Systems and methods for deterministic creation of strained color centers in nanostructures via high-stress thin films

Abstract

Devices, systems, and methods that use a structure are provided. The structure may include a waveguide layer and an intrinsically stressed thin film. The waveguide layer may include a first material. The intrinsically stressed thin film may include a second material. The intrinsically stressed thin film may be disposed on the waveguide layer, thereby inducing a strain in the waveguide layer. The first material may include at least one color center having a first pair and / or second pair of energy levels or quantum states having an optical energy separation and / or a second pair of energy levels or quantum states having a microwave energy separation. The optical energy separation and the microwave energy separation of the pair of energy levels and / or quantum states may be determined by the induced strain.

Description

HCU-06525 HU 9477 SYSTEMS AND METHODS FOR DETERMINISTIC CREATION OF STRAINED COLOR CENTERS IN NANOSTRUCTURES VIA HIGH-STRESS THIN FILMS RELATED APPLICATION

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 538,161, filed on September 13, 2023. The entire teachings of the above application(s) are incorporated herein by reference. GOVERNMENT SUPPORT

[0002] This invention was made with government support under 1541959 and 2137723 and 1941583 awarded by National Science Foundation (NSF) and under N00014-20-1-2425 awarded by U.S. Office of Naval Research (NAVY / ONR) and under W911NF1810432 awarded by U.S. Army Research Office (ARO). The government has certain rights in this invention. The government has certain rights in the invention. BACKGROUND

[0003] Color centers have emerged as a leading qubit candidate for realizing hybrid spin- photon quantum information technology. One major limitation of the platform, however, is that the characteristics of individual color-centers may often be strain dependent. As an illustrative case, the silicon-vacancy center in diamond typically requires millikelvin temperatures in order to achieve long coherence properties, but strained silicon vacancy centers have been shown to operate at temperatures beyond 1K without phonon-mediated decoherence. In spite of this, a method to reproducibly create strained silicon-vacancy centers, and devices, systems, and methods that include structures with such materials have been lacking. BRIEF SUMMARY

[0004] According to some embodiments of the present disclosure, devices, systems, and methods are provided. In first example embodiment, a device that includes at least one structure is provided. The structure includes a waveguide layer and an intrinsically stressedHCU-06525 HU 9477 thin film. The waveguide layer includes a first material. The intrinsically stressed thin film includes a second material. The intrinsically stressed thin film is disposed on the waveguide layer, thereby inducing a strain in the waveguide layer. The first material includes at least one color center having a pair of energy levels. The pair of energy levels has an optical energy separation. The optical energy separation of the pair of energy levels is determined by the induced strain.

[0005] In second example embodiment, a quantum entanglement system is provided. The quantum entanglement system includes a first structure, a second structure, a photon source, and a photon detector. Each structure includes a waveguide layer and an intrinsically stressed thin film. The waveguide layer includes a first material. The intrinsically stressed thin film includes a second material. The intrinsically stressed thin film is disposed on the waveguide layer, thereby inducing a strain in the waveguide layer. The first material includes at least one color center having a pair of quantum states. The pair of quantum states has an optical energy separation. The optical energy separation of the pair of quantum states is determined by the induced strain. The at least one color center has an optical transition between the quantum states of the pair at a characteristic wavelength. The photon source is configured to direct an excitation pulse into the waveguide layer of the first structure and the waveguide layer of the second structure, thereby causing the optical transition in the at least one of the color center of the first structure or the second structure and causing the at least one color center to emit a photon. The photon detector is configured to detect the photon emitted by the at least one color center, thereby producing an entanglement between the at least one color center in the first structure and the at least one color center in the second structure.

[0006] In third example embodiment, a system is provided. The system includes a structure and a microwave source. The structure includes a waveguide layer and an intrinsically stressed thin film. The waveguide layer includes a first material. The intrinsically stressed thin film includes a second material. The intrinsically stressed thin film is disposed on the waveguide layer, thereby inducing a strain in the waveguide layer. The first material includes at least one color center having a pair of quantum states. The pair of quantum states has a microwave energy separation. The microwave energy separation of the pair of quantum states is determined by the induced strain. The microwave source is configured to apply a microwave pulse to the at least one color center, the microwave pulseHCU-06525 HU 9477 having a frequency corresponding to the microwave energy separation, thereby inducing the at least one optical center to transition between the pair of quantum states.

[0007] In fourth example embodiment, a method of operating a quantum gate is provided. Values for a set of parameters of a microwave pulse are selected. The set of parameters are selected from a phase, a frequency, an intensity, and a pulse duration. The microwave pulse is applied to a structure. The structure includes a waveguide layer and an intrinsically stressed thin film. The waveguide layer includes a first material. The intrinsically stressed thin film includes a second material. The intrinsically stressed thin film is disposed on the waveguide layer, thereby inducing a strain in the waveguide layer. The first material includes at least one color center having a pair of quantum states. The pair of quantum states has a microwave energy separation. The microwave energy separation is determined by the induced strain. The microwave pulse induces the at least one color center to transition between the pair of quantum states.

