapping

[0174] In some embodiments, the most evident and important information in TAS mapping is the absorption band, which signifies the irreversible photodegradation or fading of a fluorophore after prolonged light exposure. The process begins with the absorption of photons by fluorophores, which are excited from their ground state to ahigher energy state. Typically, excited fluorophores return to the ground state by radiate fluorescence. However, some fluorophores undergo non-radiative processes leading to thermal dissipations, irreversible chemical modifications, or complete destruction, resulting in photobleaching. One general primary mechanism for these non-radiative transitions involves interactions between excited fluorophores and molecular oxygen in the environment, which can produce highly reactive oxygen species. These species can damage the fluorophore molecules, causing chemical alterations and permanent loss of fluorescence.

[0175] In some embodiments, the relationship between photobleaching and material bandgap is illustrated in FIG.23, which is crucial for understanding the vulnerability of fluorophores to degradation. In some embodiments, fluorophores with smaller bandgaps absorb longer wavelengths, meaning their electrons are excited to relatively lower energy states compared to those with larger bandgaps. Consequently, fluorophores with smaller bandgaps tend to have lower photobleaching thresholds.

[0176] In some embodiments, the photobleaching band represents the ground- state absorption (GSA), corresponding to the bandgap of the materials. Since GSA is an intrinsic material property, detecting the additional absorption band indicative of the giant dipole formation can be challenging. This is because the additional absorption band may be too weak to be distinguished from background noise and GSA; overlap with other spectral features, making it difficult to isolate and identify; or be influenced by environmental factors affecting the giant dipole formation.

[0177] In an example embodiment, confinement and alignment of the dipoles within the natural cavities of perovskite superlattices was achieved, promoting giant dipole formation and lowering the excitation threshold (Table 1). This approach prevented the need for intense excitation, reducing the risk of material damage by pump laser and enabling more reliable detection. The quantum behavior of the TAS was distinguishable from both the background and the original GSA band.

[0178] S5.3 Example reflection mode in TAS

[0179] In some embodiments, a femtosecond pump-probe setup can be employed to acquire TAS data in a reflection mode (FIG.23 and FIG.33) rather than a transmission mode to investigate the epitaxially grown superlattice. In some embodiments, the reflection mode was crucial due to the nature of the sample: theMAPbBr3 single-crystal substrate used in this study exceeded one millimeter in thickness and was also a fluorescent material. In some embodiments, conducting TAS measurements in the transmission mode would have likely resulted in poor-quality data due to unwanted emission from the substrate. The reflection mode can mitigate this issue. In some embodiments, the focal depth was controlled to be 100 ~ 200 nm to specifically target the surface layer of the epitaxial material system, ensuring that the collected signals were dominantly from the superlattice. In some embodiments, this approach provided reliable and accurate TAS data by minimizing interference from the substrate and focusing on the superlattice.

[0180] S5.4 Example distinct properties of the giant dipole in TAS

[0181] In some embodiments, during giant dipole formation, when the excitation fluence exceeds the threshold necessary for strong light-matter interaction, distinct energy transfer and dynamic phenomena can be observed using TAS.

[0182] In some embodiments, from the energetic aspect, an additional bleaching band, corresponding to the collective state, appears alongside the original GSA band, allowing characterization of the dependence of absorption on excitation fluence (FIG. 23 and FIGS.24A-24B). In some embodiments, the excited-state absorption band has shifted progressively from ~700^nm to ~720^nm with increasing excitation density, reflecting the renormalization of higher excited states induced by the internal collective field.

[0183] In some embodiments, from the temporal aspect, TAS reveals the delay time required for the giant dipole formation and faster decay time for the giant dipole's collective recombination, indicating the self-organization and synchronized emission processes of dipoles. In some embodiments, the giant dipole population oscillates between collective state and ground state as beating. In some embodiments, the beating phenomenon observed in the excited-state absorption (FIG.3C) is key evidence that reveals the coherent dynamics of the giant dipole. In some embodiments, this oscillation does not originate from an external driving field but is an intrinsic manifestation of the strong coupling between the giant dipole and the transient collective electromagnetic field it generates. In some embodiments, after a high-density dipole ensemble synchronizes to form a giant dipole, its collective polarization generates a transient internal electromagnetic field. In someembodiments, this internal field drives population exchange between the collective state and the ground state, which is a direct product of collective coherence. In some embodiments, this leads to a periodic modulation of the population of the giant dipole state over time. In some embodiments, transient absorption spectroscopy, being a technique highly sensitive to the population of excited states, directly captures this population change. In some embodiments, the direct observation of these population oscillations in the TAS provides population evidence for the origin of Burnham-Chiao ringing, as the number of emitted photons is directly dependent on the population of the excited state.

[0184] S5.5 Example of the role of absorption bands in giant dipole formation by TAS

[0185] In an example embodiment, from the evolution of TAS mappings with increasing excitation fluence (FIGS.2A-2B), bandgap renormalization and the delay time of formation were clearly identified. The extracted intensities at given moments provided relative ΔA / A (where A is the absorption from the pump-probe measurement), revealing the superlattice's absorption characteristics.

[0186] In an example embodiment, when the pump wavelength was below 682 nm, ΔA / A displayed a valley, indicating the ground state photobleaching band (GSPB). Beyond 682 nm, ΔA / A presented a positive peak, signifying excited-state absorption (ESA). In fluorescence, GSPB represents the material's bandgap absorption, while ESA reflects excited state absorption (FIG.2B). At low excitation fluences, only fluorescence occurred. However, with increasing excitation fluence, both GSPB and ESA exhibited changes.

[0187] In an example embodiment, for GSPB under the same excitation fluence, observed across pump delay times from 1 to 30 ps, its peak redshifted from ~648 nm to ~672 nm, becoming more pronounced with higher excitation fluences (FIG.2B). This redshift was attributed to the ground-state dipoles reaching thermal equilibrium with each other and the superlattice. First, strong internal electric fields generated by dense populations of dipoles shift energy levels of the ground state dipoles through the Stark effect, which tends to interact with the electronic states, causing the ground and excited state energy levels to shift. Because this is a closed system, the interactions always consume energy, causing an overall reduction in the energy of thesystem. Therefore, the energy gap between them is reduced, resulting in a redshift in the GSA peak. Second, energy can transfer from excited dipoles to lattice vibrations (phonons). This interaction softens the lattice, alters the electronic band structure, and reduces the energy required for electronic transitions, leading to a redshift in the GSA peaks.

[0188] In some embodiments, excited-state absorption (ESA) arises from transitions of excited carriers from a lower excited state (e.g., S₁) to higher excited states (e.g., S^), requiring the prior occupation of the initial excited state. In some embodiments, ESA signal intensity is directly proportional to the excited-state population, which makes it sensitive to probe the dynamics of excited-state populations under varying excitation conditions. In some embodiments, in the presence of strong dipole–dipole interactions leading to giant dipole formation, the collective internal field polarize the excited-state energy levels, thereby shifting the transition energy of S₁ to S^.

