Quantum light source with double optical cavities

Abstract

A quantum light source includes a quantum emitter located within both a bullseye cavity and a Fabry-Perot cavity. The Fabry-Perot cavity is formed by a first mirror and a second mirror facing each other to define an optical axis extending therebetween. The bullseye cavity is located in a plane perpendicular to the optical axis and between the first mirror and the second mirror. The quantum emitter may be a quantum dot, a point defect in a crystal (e.g., a nitrogen vacancy center in diamond), an atom, or another type of quantum system. The spontaneous emission from the quantum emitter is strongly coupled into the mode of the Fabry-Perot cavity, while the bull's eye cavity uses destructive interference to prevent emission of photons in a direction transverse to the axis of the Fabry-Perot cavity. Light leaks from the Fabry-Perot cavity into a well defined traveling wave mode that can be effectively coupled to an optical fiber.

Description

[0001] Related Applications

[0002] This application claims priority to U.S. Provisional Patent Application No. 63 / 364,231, filed on May 5, 2022, the entirety of which is incorporated herein by reference.

[0003] STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0004] This invention was made with government support under Grant No. 70NANB18H006 awarded by the National Institute of Standards and Technology (NIST). The government has certain rights in this invention. Background Art

[0005] Single-photon sources that generate individual photons on demand are used in many quantum technologies, such as quantum random number generation, quantum key distribution, and quantum metrology. Summary of the invention

[0006] The quantum light source includes a bullseye cavity, a Fabry-Perot cavity, and a quantum emitter (or quantum emitter) located in both the bullseye cavity and the Fabry-Perot cavity. The Fabry-Perot cavity is formed by a first mirror (or a reflector or mirror) and a second mirror, which face each other to define an optical axis extending therebetween. The bullseye cavity is formed by a central disk in which the quantum emitter is embedded. The bullseye cavity also includes a series of concentric rings around the central disk, which have alternating refractive indices. The bullseye cavity is located in a plane perpendicular to the optical axis and between the first mirror and the second mirror. The quantum emitter can be a quantum dot (e.g., InAs, GaAs, etc.), a point defect in a crystal (e.g., a nitrogen vacancy center in diamond, a silicon vacancy center in diamond, a carbon anti-vacancy in silicon carbide, etc.), a trapped atom or molecule, a trapped ion, or another type of quantum system that decays spontaneously when excited (e.g., optically pumped or electrically pumped).

[0007] The quantum emitter is positioned so that its spontaneous emission is strongly coupled to the mode of the Fabry-Perot cavity. The bull's-eye cavity uses destructive interference to suppress the spontaneous emission from the quantum emitter in the direction transverse to the axis of the Fabry-Perot cavity. That is, the bull's-eye cavity enhances the spontaneous emission in the direction along the axis of the Fabry-Perot cavity, thereby increasing the coupling into the mode of the Fabry-Perot cavity. The light in this mode leaks out of the Fabry-Perot cavity via the first mirror or the second mirror and enters a well-defined traveling wave mode with a Gaussian transverse intensity profile, which can be effectively coupled to the optical fiber. Since the quantum emitter is located inside the cavity, the spontaneous decay rate of the quantum emitter is increased due to the Purcell effect (compared to its spontaneous decay rate in free space).

[0008] Advantageously, the quantum light source of the present embodiment is more efficient than prior art quantum light sources that use only Fabry-Perot cavities or bull's-eye cavities. The efficiency of a light source quantifies how much of the spontaneous emission from a quantum emitter can be used for current applications. This efficiency includes not only the portion of spontaneous emission that is collected (rather than lost to the surrounding environment), but also the loss from coupling the spontaneous emission into the optical fiber, the loss from transmission along the optical fiber, and the loss from coupling the light out of the optical fiber. One factor that reduces the efficiency of a light source is the fact that quantum emitters typically emit uniformly in free space. In this case, it is challenging to collect all spontaneous emission and redirect it to one direction using conventional optical devices (such as lenses and mirrors). An alternative method is to change the emission distribution by placing a quantum emitter inside an optical cavity (which preferentially couples spontaneous emission into the mode of the cavity).

[0009] The higher efficiency that can be achieved using this embodiment will improve many applications using quantum light. One such application is quantum random number generation. In this case, the quantum light source of this embodiment can be operated as a single photon source. Due to the combination of the bull's eye cavity and the Fabry-Perot cavity, this single photon source can achieve an efficiency of more than 75%. In contrast, the highest efficiency demonstrated by the prior art single photon source is only 57%. As described in more detail below, the higher efficiency that can be achieved using this embodiment exceeds the threshold for generating private randomness with low deviation through quantum routing and the laws of quantum mechanics (such as superposition and entanglement).

[0010] In addition to single photon sources, the quantum light source of the present embodiment can also be configured to generate other types of quantum light, such as n-photon states (i.e., Fock states of n photons), entangled photons (e.g., entangled pairs), and cluster states. Therefore, other applications that can benefit from the present embodiment include, but are not limited to, quantum key distribution and other forms of quantum communication, sensing (e.g., magnetometry), and cluster state quantum computing. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 is a side cross-sectional view of a quantum light source in an embodiment.

[0012] Figure 2 yes Figure 1 A perspective view of the bullseye chamber of a quantum light source.

[0013] Figure 3 Pictured Figure 1 Operation of quantum light sources.

[0014] Figure 4 is a side cross-sectional view of a quantum light source in an embodiment, the quantum light source and Figure 1 and Figure 3 The quantum light source is similar to that of , except that the top and bottom substrates are directly bonded to each other.