[0008] In fifth example embodiment, a quantum computing device is provided. The quantum computing device includes a first structure, a second structure, a photon source, a photon detector, and a microwave source. Each structure includes a waveguide layer and an intrinsically stressed thin film. The waveguide layer includes a first material. The intrinsically stressed thin film includes a second material. The intrinsically stressed thin film is disposed on the waveguide layer, thereby inducing a strain in the waveguide layer. The first material includes at least one color center having a first pair of quantum states and a second pair of quantum states. The first pair of quantum states has an optical energy separation. The second pair of quantum states has a microwave energy separation. The optical energy separation and the microwave energy separation is determined by the induced strain. The at least one color center has an optical transition between the first pair of quantum states at a first characteristic wavelength, and a microwave transition between the second pair of quantum states at a second characteristic wavelength. The photon source is configured to direct an excitation pulse into the waveguide layer of the first structure and into the waveguide layer of the second structure, thereby causing the optical transition in the at least one of the color center of the first structure or of the second structure and causing the at least one color center to emit a photon. The photon detector is configured to detect the photon emitted by the at least one color center. The microwave source is configured to apply a microwave pulse to the at least one color center, the microwave pulse having a frequencyHCU-06525 HU 9477 corresponding to the microwave energy separation, thereby causing the microwave transition in at least one of the color center of the first structure or the second structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] A detailed description of various aspects, features, and embodiments of the subject matter described herein is provided with reference to the accompanying drawings, which are briefly described below. The drawings are illustrative and are not necessarily drawn to scale, with some components and features being exaggerated for clarity. The drawings illustrate various aspects and features of the present subject matter and may illustrate one or more embodiment(s) or example(s) of the present subject matter in whole or in part.

[0010] FIGS.1A and 1B show a level diagram and a schematic of a structure resulting from combining strained thin films with diamond nanostructures to deterministically strain silicon-vacancy centers (SiV) according to various embodiments of the present disclosure.

[0011] FIGS.2A-2C show the design of a structure including a silicon-nitride (SiN)- diamond heterostructure and its various properties according to various embodiments of the present disclosure.

[0012] FIGS.3A-3F show the design of a diamond cantilever structure with high-stress silicon-nitride (SiN) deposited therein and the results of experimental verification of strained silicon-vacancy centers (SiV) formation according to various embodiments of the present disclosure.

[0013] FIGS.4A-4C show the modeling of the coherence enhancement of strained SiVs according to various embodiments of the present disclosure.

[0014] FIG.5 is a flow chart depicting a method of operating a quantum gate according to various embodiments of the present disclosure.

[0015] FIG.6 is a schematic view of an exemplary setup and protocol for generating long-distance entanglement between pairs of color centers.

[0016] FIG.7 is a schematic view of an exemplary entanglement protocol.

[0017] FIG.8 depicts a schematic of an example of a classical computing node according to various embodiments of the present disclosure. DETAILED DESCRIPTIONHCU-06525 HU 9477

[0018] As presented herein, techniques may be used to combine high stress silicon nitride thin films with diamond nanostructures in order to reproducibly create statically strained silicon-vacancy color centers. As used herein, a color center may be point defects in crystal lattices, the point defects may include of one or more electrons trapped at an ionic vacancy in the lattice. For example, a color center may be a silicon-vacancy color center. Statically strained silicon-vacancy color centers may include a high mean ground state splitting, such as a ground state splitting of approximately 608 GHz, with particular strain magnitudes, such as strain magnitudes of ∼4E-4. Based on modeling, this strain may be sufficient to allow for operation of a majority silicon-vacancy centers within the measured sample at elevated temperatures, such as at 1.5K, without any degradation of their spin properties. Such a technique may offers a scalable way to fabricate high-temperature operation quantum memories. Beyond silicon-vacancy centers, such a technique may sufficiently general that it can be easily extended to other platforms as well.

[0019] Solid-state color-center defects are an exciting platform for quantum information technology which can combine scalable fabrication, state-of-the-art spin properties, and excellent photonic interfaces. This combination may enable the realization of interfaces between long-lived memories and individual optical photons for a variety of applications including quantum communication, computation, and sensing. Recently the silicon-vacancy (SiV) center in diamond has emerged as a leading color center defect primarily due to its inversion symmetry which enables integration of SiVs into nanostructures without a significant degradation of the defect’s spin and optical properties. Pioneering work has utilized SiVs implanted within a diamond nanophotonic resonator to perform a variety of demonstrations including deterministic spin-photon interactions, high-efficiency single photon generation, and memory-enhanced quantum communication.

[0020] One major challenge associated with color-center qubits may be their sensitivity to their local environment. In particular, the local strain environment of the defect can drastically reduce or even improve the properties of the quantum emitter. In the case of the SiV, one major limitation of the emitter may be its extreme sensitivity to phonon-induced decoherence via driving of the transition between the upper and lower branches of its ground state manifold, such as what is shown in FIG.1A. The splitting between these transitions, known as the ground state splitting (∆GSS), is 46 GHz for an unstrained SiV which necessitates operation at milliKelvin temperatures to freeze out higher-energy, resonant phonons and obtain long coherence properties.HCU-06525 HU 9477

[0021] Referring now to FIG.1, FIG.1A shows a level diagram of the SiV electron spin. Phonon mediated transitions (γup / dn) between the bottom two energy levels of the spin defect (∆GSS) may be the primary dephasing mechanism for the SiV at elevated temperatures (> 100 mK). Upon experiencing strain perpendicular to the SiV’s internal Z axis, however, a significant shift in the SiV’s energy levels may lead to a shift in optical transition frequencies and therefore a significant increase in (∆GSS). This may suppress γup / dn which enables higher temperature operation of the color center without spin coherence degradation.

[0022] Alternatively, recent work has shown that strained SiVs may be able to overcome this limitation through a strain-induced enlargening of ∆GSS, thus requiring higher-energy phonons to decohere the spin and therefore enabling higher-temperature operation. Previous work has already shown that the coherence of an SiV at 4K can be improved through dynamically straining the SiV via active MEMS tuning. More recently, a strained SiV was shown to be operable up to 1.5K without any phonon-induced degradation of its spin properties, achieving coherence times beyond 100 µs. Additionally, strain has also been shown to improve other properties of the SiV including its spectral stability and microwave susceptibility of its spin for coherent control. Despite the clear benefits of utilizing strained SiVs, a simple method to deterministically strain the static environment of the defect is lacking: previous work utilized either complex nano-electro-mechanical tuning or the random distribution of strain in the nanofabricated structures which is inherently probabilistic and severely limits yield. Thus there is a need in the art for a simple technique to deterministically strain the static environment of the defect.