[0189] In some embodiments, to elucidate the energy shifting and decay mechanism of the excited-state energy induced by giant dipole formation, the system can be analyzed from a quantum many-body perspective. In some embodiments, in the initial dipole system, each dipole, formed by Coulomb-bound electron-hole pairs,can be described by the Hamiltonian ^�^^^,

[0191] Where ^^^^gis the bandgap energy of excited dipoles, ^�^^^^^^^is the ^^^^ dipolecreation operator, ^ ( ) ^^^^2 ^^^ ^^^^ =^^^^0^^^^^^^^^^^^2is the Coulomb interaction screened by the relative dielectric constant ^^^^^^^^, where ^^^^ is the elementary charge and ^^^^0is the vacuum permittivity. In some embodiments, at low dipole density ^^^^, the dipole-dipole interactions are negligible, and the system behaves as an independent Bose gas.However, once the exciton density exceeds the threshold ^^^^ ≈where ^^^^ isBohr radius of the dipole, dipole-correlation effects dominate, driving the system into a collective state. In some embodiments, under high-density conditions, overlapping dipole wavefunctions synchronize their phases, resulting in a macroscopic quantumcoherent state called giant dipole. In some embodiments, this collective state ischaracterized by an order parameter Ψ(^^^^, ^^^^):

[0193] where ^^^^(^^^^, ^^^^) is the phase factor. In some embodiments, the intensity ofcollective polarization of the giant dipole ^^^^ is proportional to the square of the order parameter magnitude:

[0194] ^^^^ = −^^^^ ⋅ ^^^^cv ∣ Ψ ∣2

[0195] where ^^^^cvis the intrinsic dipole moment of individual electron-hole pairs oriented along z-axis in the superlattice. In some embodiments, ,the systemHamiltonian ^�^^^GD is thereby renormalized to include the internal collective electricfield ^^^^d,

[0197] where ℏ is the reduced Planck constant, ^^^^∗is the effective mass of the ||giant dipole, ^^^^ is the Coulomb interaction parameter that proportion to ^^^^cv. Notably, ^^^^dis induced by the coherent summation of all dipoles as, 3�^^^^�^^^^′�⋅^�^^^�^�′′

[0198] ^^^^ (^^^^) =1∫ ^^^−^^^^�^^^^�d4^^^^^^^^0 ∣^^^^−^^^^′∣3^^^^^^^^′, with�^�^^^ = ^^^^−^^^^∣^^^^−^^^^′∣�

[0199] where ^^^^ is the distance between dipoles.

[0200] In some embodiments, the dipole transitions from the ground state to the excited state are considered. In some embodiments, when there is no collective effect, 0 the excited state energy is ^^^^ . When the giant dipole forms, the microscopic origin ofethe excited-state renormalization then arises from the coupling between the internal field ^^^^ and the excited-state dipole moment ^^^^ , resulting in a Stark shift Δ^^^^ ,d e e

[0202] In some embodiments, this energy shift includes both linear and quadratic Stark contributions, where the linear contribution is from permanent dipole moment and the dot product of electric field, and the quadratic contribution is from the temporary dipole induced by polarizability ^^^^ of the excited state.e

[0203] In some embodiments, in the case of highly ordered perovskite superlattices, the internal field aligns predominantly along the z-axis of the quantumwells, ensuring that ^^^^e ∥ ^^^^d. As a result, the excited-state energy experiences aredshift, where

[0205] The negative sign clearly indicates that the energy of the excited state decreases, and the degree of this redshift increases with the increase of |^^^^d| at higher excitation fluence.

[0206] In some embodiments, to further investigate the light-matter coupling process in the giant dipole formation, this ensemble is treated as a macroscopic pseudospin system, where its ground-state and collective-excited-state has the degree of binary nature. In some embodiments, the coupled-interaction Hamiltonian^�^^^int of the collective state and electromagnetic field mode ^�^^^ is

[0208] where ^^^^ is the coupling strength, related to the dipole moment ^^^^eand the mode volume ^^^^, while ^^^^ is the dipole angular frequency.

[0209]

[0210] In some embodiments, after the giant dipole formation, the collective nature of ^^^^ dipole ensemble amplifies the effective giant dipole moment ^^^^effand coupling strength ^^^^effto

[0212] In some embodiments, the system thus enters a collective strong coupling regime, which is described by the Tavis–Cummings model, where diagonalization then yields the collective excited-state energy ^^^^GDas

[0213] ^^^^G ≈ ^^^^0D e − √^^^^^^^^

[0214] ^^^^GDshifts substantially below the individual excited-state energy (ESA) ^^^^e0, directly accounting for the redshift observed in the excited-state absorption spectrum.

[0215] In some embodiments, thermodynamic processes are balanced by the principle of entropy increase, where Liouville's theorem reveals the conservation of phase space volume prevents the system from spontaneously forming a low-entropy coherent state (i.e., the giant dipole). In that case, thermodynamic processes can only change the occupation numbers of states but cannot reorganize the energy level structure. The formation of giant dipoles directly modifies the eigenvalues of the Hamiltonian, resulting in an excitation-dependent energy shift, which excludes the thermodynamic-driven formation. In the example of FIG.3A, at low excitation density, where collective effects are absent, the ESA appears at 700 nm, corresponding to the individual excited-state energy. As the excitation density increases to threshold, the giant dipole formation induces an internal field, resulting in a redshift of the ESA to 710 nm. Under high excitation density, the enhanced collective field strength, leading to a further redshift of the ESA to 720 nm. Notably, the new bleaching band in the range of 717–734 nm overlaps with the redshifted ESA position, confirming it as the collective radiative decay channel of the giant dipole state.

[0216] In some embodiments, the collective nature of the giant dipole leads to enhanced radiative decay rate, following the scaling law

[0217] ^^^G^ D ∝ ^^^^^^^0^

[0218] where ^^^G^Dis the decay rate of the giant dipole, ^^^^ is the number of coupled dipoles, and ^^^0^ is the spontaneous decay rate of an individual dipole. In the example shown in FIG.2D, the decay rate of the giant dipole can exceed much faster than random dipoles. In the transient absorption spectra, this ultrafast decay channel manifests as a population depletion within specific energy window. The population depletion reflects the rapid depopulation of the collective state and can be describedby the differential absorption ^^^^^^^^(^^^^, ^^^^),

[0220] where ^^^^ is the dipole angular frequency, ^^^^ is time, ^^^^GD(^^^^) is the absorption cross-section associated with the giant dipole state, and ^^^^GD(^^^^)characterizes its exponential population decay rate. As the giant dipole collectively decays, ^^^^GD(^^^^) and ^^^^GD(^^^^) shrinks quickly, thus the differential absorption depleting at 717–734 nm corresponding to its energy state (FIG.2A). The population depletioncannot be filled by surrounding individual dipoles within the ultrafast timescale, as the energy scattering process driven by vibrational relaxation is comparatively slow.

[0221] In an example embodiment, at high excitation fluences, the morphology of the ESA clearly showed an additional absorption band corresponding to giant dipole formation where strong light-matter interactions build the dipole-dipole coherence. This process consumed energy, leading to a collective state. This collective state occupied an energy level in ESA and the related superfluorescence emission counteracted the ESA signal. Therefore, the probe at this energy experienced another absorption band (FIGS.24A-24B). The additional collective-state absorption band may be designated as CSA.

[0222] In some example embodiments, at low pump fluences (e.g., 3 μJ·cm-2and 7 μJ·cm-2, FIGS.2A-2B), there was only fluorescence. The |ΔA / A| of GSA positively correlated with excitation fluence, because the material absorbed more photons at higher excitations. However, as the pump fluence increased from 16 μJ·cm-2to 26 μJ·cm-2and 43 μJ·cm-2(FIGS.2A-2B), superfluorescence appeared. The |ΔA / A| of GSA decreased while that of CSA increased. The decrease in GSA indicated that photoexcited dipoles were collectively transitioning to a new energy state.

[0223] In some embodiments, CSA did not appear at low pump fluences initially but had a threshold, suggesting it represented a state not dependent on the original superlattice bandgap but on the density of the dipoles. In some embodiments, the super-linear increase and distinct threshold behavior of CSA indicated that its appearance is not due to direct photon absorption but rather transitioning from other photoexcited dipoles. In some embodiments, this illustrated a new energy transfer pathway at high excitation fluence: superlattices absorb photons leading to photoexcited dipoles by GSA, which then collectively form the giant dipole by CSA.

[0224] In some embodiments, compared to GSA, which was from the superlattice bandgap, CSA was narrower, appearing only at 717 ~ 734 nm. This suggests that CSA is not the intrinsic bandgap of the material but represents a new collective state formed by the giant dipole. In some embodiments, giant dipole formation correlates with the screening effect due to Coulombic interactions, which within individual dipoles is reduced due to the presence of nearby high-densitydipoles. In some embodiments, this screening effect lowers the overall energy of the system, thus resulting in the CSA at a longer wavelength.

[0225] In some embodiments, at high excitation fluence of 43 μJ·cm-2, another valley appeared at 690 ~ 705 nm, adjacent to the CSA, in the transient absorption spectra (FIG.2B). In some embodiments, it is hypothesized that this valley represents another quasi-collective state. In some embodiments, this 690 ~ 705 nm valley suggested the presence of an energy state that does not exhibit the same characteristics as the ESA but resembles the CSA. In some embodiments, its lower intensity compared to CSA indicates it is likely a byproduct of the primary collective state during giant dipole formation, hence a quasi-collective state. In some embodiments, TAS thus reveals an intricate interplay of absorption, dipole excitation, collective state transition, and emission.

[0226] In some embodiments, after detecting the energy level of giant dipole, we then trace the energy transfer between random dipoles and the giant dipole by the evolution of band intensities. In some embodiments, the GSB declined once the collective decay appeared in the ESA, suggesting that the formation of the giant dipole led to rapid electron decay, replenishing the ground state. In some embodiments, as a result, the differential absorption between probe and pump diminishes, and the GSB no longer increases at higher excitation fluence (FIGS.24A-24B). In some embodiments, meanwhile, the ESA intensity continues to rise, indicating that surrounding excited carriers transition into the collective state (FIGS.24A-24B).

[0227] S5.6 Example collective dynamics of the giant dipole

[0228] In some embodiments, the intensity of TAS signals at any given moment and wavelength reflects the dipole population at that moment. In some embodiments, by extracting time-resolved data at a fixed wavelength corresponding to the CSA peak intensity in TAS, one can elucidate the collective dynamics of the giant dipole, which can be divided into two key parts: a distinct delay and an accelerated decay. In some embodiments, by analyzing the plots of dipole population versus time, the delay and decay times can be quantified at different excitation fluences (FIG.2E).

[0229] In some embodiments, the distinct delay arose from light-matter interactions and the self-organization of dipoles, which were necessary for the dipoles to form a collective state (FIG.25 and FIG.2D). In some embodiments, at a higherexcitation fluence, the delay time was shorter, which can be attributed to the enhanced probability of dipole-dipole interactions and cooperative effects under high dipole populations, leading to a more rapid organization process.

[0230] In some embodiments, the decay in TAS signal intensity indicated a reduction in the dipole population due to recombination (FIG.2C). In some embodiments, the accelerated decay is a consequence of collective radiative recombination (i.e., superfluorescence) within the giant dipole. In fluorescence, photoexcited dipoles are in random states, and radiative recombination occurs randomly, resulting in long decay times spanning several nanoseconds. In contrast, superfluorescence exhibits markedly different dynamics. In some embodiments, after the initial delay of forming the giant dipole, the established coherence among the dipoles enables them to recombine collectively. In some embodiments, this collective behavior leads to rapid depletion of dipoles, resulting in fast decays on the order of picoseconds.

[0231] S5.7 Example coherent control of the giant dipole by pulse-area manipulation

[0232] In some embodiments, the collective quantum response of the giant dipole follows the pulse-area theorem obtained from the semiclassical Maxwell–Bloch formalism. In some embodiments, for an ensemble of ^^^^ synchronized dipoles the population of the excited collective state is, ^^^^GD = sin 2(Θ / 2)

[0233] where the pulse area Θ = (^^^^ ⋅ ^^^^)ℏ−1∫ ^^^^(^^^^)d^^^^ depends on the transitiondipole moment ^^^^, the unit polarization vector ^^^^, and the temporal envelope ^^^^(^^^^). In some embodiments, a sine-squared dependence therefore signals macroscopic coherence of the giant dipole. In some embodiments, the pulse areas enable manipulation of the macroscopic state. In some embodiments, a π-pulse coherently rotates the population from the ground state to the giant-dipole state, achieving full population inversion. In some embodiments, a 2π-pulse completes the rotation and inverts the phase, then decays back to the ground state. In some embodiments, the transient-absorption signal at 3 ps is extracted because even at the lowest fluence the build-up delay of the giant dipole is lower than 4 ps, whereas at higher fluence it falls below 1 ps (FIG.3E). In some embodiments, a 3-ps gate therefore captures the giantdipole once synchronization is complete but while a large fraction of the collective population is still present before decaying, giving maximal signal-to-noise feature. In some embodiments, the same pulse-area approach thus provides both precise population control and a fast on-demand emission, confirming the feasibility of macroscopic quantum gating with the giant-dipole ensemble.

[0234] S6. Example superfluorescence-based optical transistors

[0235] S6.1 Example role of giant dipole and superfluorescence for optical transistors

[0236] Optical transistors, which utilize light to perform logical operations, can potentially surpass the physical limitations of traditional electrical transistors. Optical transistors often require signal amplification, characterized by a superlinear relationship between excitation and emission with a power-law dependence (i.e., ^^^^P~ ^^^^αin the main text). Typically, achieving optical amplification necessitates embedding optically active materials into cavities and operating at cryogenic temperatures or under strong magnetic fields. Cryogenic temperatures help stabilize these collective states by minimizing thermal fluctuations and enhancing optical transistor performance. Strong magnetic fields can manipulate energy levels and spin states, contributing to the stabilization of collective phenomena. Collective states are crucial for optical transistors because they enable sharp, switch-like transitions between optical properties, crucial for transistor functionality. Collective states offer higher signal intensity and robustness than individual states that are more prone to fluctuation and instability. The ability to control these transitions with light is important for the development of efficient and stable optical transistors. Besides, cavities enhance light-matter interactions by confining light within a volume, which amplifies the response and helps achieve the superlinear relationship. However, such stringent conditions complicate the design, fabrication, and operational environments, presenting challenges for miniaturization, cost-effective integration, and stability of optical transistors. Furthermore, the nonlinear optical processes within cavities suffer from incomplete isolation between input and output, leading to degraded signal-to- noise ratios.