[0023] In this work, a new technique for reproducibly creating strained SiVs through integrating intrinsically strained thin film stressors with diamond nanostructures is disclosed.

[0024] In various embodiments, High stress silicon-nitride (SiN) thin films may be integrated with diamond cantilevers containing SiVs, such as what is shown in FIG.1B.

[0025] Referring now to FIG.1, FIG.1B shows a schematic of the proposed diamond- SiN nanostructure whereby SiN is deposited on diamond cantilevers to introduce significant strain into the cantilever and thereby deterministically strain the SiVs. In various embodiments, the optical properties of the SiVs may be measured within these nanostructures before and after SiN deposition. For example, in experiments, a significantincrease in the average ∆GSS o f up to 608 GHz was observed. This increase was over 10times the ∆GSS,0for an unstrained SiV indicating the introduction of significant strain. Through modeling based on previous published results, it was estimated that this splitting isHCU-06525 HU 9477 sufficient to enable 1.5K operation for a majority of SiVs in the sample. This, therefore, may be a suitable technique for reproducibly creating highly-strained SiVs in nanostructures.

[0026] For the design a freestanding diamond cantilever aligned to the

[0110] direction of the diamond with a 60 nm thin film of tensile-stress SiN on the top surface and SiVs integrated via ion implantation was developed, such as what is shown in FIG.2A. SiN may be selected as the stressor due to the high intrinsic stress achievable with the material, ease of deposition, and its previous use as a stressor for other integrated photonics applications. Tensile stress may be selected so that the additional thermal stress between the SiN film and diamond cantilever upon cooling down due to a mis-match in thermal expansion coefficients adds constructively to this intrinsic stress.

[0027] In order to estimate the distribution of expected strains, Finite-Element-Method (FEM, COMSOL) simulations were performed. A significant strain in the cantilever was observed, such as what is shown in FIG.2B. The axial strain components located parallel (εyy) and perpendicular in-plane (εxx) relative to the cantilever, such as what is shown in FIG. 2C, were dominant and strongly depth dependent. To account for this, an SiV implantation depth, which is greater than or equal to a threshold, may be targeted as a trade-off between maximizing the strain experienced by the defect and ensuring they may be far enough from the surface to not experience potentially detrimental surface noise. For example, a depth a depth of 35 nm may be targeted. The bi-axial nature of the strain may ensure that the SiV will experience a strain perpendicular to its internal Z-axis of sufficient magnitude to significantly increase ∆GSSregardless of its orientation within the crystal.

[0028] Referring now to FIG.2, which shows structures as described herein, FIG.2A shows a cross-sectional schematic of a structure that includes an intrinsically stressed thin- film, for example made of SiN, on a waveguide layer made of a material, for example a free standing diamond cantilever. A triangular cross-section diamond device fabricated via reactive ion-beam angled etching may be used. FEM simulations of SiN-diamond cantilevers, showing significant strain that may be imparted into the nanostructure through utilization of a high-intrinsic stress SiN thin film is shown in FIG.2B. FIG.2B shows a structure as described herein, such as a SiN-diamond cantilever, which includes a longitudinal dimension, and a cross-sectional dimension. As shown in FIG.2B, and as used herein, the longitudinal dimension may be the elongated portion of the structure, such as what is shown as elongated along the y-axis, while the cross-sectional dimension may be the portion of the structure that is not elongated, such as what is shown on the x-axis. ColorHCU-06525 HU 9477 centers may be disposed in the waveguide portion, which may include the diamond material, along the longitudinal dimension. The stress of the thin film used in the simulations may be based on the fitting of the experimentally measured color center, such as SiV distributions (See, FIG.4.). FIG.2C shows a cross-sectional strain profile of the cantilevers taken at the center of the cantilever showing that significant axial strain (> 1E-4) is present at the target implantation point of the SiVs parallel and in-plane perpendicular to the beam. Although the profile is taken from the center of the cantilever, it should be noted that the strain within the beam is quite uniform along the beam.

[0029] Having numerically shown the ability for stressed SiN films to impart significant strain in diamond cantilevers, corresponding samples were fabricated. Free-standing diamond cantilevers may be fabricated using angled ion-beam etching. SiVs may be precisely formed within the cantilever through combining masked ion-implantation of Si atoms (50 keV) with high temperature annealing at 1250C in an ultra-high vacuum. The density of the SiVs may be kept low such that individual SiV centers are spectrally resolvable. After device fabrication, a thin-film of a particular thickness, such as a 60 nm thin-film of SiN, may be deposited using plasma-enhanced chemical-vapor deposition (PECVD). The low deposition temperature required by PECVD may ensure process compatibility both with the diamond nanostructures used in this work and potentially a variety of other quantum photonic platforms. A significant bending may be observed in the cantilever upon such SiN deposition, indicative of thin-film induced strain in the nanostructure, such as what is shown in FIG.3A.

[0030] Referring now to FIG.3, FIG.3A shows a scanning electron micrograph (SEM) of a diamond cantilever structure with high-stress SiN deposited, showing a significant strain imparted on the cantilever.

[0031] In order to observe the effects of the SiN stressor on the SiVs, off-resonance excitation based photo-luminescence (PL) spectra may be taken of the SiVs at 4K before and after deposition of the SiN. A significant shift of the spectral lines is observed after the SiN is deposited, which may be attributed to the strain induced by the SiN, such as what is shown in FIG.3B. Specifically an increased separation between the individual transitions which is indicative of an increasing of the ∆GSS may be observed,as expected and desired.

[0032] To better quantify this, PL spectra from approximately 100 implantation spots were taken and individual peaks in each spectra were located. Upon deposition of the SiN, a significant broadening in the distribution of the peaks was seen, again indicating a shift inHCU-06525 HU 9477 the optical lines that may be attributed to strain induced by the SiN, such as what is shown in FIG.3C. As further verification that strain induced by the SiN stressor is indeed responsible for this broadening, spectra was taken from SiVs implanted at the base of the cantilever where less stress was expected due to the mechanical tether to the substrate, and no significant broadening was observed (see SI).

[0033] Referring now to FIG.3, photo-luminescence spectra of the same SiV before (FIG.3B) and after (FIG.3C) deposition of the SiN are shown. These figures show a shift in all four optical lines and an increase in the ∆GSSof the SiV due to the imparted strain. In various embodiments, as shown in FIG.3C, the at least one color center, such as the SiV, has an optical transition at a characteristic wavelength. In various embodiments, the cross- sectional dimension of the structure, such as one of the structures shown in FIG.2, is less than or equal to this characteristic wavelength.

[0034] In order to better quantify the magnitude of strain observed, PL spectra where four or fewer clear lines are observed were identified. This was interpreted as being from an individual SiV. From these spectra, it was assumed that the two lowest-energy transitions correspond to the C and D transitions of the SiV respectively, and thus the difference in frequencies of the transitions corresponds to ∆GSSof the SiV. From this ∆GSSwas extracted for a handful of SiVs before and after SiN deposition, such as what is shown in FIG.3D. A significant increase in the mean of the GSS from 119 ± 22 GHz error to 608 ± 89 GHz, a > 5x increase was estimated indicating strains on the order of 4E-4 within the nanostructure. Thus, the ability to reproducibly realize strained SiVs through integration of strained thin films with nanostructures was verified.

[0035] Referring now to FIG.3, FIG.3D shows a histogram of all observed SiV transition locations before and after SiN deposition, showing a significant increase in the distribution of transition locations upon deposition of nitride, which is indicative of strain. FIG.3E shows the measured ∆GSS for a subset of SiVs before and after the deposition of SiN, showing a large increase in ∆GSS upon the deposition of SiN as desired. FIG.3F shows the average ∆GSSand the standard error of the mean for the distributions of measured SiVs before and after SiN deposition.

[0036] To better understand the potential benefits of thin film induced static strain for SiVs, the measured experimental results were combined with modeling to extrapolate the high-temperature performance of the SiVs in the nanostructures. As a first step, distributions for the ∆GSSof the SiVs in the cantilever were extrapolated before and after deposition ofHCU-06525 HU 9477 the SiN stressor based on the experimental results. For the case of the SiVs prior to SiN deposition, since the strain experienced by the SiV may be dominated by random fabrication- induced strain each component of the strain tensor experienced by the SiV was modeled as an independent normally distributed random variable with a mean of zero and a standard deviation σunstrained. From this random tensor distribution, the expected distribution of ∆GSSwas computed, such as what is shown in FIG.4A. To fit this to the experimental results, σunstrained was variedso that the mean of the simulated ∆GSSdistribution matched the mean of the measured distribution, yielding σunstrained= 1.9E − 5. As validation of the model, the measured standard deviation of the ∆GSSdistribution of 68 GHz closely matches the simulated standard deviation of 52 GHz.

[0037] Referring now to FIG.4, FIG.4A shows a modeled probability density function for ∆GSSof the SiVs in the cantilever before (curve that has a high probability of low ∆GSS) and after (curve that has a low probability of low ∆GSS) deposition of SiN, showing a significant increase in probability of larger ∆GSS splittings in the SiN case.

[0038] For the case of post-SiN deposition, it was assumed that the strain profile of the cantilever was dominated by the SiN-induced strain and thus was accurately captured by the FEM numerical model. In addition, a random distribution of SiV positions given by the combination of the straggle of the Si atom upon ion implantation (estimated using Stopping-Range-in-Matter simulations) and the dimensions of the mask aperture (see SI) was assumed. A random sampling of strains experienced by the SiV was then polled based on this random position distribution and the FEM simulation. From this strain distribution, the resulting SiV ∆GSSdistribution was then computed for the different SiV orientations, such as what is shown in FIG.4B. In order to fit this to the experimental results, the initial intrinsic stress of the SiN thin film in the FEM simulation was scaled so that the mean of the simulated ∆GSSdistribution matched the measured mean ∆GSSin the nanostructures. This yielded an equivalent thin film stress of 700 MPa of the SiN thin film. This stress may be likely a combination of the intrinsic stress of the SiN and the thermally induced stress due to its differing thermal expansion coefficient from diamond. A close correspondence between the measured standard deviation of the ∆GSSdistribution of 295 GHz and the simulated standard deviation of 249 GHz was again observed, providing validation of the approach. As expected, the modeled distribution of ∆GSSwith SiN had a significantly higher proportion of SiVs with a large ∆GSSthan without SiN.HCU-06525 HU 9477

[0039] Referring now to FIG.4, FIG.4B shows the estimated operational temperature (Top) of an SiV with a given ∆GSSwithout degradation of coherence properties, demonstrating that an increased ∆GSSsignificantly enhances an SiV’s operational temperature.