[0237] Some example embodiments relate to giant dipole and superfluorescence which can open new avenues for developing optical transistors under ambient conditions. In some embodiments, the natural cavities in the halide perovskitesuperlattice facilitated giant dipole formation, resulting in high-quality superfluorescence. In some embodiments, the superlattice allowed probing the giant dipole through transient absorption spectroscopy and observing the Burnham-Chiao ringing using a streak camera, which provided strong evidence of superfluorescence. In some embodiments, superfluorescence is a highly coherent and intense burst of light, which can be used to generate high-quality optical signals with low noise for applications requiring precise and reliable optical computing.

[0238] In some embodiments, the threshold behavior of giant dipole enabled clear binary state transitions, corresponding to transitions from the ground state to a collective state, crucial for digital logic operations. In some embodiments, the coherence of giant dipole and its superfluorescence emission enhanced signal integrity, effectively addressing the issue of degraded signal-to-noise ratios prevalent in conventional systems. In some embodiments, this made giant dipole-based optical transistors a compelling option for advancing integrated circuit technology with simplified setups and improved environmental stability.

[0239] S6.2 Example of the mechanism of giant dipole-based quantum logic

[0240] One function of transistors is data processing or computing, where digital binary input ensures precision and accuracy. In conventional optical transistors, loss- dependent logic levels are based on signal intensity to encode binary inputs. While continuous analog signals are common in nature and necessary for high-fidelity media and sensor applications, they are unsuitable for computing and must be converted into digital binary signals for efficient data processing. Typically, a small signal represents [0], and a large signal represents [1]. As light travels, optical loss inevitably reduces the signal intensity, potentially unintentionally transforming a large signal [1] into a small one [0], leading to logic errors. However, polarization, an inherent property of light, remains unchanged during transmission. Therefore, even if there is a loss in light intensity, the polarization state is preserved. Using polarization instead of intensity to encode binary inputs can mitigate the problems with loss-dependent logic levels, ensuring more reliable data transmission.

[0241] In some embodiments, the extinction ratio of an optical transistor is calculated as the ratio of the signal intensities between its ‘on’ state [1] and ‘off’ state [0]. In an example embodiment of a giant dipole-based optical transistor, the extinctionratio was determined by comparing the intensity of superfluorescence to that of normal fluorescence, since the giant dipole state |1^ and the ground state |0^ can be non-destructively (that is, without changing the original state) read out through the superfluorescence burst. In some embodiments, due to the nonlinear amplification effect inherent in superfluorescence, the extinction ratio can easily reach 7 dB, because superfluorescence is a cooperative and coherent emission involving a large number of excited dipoles that emit photons simultaneously with synchronized phases. In some embodiments, unlike quantum dot systems that rely on spatial confinement to suppress decoherence, the giant dipole protects quantum information through many-body macroscopic phase coherence. In some embodiments, the energy gap between the coherent state absorption band and the surrounding random excited states exceeds ^^^^B^^^^R(where ^^^^Bis Boltzmann's constant and ^^^^Ris the room temperature), thereby suppressing thermally induced state mixing. As a result, in contrast to conventional qubits that require extreme environmental conditions, the giant dipole-based qubit remains stable and operational at ambient temperature.

[0242] In some embodiments, the observed sin2^^^^ oscillations in the collective state population as a function of pulse area (Fig.2f) reflects a direct manifestation of coherent macroscopic quantum control, where the pulse area acts as an effective rotation angle on the Bloch sphere of the collective dipole system. In some embodiments, the appearance of the π-pulse threshold reflects the saturation limit population in an excitation-driven two-level system. the system rapidly reaches fullinversion upon applying a pulse area of ^^^^ = ^^^^, corresponding to a completepopulation transfer between the ground state and the collective excited state (i.e., the giant dipole). In some embodiments, while increasing excitation fluence over π-pulse area, the giant dipole experience collective decay that the probing at the same time would only detect a low population. This threshold-like switching is distinct from random dipoles where the population goes linearly with excitation fluence. In this context, the giant dipole acts as a controllable macroscopic qubit, where the π-pulse behavior naturally maps onto discrete state flips characteristic of quantum logic operations such as control-NOT gates, as further demonstrated in Fig.4e.

[0243] In some embodiments, throughout the excitation process, the system undergoes unitary evolution of the collective state vector, following Schrödinger's equation|ΨGD(^^^^)^ = ^^^^(^^^^)|^^^^^^^^^^^^(0)^

[0244] with |ΨGD(^^^^)^ being the order parameter of the giant dipole and ^^^^(^^^^) being unitary operator governed by the driven pulse. In some embodiments, applying different ^^^^(^^^^) rotates the giant dipole state on the Bloch sphere, with the rotation angle (i.e., giant dipole phase) directly proportional to the pulse area, thereby reflecting the total action of the applied optical field.

[0245] In some embodiments, when the pulse area completes a closed-loopevolution from ^^^^ = 0 to 2^^^^, the wavefunction of the giant dipole accumulates a globalphase of ei^^^^. This geometric phase depends on the enclosed area of the path on the Bloch sphere, and is thus protected against small fluctuations in pulse amplitude or duration, enhancing the robustness of coherent phase manipulations. In an example demonstration, an experimentally observed periodicity (Fig.2f) directly confirms the preservation of quantum coherence throughout the entire driving cycle. Moreover, the absence of external modulation elements provide a naturally synchronization for quantum operations, facilitating ultrafast control in photonic quantum processors.

[0246] Some example embodiments enable control-NOT logic operations based on polarization dependence of the dipole coupling in the superlattice. In some embodiments, building on the ability to coherently manipulate the population and phase of the giant dipole using pulse area control, control-NOT logic operations based on polarization dependence of the dipole coupling in the superlattice can be achieved. In some embodiments, the control bit is defined by the absence (logic [0]) or presence (logic [1]) of dipole-dipole coupling, which is practically governed by the excitation polarization. In some embodiments, s-polarized pump activates dipole coupling along the z-direction, further enabling the formation and manipulation of giant dipole state, while p-polarized pump induces quantum fluctuations in the xy-plane that suppress coupling. In some embodiments , the target bit is represented by the nearby excited dipole, where the absence and presence correspond to logic [0] and logic [1], respectively.