[0040] Finally, based on the modeled enhancement in ∆GSS, the improvement in the high-temperature coherence properties of the strained SiVs was estimated. The analysis was based on previous results in which a strained SiV with a ground state splitting of ∆GSS,0= 554 GHz showed no phonon-induced degradation of the spin coherence properties (with T 2 > 300µs) up to a temperature of T0= 1.5K. The rate of excitation of the SiV electron from the lower branch of the ground state manifold to the upper branch, which is the primary phonon-induced dephasing pathway, may be given by γup(∆GSS, T ) = (∆GSS)3nth(∆GSS, T ) where T is the temperature of the SiV and nthis the proportion of thermal occupation of the excited branch, which is given by the Boltzmann distribution. Given the previous results, γup(∆GSS,0, T0) may be sufficiently suppressed by the SiV’s ∆GSS,0such that it negligibly impacts the coherence. From this the necessary ∆GSSfor an SiV to be operated at an arbitrary temperature Topwith an equivalent suppression of phonon-induced decoherence, γup(∆GSS, Top) = γup(∆GSS,0, T0) and thus an equivalent suppression of phonon-induced decoherence may be extrapolated, such as in FIG.4B. By combining this with the modeled ∆GSSdistributions, the probability of finding an SiV within the device which is operable up to a given temperature without phonon-induced decoherence may be estimated, such as in FIG.4C. It was observed that due to the presence of the SiN on the cantilever, a majority of SiVs can be operated beyond 1.5 K. Beyond that, a significant portion (> 20%) can be operated beyond 2K. In comparison, the probability of finding an SiV that is sufficiently strained to be operated at these temperatures prior to the deposition of SiN in the measured samples may be negligible, highlighting the key role the stressor plays. This indicates that through utilization of this strained thin film, SiVs with sufficient strain to be operated at elevated temperatures beyond 1K may be reproducibly created, which substantially relaxes the cryogenic requirements of the platform thereby significantly enhancing its scalability, as compared to conventional platforms and / or techniques.

[0041] Referring now to FIG.4, FIG.4C shows the probability of finding an SiV with an operational temperature above a given temperature T, before (bottom curve) and after (top curve) SiN deposition. After SiN deposition, there is a significant enhancement in the probability of finding an SiV operational at 1.5K and beyond, thus highlighting that sufficientHCU-06525 HU 9477 strain is generated in the nanostructure by the thin film to enhance coherence properties at elevated temperatures.

[0042] In conclusion, a new technique has been demonstrated herein to reproducibly fabricate strained color centers through combining nanostructures with strained SiN thin films. Through utilizing this technique with SiVs in diamond cantilevers, a significant deterministic straining of SiVs with strains on the order of 4E-4and an an average ∆GSSof the emitter of 608 GHz was observed. Based on the observed strains, it is expected that the majority of SiVs within this sample can operated at 1.5K and over 20% at 2K without any significant phonon-induced degradation of coherence properties. These results thus pave the way towards ensuring the scalability of the state-of-the-art performance achieved with SiV based spin-photon interfaces to realize true large-scale color-center based quantum photonic systems. Future work may probe the coherence properties of these strained SiVs at 1.5K and beyond to demonstrate the benefit of strain, further maximize the strain in the nanostructure through further process optimizations, and explore integration of stressed thin films with other diamond nanostructures, namely nanophotnoic cavities, to realize high-yield high- operation temperature spin-photon interfaces. Beyond SiVs, the relative simplicity of the technique and ease of compatibility of deposition of SiN thin films may ensure that this same technique can be applied to other color centers in both diamond and other material platforms to create a variety of different reproducibly strained defects.

[0043] A structure, such as one shown and described with reference to one or more of FIG.1B, FIG.2A, FIG.2B, FIG.2C, and FIG.3A, may include a waveguide layer and an intrinsically stressed thin film. The waveguide layer may include a first material. The intrinsically stressed thin film may include a second material. The intrinsically stressed thin film may be disposed on the waveguide layer, thereby inducing a strain in the waveguide layer. The first material may include at least one color center having a pair of energy levels having an optical energy separation. The optical energy separation of the pair of energy levels of the at least one color center may be determined by the induced strain.

[0044] It should be noted that although a waveguide layer, which includes a diamond material, and which is included in a structure, is referred to in various embodiments and experiments described herein, the waveguide layer may instead or additionally include other materials such as silicon nitride, silicon, and / or the like. In addition, it should be noted that although an intrinsically stressed thin film, which includes a silicon nitride (SiN) material, and which is included in the structure, is referred to in various embodiments and experimentsHCU-06525 HU 9477 described herein, the intrinsically stressed thin film may instead or additionally include other materials such as hafnium oxide, aluminum nitride, aluminum oxide, silicon oxide, magnesium oxide, magnesium fluoride, and / or the like. A silicon vacancy color center included in a waveguide layer, which includes a diamond material, is referred to in various embodiments and experiments making use of the structure described herein. However, such a color center may instead or additionally be a nitrogen vacancy, a tin vacancy, a germanium vacancy, and / or the like. In addition, when a silicon carbide (SiC) material is used instead of the diamond material, the color center may instead or additionally be a silicon vacancy, a neutral vacancy, and / or the like. In addition, when a silicon material is used instead of the diamond material, the color center may instead or additionally be a T-center, a G-center, and / or the like. In various embodiments, the structure may have a longitudinal dimension and a cross-sectional dimension. In various embodiments, the structure may include a plurality of color centers disposed in the first material along the longitudinal dimension. In various embodiments, the at least one color center may have an optical transition at a characteristic wavelength, and the cross-sectional dimension may be less than or equal to the characteristic wavelength. In various embodiments, the structure may be configured to guide an optical electromagnetic wave along the longitudinal dimension, and the optical electromagnetic wave may be confined to the waveguide layer. In various embodiments, the structure may have a first terminus and a second terminus separated by the longitudinal dimension, and a device including at least one structure may further include a substrate, wherein the first terminus is attached to the substrate. In various embodiments, the device may include multiple structures. In various embodiments, the substrate may include the first material.

[0045] Referring now to FIG.5, method 500 of operating a quantum gate, at step 502, values for a set of parameters of a microwave pulse are selected. The parameters are selected from a phase, a frequency, an intensity, and a pulse duration.