[0247] Some architectures based on the disclosed technology enable quantum gate operations that can be implemented by applying an operational pulse, enabling a full set of control-NOT logic transitions among the four basis states. In an example embodiment, for the input state |00^, where the whole system remains in its groundstate and lacks dipole-coupling channel, the operational pulse cannot induce any effective transition. As a result, the output remains |00^, and experimentally, no considerable fluorescence is observed with negligible excited-state absorption signal. For the input state |01^, corresponding to excited dipoles lacking coupling, the operational pulse, constrained by weak dipole-dipole interactions and xy-plane quantum fluctuations, is unable to induce collective synchronization. The superlattice sustains only individual dipoles, manifesting as a conventional excited-state absorption band at 705^nm. Moreover, the observed nanosecond-scale random decay maintains its |10^ state. For the input state |10^, where z-direction dipole coupling is established but nearby excited dipole is absent, the operational pulse with π-pulse area drives population inversion, collectively exciting neighboring dipoles and inducing the formation of a giant dipole state |11^. This transition is evidenced by the redshift of the excited-state absorption band to ~720^nm, as the collective internal field polarizes the excited-state energy levels and renormalizes the transition energy. For the input state |11^, the nearby dipoles are already strongly coupled and form the giant dipole state. Upon applying the operational pulse with an additional π-pulse area, the giant dipole undergoes stimulated collective decay that returns to |10^ of ground state in ultrafast timescale. Its released energy manifests as a burst of superfluorescence. This process is further confirmed by the simultaneous depletion of the excited-state absorption band associated with the collective state. The inversion operation between |10^ and |11^ is essentially the ^^^^(^^^^) corresponding to the π-pulse area thatreconstructs|ΨGD(^^^^)^.

[0248] S.7 Example anisotropy of the photoexcited dipole density

[0249] In some embodiments, during photoexcitation, electrons are promoted from the valence bands, starting from the valence band maximum state and then gradually to lower energies, creating positively charged holes. Simultaneously, the conduction bands gradually populated starting from the conduction band minimum state and then gradually to higher energies, creating negatively charged electrons.

[0250] In some embodiments, the photoexcited dipole (i.e., electron-hole pair) density (per unit cell), Ne, is calculated by:where R and α are the effective reflectivity and absorption coefficient from time- dependent Hartree-Fock calculation, F is the excitation fluence, and Ephoton is the photon energy. In some embodiments, the photoexcited dipole density (per unit cell) can be converted into the carrier density within the material. For example, a 0.05 dipole per unit cell can be divided by the volume of the unit cell, corresponding to 0.0519 −33= 2.525 × 10 cm1980 Å as the carrier density. In some embodiments, at a high Ne, when the photon energies are at least the energy difference between the highest occupied conduction band and the lowest unoccupied valence band, a steady state will be created with electrons populating up to the highest-occupied conduction band and holes populating up to the lowest-unoccupied valence band.

[0251] In some embodiments, a high photoexcited carrier density in the perovskite superlattice was most effectively achieved along the z-direction, because the anisotropic structure of perovskite superlattices in the xz and xy planes resulted in different reflection and absorption properties under polarized excitations along the x- and z- directions (FIGS.26A-26B and FIG.1D). In some embodiments, this anisotropy leads to higher absorption and lower reflection in the z-direction, allowing the z-direction to generate a higher density of photoexcited dipoles compared to the x-direction.

[0252] In some embodiments, this difference in optical behavior is explained by the anisotropic dielectric properties of the material. In the z-direction, the dielectric properties differ from those in the x-direction due to the anisotropic arrangement of atoms and bonds. In some embodiments, organic spacers, which have lower dielectric constants compared to the inorganic perovskite layers, reduce the overall dielectric constant and refractive index in the z-direction. In some embodiments, this results in a smaller refractive index contrast between the perovskite superlattice and the surrounding medium (e.g., air) when light is incident along the z-direction. In some embodiments, according to the Fresnel equation:where R is the reflection coefficient, n1 is the refractive index of the surrounding medium (for air, n1 ≈ 1) and n2 is the refractive index of materials (n2 > 1), a smaller refractive index contrast leads to a lower reflection coefficient at the interface. In someembodiments, this means less light is reflected at the surface, and more light enters the material for absorption. In contrast, in the x-direction, the homogeneous perovskite slabs are connected by continuous ionic bonds, forming a uniform inorganic framework. In some embodiments, this results in a higher dielectric constant and refractive index in the x-direction due to the dense arrangement of inorganic ions. In some embodiments, the refractive index contrast between the perovskite material and the surrounding medium is therefore greater when light is incident along the x-direction.

[0253] In some embodiments, the difference in absorption can be explained by the material's anisotropic structural complexity and polarizability. In some embodiments, the presence of organic spacers in the z-direction creates layered structures that light must navigate, leading to increased scattering and internal diffusion.

[0254] In some embodiments, the organic spacers in the z-direction are more polarizable than the inorganic framework, which means their molecular structures allow for greater electron cloud distortion by incident light. In some embodiments, higher polarizability responds more readily to the electric field of light, enhancing light absorption in the z-direction.

[0255] To further clarify, some example results disclosed in the present patent document do not imply that dipoles oriented along the z-direction intrinsically possess suppressed scattering or inherently longer coherence lifetimes. In fact, scattering processes—whether phonon-induced, defect-mediated, or Coulombic—can occur in all directions, including out-of-plane. The key point is that, in some embodiments, the out- of-plane dipole orientation in the system facilitates higher photoexcited dipole density due to enhanced absorption and reduced reflection along the z-direction, as revealed by both experimental measurement and first-principles calculations. In some embodiments, this higher dipole density in turn strengthens dipole–dipole interactions, which are crucial for initiating the phase synchronization that leads to the formation of giant dipole. In some embodiments, the long coherence time reported is not due to directional suppression of scattering but rather stems from the fact that, once formed, the giant dipole state exhibits collective behaviors, which are known to enhance coherence. In this context, the out-of-plane geometry in some embodiments does not selectively suppress decoherence, but it does promote the conditions necessary for coherence and persist at room temperature.

[0256] In some embodiments, at low excitation fluence, neither s- nor p-polarized excitation generates sufficient dipole density to support strong coupling or collective coherence, so the emission arises from uncorrelated dipoles and exhibits similar broad spectral features in both cases. In some embodiments, the narrower emission linewidth associated with superfluorescence only emerges once the excitation fluence exceeds the threshold necessary for giant dipole formation under s-polarized excitation.

[0257] Table 1 shows some example conditions of generating superfluorescence in materials based on the disclosed technology and other materials in the literature. In some embodiments, the perovskite superlattice of Table 1 reached superfluorescence with the lowest threshold in ambient conditions.

[0258] Table 1: Conditions of generating superfluorescence in different materials

[0259] Previous reports, described elsewhere, have primarily focused on characterizing the emission properties of perovskite superfluorescence and investigating the mechanisms by which collective emission coherence can persist under ambient conditions. However, none have resolved the formation dynamics of the underlying macroscopic coherent state, nor demonstrated active control over its emission. Without direct access to the evolution and manipulability of the collective state, existing techniques cannot establish the microscopic origin of superfluorescence or harness it for functional quantum operations.

[0260] The disclosed embodiments can be implemented with various materials including those described in PCT Publication No. WO2023 / 076550 A1, which is incorporated by reference in its entirety as part of the disclosure of this patent document.

[0261] Examples of correlated behaviors in giant dipole

[0262] In some embodiments, an optical pulse having a polarization causes a population of dipoles to synchronize with one another forming a giant dipole, in a material, that exhibits one or more correlated behaviors.

[0263] Various examples related to correlated behaviors of giant dipoles are disclosed herein.

[0264] In some embodiments, upon reaching the superfluorescence (SF) threshold, a disclosed system exhibits a set of temporally and spectrally correlated phenomena that collectively confirm the cooperative emergence of the macroscopic giant dipole state. These behaviors are manifested simultaneously across the excitation, absorption, and emission channels, establishing a coherent linkage among population dynamics, energetic shifts, and radiative response.

[0265] Some embodiments include collective bleaching and excited-state redshift. In some embodiments, when the excitation fluence exceeds the SF threshold, a new bleaching band appears at the excitonic resonance, accompanied by a redshift of the excited-state absorption band. The onset of these two signatures is temporally coincident within the instrument resolution (e.g., <200 fs), signifying correlated depopulation of the same collective quantum state. The redshift magnitude (e.g., ΔE ≈ 25–30 meV) scales nonlinearly with fluence, confirming many-body energy renormalization driven by dipole–dipole coupling rather than single-exciton screening.

[0266] Some embodiments include fluence-dependent acceleration of buildup dynamics. In some embodiments, time-resolved transient absorption traces show that the rise time of the coherent bleaching feature shortens (e.g., from ~8 ps to <2 ps) as the excitation fluence increases. This acceleration indicates a cooperative growth mechanism in which higher dipole densities strengthen the collective coupling field, promoting faster phase synchronization among emitters.

[0267] Some embodiments include oscillatory population beats signifying coherent light–matter exchange. In an example embodiment, within the excited-state absorption channel, oscillations at a frequency of ~50 ps⁻¹ emerge exclusively above the SF threshold. These oscillations persist over several cycles and are phase-locked across the detection window, revealing coherent Rabi-like exchange between the macroscopic dipole and the radiation field. Their presence directly correlates with thedelayed SF burst, demonstrating that the emission originates from a dynamically coherent light–matter interaction rather than spontaneous decay.

[0268] Some embodiments include temporal anticorrelation between absorption recovery and emission burst. In some embodiments, as the coherent bleaching relaxes, a delayed emission burst appears in photoluminescence kinetics (e.g., ~60– 80 ps delay). The intensity of this emission is anticorrelated with the recovery amplitude of the bleaching, indicating that radiative release occurs through collective recombination of the dipoles that previously formed the coherent state.

[0269] Some embodiments include phase correlation revealed by polarization- dependent excitation. In some embodiments, when the excitation polarization is rotated from s- to p-polarization, the amplitude of both the coherent bleaching and population oscillations diminishes simultaneously. This concurrent suppression across distinct observables verifies that the coupling among dipoles—and hence the formation of the giant dipole—is governed by the polarization-aligned field component. Such phase-coordinated response further supports the anisotropic collective nature of the state.

[0270] Some embodiments include emission coherence linked to absorption dynamics. In some embodiments, Michelson interferometry confirms a first-order coherence time (e.g., exceeding 5 ps), coinciding with the duration of the coherent bleaching plateau in transient absorption. This temporal overlap establishes that emission coherence directly originates from the lifetime of the macroscopic dipole rather than from delayed stimulated emission or optical feedback effects.

[0271] Together, these correlated observables—simultaneous spectral shifts, temporal synchronization, polarization dependence, and emission–absorption coupling—define the microscopic-to-macroscopic transition through which individual excitons self-organize into a single giant dipole state. The ensemble thereby behaves as a unified quantum oscillator whose energy, phase, and population evolutions are collectively correlated across multiple optical observables.

[0272] FIG.37 shows a flow chart of an example method 3700 for detecting a giant dipole in a material. At step 3710, the method 3700 comprises applying, to a material comprising dipoles configured to couple to one another via dipole-dipole coupling, an optical pulse having a polarization, wherein the optical pulse having the polarizationcauses a population of the dipoles to synchronize with one another forming the giant dipole in the material that exhibits one or more correlated behaviors. At step 3720, the method 3700 comprises detecting the giant dipole in the material based on one or more of: a time evolution of an excited energy state associated with the population, wherein the time evolution is detected based on measured absorption data of the material, an emission signal in measured photoluminescence data of the material, wherein the emission signal is indicative of a superfluorescence emission by the population, or one or more temporal correlations between a first photoemission data obtained from the material at a first time and a second photoemission data obtained from the material at a second time, wherein the first time is different from the second time.

[0273] FIG. 38 shows a flow chart of an example method 3800 of controlling a giant dipole. At step 3810, the method 3800 comprises providing a material comprising dipoles configured to couple to one another via dipole-dipole coupling. Ats step 3820, the method 3800 comprises applying, to the material, a first optical pulse to cause the giant dipole to form in the material, wherein the giant dipole is formed from a population of the dipoles that is excited by the first optical pulse into an excited energy state, wherein the population is excited into the excited energy state based on a polarization of the first optical pulse. At step 3830, the method 3800 comprises applying, to the material, a second optical pulse configured to cause the population to transition from the excited energy state to another energy state, wherein the second optical pulse is configured to cause decay of the giant dipole in the material.

[0274] The present patent document discloses embodiments that introduce a new class of hybrid perovskite systems that enable direct access to, and coherent control of, the macroscopic quantum state underlying room-temperature superfluorescence (SF). Unlike existing techniques that only characterize emission- level observables such as thresholds and superlinearity, the disclosed embodiments can enable experimental access to the formation, evolution, and manipulation of the collective giant dipole state that governs SF. Some example features and benefits that can be provided by some disclosed embodiments include: • Direct probing of macroscopic coherent-state formation. In some example embodiments, an approach to directly resolve the formation dynamics of the giant dipole—representing the macroscopic coherent state responsible for SF—through ultrafast transient absorption spectroscopy is disclosed.• Identification of the energetic fingerprint of the collective dipole state. In some disclosed systems, above the SF threshold, the system exhibits a coherent- state bleaching band and fluence-dependent excited-state absorption redshift, together forming a unique energetic signature of collective dipole–dipole coupling. • Observation of coherent light–matter exchange during formation. In some disclosed embodiments, time-resolved oscillations within the excited-state absorption channel reveal Rabi-like coupling between the macroscopic dipole and the electromagnetic field, demonstrating sustained coherence during state buildup. • Differentiation between emission coherence and state coherence. In some disclosed embodiments, Michelson interferometry and photon-correlation measurements confirm that the emission arises from synchronized dipole recombination rather than amplified spontaneous emission, thus distinguishing macroscopic coherence from ordinary lasing. • Demonstration of coherent control and quantum-logic operation. In some embodiments, by exploiting the anisotropy of the perovskite superlattice, polarization-selective excitation enables deterministic control of dipole–dipole coupling. This control mechanism can be used to realize an all-optical controlled-NOT (CNOT) operation, marking the first demonstration of quantum logic based on a collective dipole state. • Advancement from emission observation to functional quantum platform. Embodiments of the disclosed technology transform room-temperature SF from a passive emission phenomenon into an actively controllable macroscopic quantum system, providing both mechanistic understanding and a practical framework for quantum information processing.