[0046] With continued reference to FIG.5, method 500 includes, at step 504, the microwave pulse is applied to a structure. The structure includes a waveguide layer and an intrinsically stressed thin film. The waveguide layer includes a first material. The intrinsically stressed thin film includes a second material. The intrinsically stressed thin film is disposed on the waveguide layer, thereby inducing a strain in the waveguide layer. The first material includes at least one color center having a pair of quantum states having a microwave energy separation. The microwave energy separation of the pair of quantumHCU-06525 HU 9477 states of the at least one color center is determined by the induced strain, thereby inducing the at least one color center to transition between the pair of quantum states.

[0047] Exemplary Single-Qubit Gate Implementation

[0048] In various embodiments, a SiV spin is coherently controlled using amplitude and phase controlled microwave pulses generated by a Hittite signal generator (HMC-T2220). A target pulse sequence is loaded onto an arbitrary waveform generator (Tektronix AWG 7122B), which uses a digital channel to control a fast, high-extinction MW-switch (Custom Microwave Components, CMCS0947A-C2), and the analog channels adjust the amplitude and phase via an IQ-mixer (Marki, MMIQ-0416LSM). The resulting pulse train is subsequently amplified (Minicircuits, ZVE-3W-183+) to roughly 3W of power, and sent via a coaxial cable into a dilution refrigerator. At each cryogenic range, a 0 dB attenuator is used to thermalize the inner and outer conductors of the coaxial line while minimizing microwave dissipation. The signal is then launched into a coplanar waveguide on a custom-built circuit board (Rogers4003C, Bay Area Circuits) so it can be wire-bonded directly to the chip. The qubit frequency (^↓↑) is measured by its optically detected magnetic resonance spectrum (ODMR). ODMR is observed from 2 GHz to 20 GHz (corresponding to fields from 0:1T to 0:7 T), implying that microwave control of SiV centers in this configuration is possible at a wide variety of external field magnitudes. This allows tuning the field to optimize other constraints, such as for resolving spin transitions and identifying ancillary nuclear spins.

[0049] Once the qubit frequency has been determined for a given field, single-qubit gates are tuned up by measuring Rabi oscillations. The frequency of these oscillations scales with the applied microwave powerand determines the single-qubit gate times. One can perform ^-pulses (^^^) in under 12 ns, corresponding to a Rabi frequency exceeding 80MHz. This coherent control is used to implement pulse-error correcting dynamical decoupling ^ sequences, either CPMG-N sequences of the form= ^ −^^^^ − ^ or ^^8 − ! sequences of the form ^ − ^^^ ^^ ^ ^^ ^^^ − ^. Sweeping theinter-pulse delay ^ measures the coherence time "^of the vacancy.

[0050] Exemplary Entanglement Implementation

[0051] Referring to Fig.6, an experimental setup and protocol for generating long- distance entanglement between two color centers is illustrated. Each color center is provided in a structure as described herein. The two structures are located in two independent low- temperature confocal microscope setups separated by 3 meters. The color centers can be individually excited resonantly by a red laser and off-resonantly by a green laser. TheHCU-06525 HU 9477 emission (dashed arrows) is spectrally separated into an off-resonant part (phonon side band, PSB) and a resonant part (zero-phonon line, ZPL). The PSB emission is used for independent single-shot readout of the spin qubits. The ZPL photons from the two color centers are overlapped on a fiber-coupled beamsplitter.

[0052] Microwave pulses for spin control are applied via on-chip microwave striplines.An applied magnetic field of 17.5 G splits the #$ = ±1 levels in energy. The opticalfrequencies of one color center are tuned by a d.c. electric field applied to the gate electrodes.

[0053] To generate and detect remote entanglement, the following sequence is run. First, both color centers are independently prepared into the correct charge state and brought into optical resonance. Then the entangling protocol depicted in Fig.7 is applied using a 600 ns delay between the two optical excitation rounds. The protocol is repeated before the resonance preparation in order to maximize the attempt rate while minimizing the probability of color center ionization. A fast logic circuit monitors the photon counts in real time and triggers single-shot qubit readout on each setup whenever entanglement is heralded, i.e. whenever a single photon is detected in each round of the protocol. The readout projectseach qubit onto the '|↑^, |↓^+ states (, basis), or on the '|↑^ + / −|↓^, |↑^ − / +|↓^+ states (^ or−^ basis). The latter two are achieved by first rotating the qubit by ^ / 2 using a microwave pulse before readout. By correlating the resulting single-qubit readout outcomes the generation of the desired entangled states is verified. To obtain reliable estimates of the two- qubit state probabilities, the raw data are corrected with a maximum-likelihood method for local readout infidelities. These readout errors are known accurately from regular calibrations performed during the experiment.

[0054] Fig.7 shows the exemplary entanglement protocol referenced above. The pulse sequence is applied simultaneously to both color centers. Both color centers are initiallyprepared in a superposition 1 / √2^|↑^ + |↓^^. A short 2 ns spin-selective resonant laser pulsecreates spin-photon entanglement 1 / √2^|↑ 1^ + |↓ 0^^. The photons are overlapped on thebeamsplitter and detected in the two output ports. Both spins are then flipped, and the color centers are excited a second time. The detection of one photon in each excitation round heralds the entanglement and triggers individual spin readout.

[0055] Referring now to FIG.8, a schematic of an example of a classical computing node is shown. Computing node 10 is only one example of a suitable computing node and is not intended to suggest any limitation as to the scope of use or functionality of embodiments described herein. Regardless, computing node 10 is capable of being implemented and / orHCU-06525 HU 9477 performing any of the functionality set forth hereinabove, such as performing method 100 for example.

[0056] In computing node 10 there is a computer system / server 12, which is operational with numerous other general purpose or special purpose computing system environments or configurations. Examples of well-known computing systems, environments, and / or configurations that may be suitable for use with computer system / server 12 include, but are not limited to, personal computer systems, server computer systems, thin clients, thick clients, handheld or laptop devices, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics, network PCs, minicomputer systems, mainframe computer systems, and distributed cloud computing environments that include any of the above systems or devices, and the like.

[0057] Computer system / server 12 may be described in the general context of computer system-executable instructions, such as program modules, being executed by a computer system. Generally, program modules may include routines, programs, objects, components, logic, data structures, and so on that perform particular tasks or implement particular abstract data types. Computer system / server 12 may be practiced in distributed cloud computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed cloud computing environment, program modules may be located in both local and remote computer system storage media including memory storage devices.

[0058] As shown in FIG.8, computer system / server 12 in computing node 10 is shown in the form of a general-purpose computing device. The components of computer system / server 12 may include, but are not limited to, one or more processors or processing units 16, a system memory 28, and a bus 18 that couples various system components including system memory 28 to processor 16.

[0059] Bus 18 represents one or more of any of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, and a processor or local bus using any of a variety of bus architectures. By way of example, and not limitation, such architectures include Industry Standard Architecture (ISA) bus, Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA) bus, Video Electronics Standards Association (VESA) local bus, Peripheral Component Interconnect (PCI) bus, Peripheral Component Interconnect Express (PCIe), and Advanced Microcontroller Bus Architecture (AMBA).HCU-06525 HU 9477

[0060] Computer system / server 12 typically includes a variety of computer system readable media. Such media may be any available media that is accessible by computer system / server 12, and it includes both volatile and non-volatile media, removable and non- removable media.

[0061] System memory 28 can include computer system readable media in the form of volatile memory, such as random access memory (RAM) 30 and / or cache memory 32. Computer system / server 12 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, storage system 34 can be provided for reading from and writing to a non-removable, non-volatile magnetic media (not shown and typically called a "hard drive"). Although not shown, a magnetic disk drive for reading from and writing to a removable, non-volatile magnetic disk (e.g., a "floppy disk"), and an optical disk drive for reading from or writing to a removable, non-volatile optical disk such as a CD-ROM, DVD-ROM or other optical media can be provided. In such instances, each can be connected to bus 18 by one or more data media interfaces. As will be further depicted and described below, memory 28 may include at least one program product having a set (e.g., at least one) of program modules that are configured to carry out the functions of embodiments of the disclosure.

[0062] Program / utility 40, having a set (at least one) of program modules 42, may be stored in memory 28 by way of example, and not limitation, as well as an operating system, one or more application programs, other program modules, and program data. Each of the operating system, one or more application programs, other program modules, and program data or some combination thereof, may include an implementation of a networking environment. Program modules 42 generally carry out the functions and / or methodologies of embodiments described herein.

[0063] Computer system / server 12 may also communicate with one or more external devices 14 such as a keyboard, a pointing device, a display 24, etc.; one or more devices that enable a user to interact with computer system / server 12; and / or any devices (e.g., network card, modem, etc.) that enable computer system / server 12 to communicate with one or more other computing devices. Such communication can occur via Input / Output (I / O) interfaces 22. Still yet, computer system / server 12 can communicate with one or more networks such as a local area network (LAN), a general wide area network (WAN), and / or a public network (e.g., the Internet) via network adapter 20. As depicted, network adapter 20 communicates with the other components of computer system / server 12 via bus 18. It should be understoodHCU-06525 HU 9477 that although not shown, other hardware and / or software components could be used in conjunction with computer system / server 12. Examples, include, but are not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data archival storage systems, etc.

[0064] In various embodiments, one or more core (not pictured) is coupled to bus 18. In such embodiments, a core may receive data from or write data to memory 28 via bus 18. In various embodiments, a core may include one or more local controller, memory, or clock, for example as set forth elsewhere herein.

[0065] The present disclosure may be embodied as a device, a system, a method, and / or a computer program product. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present disclosure.

[0066] The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non- exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.

[0067] Computer readable program instructions described herein can be downloaded to respective computing / processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and / or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers,HCU-06525 HU 9477 firewalls, switches, gateway computers and / or edge servers. A network adapter card or network interface in each computing / processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing / processing device.

[0068] Computer readable program instructions for carrying out operations of the present disclosure may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like, and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The computer readable program instructions may execute entirely on the user’s computer, partly on the user’s computer, as a stand-alone software package, partly on the user’s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user’s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present disclosure.

[0069] Aspects of the present disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer readable program instructions.

[0070] These computer readable program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means forHCU-06525 HU 9477 implementing the functions / acts specified in the flowchart and / or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and / or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function / act specified in the flowchart and / or block diagram block or blocks.

[0071] The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0072] The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flowchart illustration, and combinations of blocks in the block diagrams and / or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions.

[0073] The descriptions of the various embodiments of the present disclosure have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found inHCU-06525 HU 9477 the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.

[0074] While the disclosed subject matter is described herein in terms of certain preferred embodiments, those skilled in the art will recognize that various modifications and improvements may be made to the disclosed subject matter without departing from the scope thereof. Moreover, although individual features of one embodiment of the disclosed subject matter may be discussed herein or shown in the drawings of the one embodiment and not in other embodiments, it should be apparent that individual features of one embodiment may be combined with one or more features of another embodiment or features from a plurality of embodiments.

[0075] In addition to the specific embodiments claimed below, the disclosed subject matter is also directed to other embodiments having any other possible combination of the dependent features claimed below and those disclosed above. As such, the particular features presented in the dependent claims and disclosed above can be combined with each other in other manners within the scope of the disclosed subject matter such that the disclosed subject matter should be recognized as also specifically directed to other embodiments having any other possible combinations. Thus, the foregoing description of specific embodiments of the disclosed subject matter has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosed subject matter to those embodiments disclosed.