[0275] Embodiments of the disclosed technology support inter alia the following technical solutions.

[0276] 1. A device based on giant dipole superfluorescence, comprising: a substrate; a material, disposed on the substrate, comprising dipoles configured to couple to one another via dipole-dipole coupling, wherein the material is configured toreceive a first optical pulse and a second optical pulse, the first optical pulse and the second optical pulse each having a polarization selected to control the dipole-dipole coupling to cause a giant dipole to form in the material, wherein the giant dipole is formed from a population of the dipoles that is excited by the first optical pulse and the second optical pulse; and a logic system comprising the substrate and the material, wherein: the polarization of the first optical pulse defines a binary input of the logic system, the polarization of a second optical pulse defines a second binary input of the logic system, a superfluorescence emission detected from the material in response to the first optical pulse and the second optical pulse defines a first binary output of the logic system, and absence of the superfluorescence emission defines a second binary output of the logic system.

[0277] 2. The device of solution 1, wherein the device is operable to provide a logic gate.

[0278] 3. The device of solution 2, wherein the logic gate is of a type, wherein the type is selectable based on a fluence of the first optical pulse and the second optical pulse.

[0279] 4. The device of solution 3, wherein the type corresponds to an OR, NOR, AND, NAND, or NOT type.

[0280] 5. The device of solution 1, wherein the first optical pulse has a first intensity and the second optical pulse has a second intensity, wherein the superfluorescence emission is produced from the material when a sum of the first intensity and the second intensity exceeds a threshold value.

[0281] 6. The device of solution 1, wherein the material comprises a superlattice.

[0282] 7. The device of solution 6, wherein the material comprises a perovskite superlattice.

[0283] 8. The device of solution 6, wherein the first optical pulse and the second optical pulse are incident upon a same plane of the superlattice.

[0284] 9. The device of solution 6, wherein some or all of the dipoles are oriented along a selected direction in the material based the polarization of the first optical pulse or the polarization of the second optical pulse.

[0285] 10. The device of any one of solutions 1-9, wherein the device is operated at ambient temperature.

[0286] 11. A method for detecting a giant dipole in a material, the method comprising: applying, to a material comprising dipoles configured to couple to one another via dipole-dipole coupling, an optical pulse having a polarization, wherein the optical pulse having the polarization causes a population of the dipoles to synchronize with one another forming the giant dipole in the material that exhibits one or more correlated behaviors; and detecting the giant dipole in the material based on one or more of: a time evolution of an excited energy state associated with the population, wherein the time evolution is detected based on measured absorption data of the material, an emission signal in measured photoluminescence data of the material, wherein the emission signal is indicative of a superfluorescence emission by the population, or one or more temporal correlations between a first photoemission data obtained from the material at a first time and a second photoemission data obtained from the material at a second time, wherein the first time is different from the second time.

[0287] 12. The method of solution 11, wherein the material is a two-dimensional epitaxial halide perovskite superlattice.

[0288] 13. The method of solution 11, wherein the dipoles in the population are synchronized with one another during the first time or the second time.

[0289] 14. The method of solution 11, wherein the dipoles in the population have a same phase.

[0290] 15. The method of solution 11, comprising: determining a property of the giant dipole based on the time evolution, the emission signal, or the one or more temporal correlations, wherein the property is related to formation, dynamics, or behavior of the giant dipole.

[0291] 16. The method of solution 11, comprising: controlling an energy state of the giant dipole by applying one or more additional optical pulses to the material to cause at least some of the dipoles to transition from a first energy state to another state.

[0292] 17. The method of solution 16, wherein the first energy state is the excited energy state.

[0293] 18. The method of solution 11, wherein the one or more temporal correlations are determined based on measured optical coherence data of the material.

[0294] 19. The method of solution 18, comprising: determining a coherence time of the giant dipole based on the measured optical coherence data of the material, wherein the coherence time is associated with a phase coherence of the population.

[0295] 20. The method of solution 11, wherein the measured photoluminescence data of the material comprises Rabi oscillations.

[0296] 21. The method of solution 11, wherein the measured absorption data comprises beating, wherein the beating is associated with the excited energy state.

[0297] 22. A method of controlling a giant dipole, comprising: providing a material comprising dipoles configured to couple to one another via dipole-dipole coupling; applying, to the material, a first optical pulse to cause the giant dipole to form in the material, wherein the giant dipole is formed from a population of the dipoles that is excited by the first optical pulse into an excited energy state, wherein the population is excited into the excited energy state based on a polarization of the first optical pulse; and applying, to the material, a second optical pulse configured to cause the population to transition from the excited energy state to another energy state, wherein the second optical pulse is configured to cause decay of the giant dipole in the material.

[0298] 23. The method of solution 22, wherein the polarization of the first optical pulse modifies the dipole-dipole coupling between some or all of the dipoles.

[0299] 24. The method of solution 23, wherein some or all of the dipoles are oriented along a selected direction in the material based the polarization of the first optical pulse.

[0300] 25. The method of solution 22, wherein the material comprises a superlattice, wherein the first optical pulse and the second optical pulse are incident upon a same plane of the superlattice.

[0301] 26. The method of solution 22, comprising: using the material, the first optical pulse, the second optical pulse, and one or more additional optical pulses to provide a logic system capable to perform a logic operation, wherein: a polarization of the first optical pulse defines a first binary input of the logic system, a polarization of the second optical pulse defines a second binary input of the logic system, a superfluorescence emission detected from the material in response to the first optical pulse, the second optical pulse, or the one or more additional optical pulses defines a first binary output of the logic system, and absence of the superfluorescence emission defines a second binary output of the logic system.

[0302] 27. The method of solution 26, comprising: performing the logic operation using the logic system.

[0303] 28. The method of solution 27, wherein the logic operation is a control- NOT logic operation.

[0304] 29. The method of solution 23, wherein the material comprises a perovskite superlattice.

[0305] 30. The method as in any one of solutions 11-29, wherein the method is performed at ambient temperature.

[0306] 31. An optical system configured to implement any one of the solutions 11-30.

[0307] 32. A device configured to implement any one of the solutions 11-30.

[0308] 33. A method for creating a giant dipole at room temperature, comprising using an epitaxial two-dimensional halide perovskite superlattice to confine photoexcited carriers.

[0309] 34. The method of solution 33, comprising capturing superfluorescence bursts from the giant dipole.

[0310] 35. The method of solution 34, wherein the superfluorescence bursts exhibit distinct Rabi oscillations.

[0311] 36. The method of solution 34, wherein the superfluorescence bursts depend on photoexcitation polarization.

[0312] 37. An optical transistor operable based on a creating of a giant dipole a room temperature, as disclosed in this patent document.