[0076] It will be apparent to those skilled in the art that various modifications and variations can be made in the method and system of the disclosed subject matter without departing from the spirit or scope of the disclosed subject matter. Thus, it is intended that the disclosed subject matter include modifications and variations that are within the scope of the appended claims and their equivalents.

Claims

HCU-06525 HU 9477 CLAIMS What is claimed is:

1. A device, comprising at least one structure, the structure comprising: a waveguide layer comprising a first material; and an intrinsically stressed thin film comprising a second material, the intrinsically stressed thin film being disposed on the waveguide layer, thereby inducing a strain in the waveguide layer, wherein the first material comprises at least one color center having a pair of energy levels, the pair of energy levels has an optical energy separation, and the optical energy separation of the pair of energy levels being determined by the induced strain.

2. The device of Claim 1, wherein the first material is diamond, silicon nitride, or silicon.

3. The device of Claim 1, wherein the second material is silicon nitride, hafnium oxide, aluminum nitride, aluminum oxide, silicon oxide, magnesium oxide, or magnesium fluoride.

4. The device of Claim 1, wherein the first material is diamond and the at least one color center is selected from a silicon vacancy, nitrogen vacancy, tin vacancy, or germanium vacancy.

5. The device of Claim 1, wherein the first material is silicon carbide (SiC), and the at least one color center is selected from a silicon vacancy or neutral vacancy.

6. The device of Claim 1, wherein the first material is silicon, and the at least one color center is selected from a T-center or a G-center.

7. The device of Claim 1, the structure having a longitudinal dimension and a cross- sectional dimension.HCU-06525 HU 9477 8. The device of Claim 7, wherein the structure comprises a plurality of color centers disposed in the first material along the longitudinal dimension.

9. The device of Claim 7, wherein the at least one color center has an optical transition at a characteristic wavelength, and wherein the cross-sectional dimension is less than or equal to the characteristic wavelength.

10. The device of Claim 7, the structure being configured to guide an optical electromagnetic wave along the longitudinal dimension, the optical electromagnetic wave being confined to the waveguide layer.

11. The device of Claim 7, the structure having a first terminus and a second terminus separated by the longitudinal dimension, the device further comprising a substrate, wherein the first terminus is attached to the substrate.

12. The device of Claim 11, comprising a plurality of the structures.

13. The device of Claims 11, wherein the substrate comprises the first material.

14. A quantum entanglement system, comprising: a first structure and a second structure, each structure comprising: a waveguide layer comprising a first material; and an intrinsically stressed thin film comprising a second material, the intrinsically stressed thin film being disposed on the waveguide layer, and thereby inducing a strain in the waveguide layer, wherein the first material comprises at least one color center having a pair of quantum states, the pair of quantum states having an optical energy separation, the optical energy separation of the pair of quantum states being determined by the induced strain, and the at least one color center having an optical transition between the quantum states of the pair at a characteristic wavelength;HCU-06525 HU 9477 a photon source configured to direct an excitation pulse into the waveguide layer of the first structure and the waveguide layer of the second structure, thereby causing the optical transition in the at least one of the color center of the first structure or the second structure and causing the at least one color center to emit a photon; and a photon detector configured to detect the photon emitted by the at least one color center, thereby producing an entanglement between the at least one color center in the first structure and the at least one color center in the second structure.

15. A system, comprising: a structure, comprising: a waveguide layer, comprising a first material; and an intrinsically stressed thin film comprising a second material, the intrinsically stressed thin film being disposed on the waveguide layer, thereby inducing a strain in the waveguide layer, wherein the first material comprises at least one color center having a pair of quantum states, the pair of quantum states having a microwave energy separation, and the microwave energy separation of the pair of quantum states being determined by the induced strain; and a microwave source configured to apply a microwave pulse to the at least one color center, the microwave pulse having a frequency corresponding to the microwave energy separation, thereby inducing the at least one optical center to transition between the pair of quantum states.

16. A method of operating a quantum gate, comprising: selecting values for a set of parameters of a microwave pulse, the set of parameters selected from a phase, a frequency, an intensity, and a pulse duration; and applying the microwave pulse to a structure, the structure comprising: a waveguide layer comprising a first material; and an intrinsically stressed thin film comprising a second material, the intrinsically stressed thin film being disposed on the waveguide layer, thereby inducing a strain in the waveguide layer, whereinHCU-06525 HU 9477 the first material comprises at least one color center having a pair of quantum states, the pair of quantum states having a microwave energy separation, the microwave energy separation being determined by the induced strain, the microwave pulse inducing the at least one color center to transition between the pair of quantum states.

17. A quantum computing device, comprising: a first structure and a second structure, each structure comprising: a waveguide layer comprising a first material; and an intrinsically stressed thin film comprising a second material, the intrinsically stressed thin film being disposed on the waveguide layer, and thereby inducing a strain in the waveguide layer, wherein the first material comprises at least one color center having a first pair of quantum states and a second pair of quantum states, the first pair of quantum states having an optical energy separation, the second pair of quantum states having a microwave energy separation, the optical energy separation and the microwave energy separation being determined by the induced strain, the at least one color center having an optical transition between the first pair of quantum states at a first characteristic wavelength, and a microwave transition between the second pair of quantum states at a second characteristic wavelength; a photon source configured to direct an excitation pulse into the waveguide layer of the first structure and into the waveguide layer of the second structure, thereby causing the optical transition in at least one of the color center of the first structure or of the second structure and causing the at least one color center to emit a photon; a photon detector configured to detect the photon emitted by the at least one color center; andHCU-06525 HU 9477 a microwave source configured to apply a microwave pulse to the at least one color center, the microwave pulse having a frequency corresponding to the microwave energy separation, thereby causing the microwave transition in at least one of the color center of the first structure or the second structure.