[0313] 38. Methods, devices and materials for creation of a giant dipole at room temperature, as disclosed in this patent document.

[0314] Implementations of the subject matter and the functional operations described in this patent document can be implemented in various systems, digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Implementations of the subject matter described in this specification can be implemented as one or more computer program products, i.e., one or more modules of computer program instructions encoded on a tangible and non-transitory computer readable medium for execution by, or to control the operation of, data processing apparatus. The computer readable medium can be a machine- readable storage device, a machine-readable storage substrate, a memory device, a composition of matter effecting a machine-readable propagated signal, or a combination of one or more of them. The term “data processing unit” or “data processing apparatus” encompasses all apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.

[0315] A computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or onmultiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.

[0316] The processes and logic flows described in this specification can be performed by one or more programmable processors executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

[0317] Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read only memory or a random-access memory or both. The essential elements of a computer are a processor for performing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Computer readable media suitable for storing computer program instructions and data include all forms of nonvolatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

[0318] While this patent document contains many specifics, these should not be construed as limitations on the scope of any invention or of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of particular inventions. Certain features that are described in this patent document in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, andthe claimed combination may be directed to a subcombination or variation of a subcombination.

[0319] Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. Moreover, the separation of various system components in the embodiments described in this patent document should not be understood as requiring such separation in all embodiments.

[0320] Only a few implementations and examples are described and other implementations, enhancements and variations can be made based on what is described and illustrated in this patent document.

Claims

CLAIMS What is claimed is:

1. A device based on giant dipole superfluorescence, comprising: a substrate; a material, disposed on the substrate, comprising dipoles configured to couple to one another via dipole-dipole coupling, wherein the material is configured to receive a first optical pulse and a second optical pulse, the first optical pulse and the second optical pulse each having a polarization selected to control the dipole-dipole coupling to cause a giant dipole to form in the material, wherein the giant dipole is formed from a population of the dipoles that is excited by the first optical pulse and the second optical pulse; and a logic system comprising the substrate and the material, wherein: the polarization of the first optical pulse defines a binary input of the logic system, the polarization of a second optical pulse defines a second binary input of the logic system, a superfluorescence emission detected from the material in response to the first optical pulse and the second optical pulse defines a first binary output of the logic system, and absence of the superfluorescence emission defines a second binary output of the logic system.

2. The device of claim 1, wherein the device is operable to provide a logic gate.

3. The device of claim 2, wherein the logic gate is of a type, wherein the type is selectable based on a fluence of the first optical pulse and the second optical pulse.

4. The device of claim 3, wherein the type corresponds to an OR, NOR, AND, NAND, or NOT type.

5. The device of claim 1, wherein the first optical pulse has a first intensityand the second optical pulse has a second intensity, wherein the superfluorescence emission is produced from the material when a sum of the first intensity and the second intensity exceeds a threshold value.

6. The device of claim 1, wherein the material comprises a superlattice.

7. The device of claim 6, wherein the material comprises a perovskite superlattice.

8. The device of claim 6, wherein the first optical pulse and the second optical pulse are incident upon a same plane of the superlattice.

9. The device of claim 6, wherein some or all of the dipoles are oriented along a selected direction in the material based the polarization of the first optical pulse or the polarization of the second optical pulse.

10. The device of any one of claims 1-9, wherein the device is operated at ambient temperature.

11. A method for detecting a giant dipole in a material, the method comprising: applying, to a material comprising dipoles configured to couple to one another via dipole-dipole coupling, an optical pulse having a polarization, wherein the optical pulse having the polarization causes a population of the dipoles to synchronize with one another forming the giant dipole in the material that exhibits one or more correlated behaviors; and detecting the giant dipole in the material based on one or more of: a time evolution of an excited energy state associated with the population, wherein the time evolution is detected based on measured absorption data of the material, an emission signal in measured photoluminescence data of the material, wherein the emission signal is indicative of a superfluorescence emission by the population, orone or more temporal correlations between a first photoemission data obtained from the material at a first time and a second photoemission data obtained from the material at a second time, wherein the first time is different from the second time.

12. The method of claim 11, wherein the material is a two-dimensional epitaxial halide perovskite superlattice.

13. The method of claim 11, wherein the dipoles in the population are synchronized with one another during the first time or the second time.

14. The method of claim 11, wherein the dipoles in the population have a same phase.

15. The method of claim 11, comprising: determining a property of the giant dipole based on the time evolution, the emission signal, or the one or more temporal correlations, wherein the property is related to formation, dynamics, or behavior of the giant dipole.

16. The method of claim 11, comprising: controlling an energy state of the giant dipole by applying one or more additional optical pulses to the material to cause at least some of the dipoles to transition from a first energy state to another state.

17. The method of claim 16, wherein the first energy state is the excited energy state.

18. The method of claim 11, wherein the one or more temporal correlations are determined based on measured optical coherence data of the material.

19. The method of claim 18, comprising: determining a coherence time of the giant dipole based on the measured optical coherence data of the material,wherein the coherence time is associated with a phase coherence of the population.

20. The method of claim 11, wherein the measured photoluminescence data of the material comprises Rabi oscillations.

21. The method of claim 11, wherein the measured absorption data comprises beating, wherein the beating is associated with the excited energy state.

22. A method of controlling a giant dipole, comprising: providing a material comprising dipoles configured to couple to one another via dipole-dipole coupling; applying, to the material, a first optical pulse to cause the giant dipole to form in the material, wherein the giant dipole is formed from a population of the dipoles that is excited by the first optical pulse into an excited energy state, wherein the population is excited into the excited energy state based on a polarization of the first optical pulse; and applying, to the material, a second optical pulse configured to cause the population to transition from the excited energy state to another energy state, wherein the second optical pulse is configured to cause decay of the giant dipole in the material.

23. The method of claim 22, wherein the polarization of the first optical pulse modifies the dipole-dipole coupling between some or all of the dipoles.

24. The method of claim 23, wherein some or all of the dipoles are oriented along a selected direction in the material based the polarization of the first optical pulse.

25. The method of claim 22, wherein the material comprises a superlattice, wherein the first optical pulse and the second optical pulse are incident upon a same plane of the superlattice.

26. The method of claim 22, comprising: using the material, the first optical pulse, the second optical pulse, and one or more additional optical pulses to provide a logic system capable to perform a logic operation, wherein: a polarization of the first optical pulse defines a first binary input of the logic system, a polarization of the second optical pulse defines a second binary input of the logic system, a superfluorescence emission detected from the material in response to the first optical pulse, the second optical pulse, or the one or more additional optical pulses defines a first binary output of the logic system, and absence of the superfluorescence emission defines a second binary output of the logic system.

27. The method of claim 26, comprising: performing the logic operation using the logic system.

28. The method of claim 27, wherein the logic operation is a control-NOT logic operation.

29. The method of claim 23, wherein the material comprises a perovskite superlattice.

30. The method as in any one of claims 11-29, wherein the method is performed at ambient temperature.

31. An optical system configured to implement any one of the methods 11-30.

32. A device configured to implement any one of the methods 11-30.

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