[0015] Figure 5 is one of the implementation schemes that can be used with Figure 1 , Figure 3 and Figure 4 A side cross-sectional view of the heterostructure used in conjunction with a quantum light source.

[0016] Fig. 6A is from Figure 1 A plot of the Purcell factor versus wavelength obtained from numerical simulations of a quantum light source.

[0017] Figure 6B is the square of the absolute value of the electric field of the cavity mode with a Purcell factor exceeding five (|E| 2 )’s picture.

[0018] Figure 6C It passes through Figure 1 The transmittance of the top mirror of the quantum light source relative to Figure 2 Diagram of the number of grooves of the bullseye cavity.

[0019] Fig.6D is a plot of the lateral intensity distribution of the output mode just above the top mirror.

[0020] Figure 7is the photoluminescence spectrum of a quantum dot measured for different voltages applied across the Schottky barrier.

[0021] Figure 8 Two measured photoluminescence spectra of an ensemble of quantum dots are shown, illustrating the improved photon collection when the ensemble is located inside a bullseye cavity. DETAILED DESCRIPTION

[0022] Figure 1 1 is a side cross-sectional view of a quantum light source 100. The quantum light source 100 includes a quantum emitter 106 located in a composite optical cavity formed by a spatially overlapping bullseye cavity 104 and a Fabry-Perot cavity 102. The quantum emitter 106 is located on or near an optical axis 110 that is parallel to the z-axis of a coordinate system 120. For clarity herein, the terms "axial" and "longitudinal" refer to directions parallel to the optical axis 110, while the terms "radial" and "lateral" refer to directions perpendicular to the optical axis 110. The Fabry-Perot cavity 102 is also referred to as a "top-down" cavity.

[0023] The Fabry-Perot cavity 102 is formed by a top mirror 114 and a bottom mirror 116 facing each other to form a longitudinal mode therebetween. Figure 1 , the top mirror 114 has a reflective front face 146 formed on a top substrate 148. Similarly, the bottom mirror 116 has a reflective front face 136 formed on a bottom substrate 138. Thus, the Fabry-Perot cavity 102 is formed by the reflective front faces 136 and 146. The reflective front faces 136 and 146 are axially separated by a cavity length L. When the cavity length L is equal to an integer multiple of λ / 2, light of wavelength λ can excite a longitudinal mode. The optical axis 110 extends between the lateral centers of the reflective faces 136 and 146.

[0024] Figure 2 1 is a perspective view of the bull's-eye cavity 104 illustrating the structure of the bull's-eye cavity 104 in more detail. The quantum emitter 106 is embedded in or on a central disk 122 formed of a first material having a first refractive index n1. The central disk 122 is centered on the optical axis 110. Surrounding the central disk 122 is an alternating sequence of rings concentric with the central disk 122. This alternating sequence includes a first subset of rings 124 formed of the first material and a second subset of rings 128 formed of a second material having a second refractive index n2 different from the first refractive index n1. The radially innermost ring of the alternating sequence is formed of the second material (i.e., one of the rings 128). Figure 1 and 2 For the sake of clarity, not all rings 124 and 128 are labeled. Also for the sake of clarity, Figure 2 The quantum emitter 106 is not shown.

[0025] Thus, the bull's-eye cavity 104 lies flat in a plane that is perpendicular to the optical axis 110. The bull's-eye cavity 104 is also located within the Fabry-Perot cavity 102 because it is axially located between the reflective front faces 136 and 146. The radial widths of the rings 124 and 128 are selected based on the refractive indices n1 and n2 so that the bull's-eye cavity 104 suppresses spontaneous emission from the quantum emitter 106 in all radial directions around the quantum emitter 106. Therefore, using the bull's-eye cavity 104, spontaneous emission from the quantum emitter 106 is preferably emitted along the optical axis 110. The bottom mirror 116 reflects spontaneous emission emitted downward (i.e., in the -z direction). Using this reflection, all spontaneous emission from the quantum emitter 106 propagates vertically upward, as shown in FIG. Figure 1 Indicated by the emission direction 126.

[0026] In free space (i.e., in the absence of the bull's-eye cavity 104 and the Fabry-Perot cavity 102), the quantum emitter 106 can spontaneously emit in all directions. In this case, spontaneous emission emitted radially outward (i.e., in a direction primarily perpendicular to the optical axis 110) may be lost compared to spontaneous emission emitted axially (i.e., in a direction primarily along the optical axis 110). Therefore, the bull's-eye cavity 104 reduces wasted light, thereby increasing the efficiency of collecting light and thereby using it for the current application.

[0027] Figure 3 The operation of the quantum light source 100 is illustrated. With a quantum emitter 106 located within a Fabry-Perot cavity 102, when the wavelength λ of the spontaneous emission from the quantum emitter 106 is resonant with the Fabry-Perot cavity 102, the spontaneous emission is strongly coupled to the longitudinal modes of the Fabry-Perot cavity 102. The bulls-eye cavity 104 increases the coupling to the longitudinal modes, thereby enhancing the probability that the spontaneously emitted photons excite the longitudinal modes.

[0028] Due to the finite Q or finesse of the Fabry-Perot cavity 102, the energy in the longitudinal mode will eventually leak out of the Fabry-Perot cavity 102. Figure 1, the leakage light 326 is transmitted through the top mirror 114. However, light may also leak through the bottom mirror 116. It is assumed that the intracavity losses due to diffraction (e.g., surface scattering of the reflective front surfaces 136 and 146) and bulk absorption (e.g., the center disk 122) are minimal compared to the leakage through the top mirror 114 (or the bottom mirror 116). In an embodiment, the reflectivity of the bottom mirror 116 (i.e., the reflective surface 136) is higher than the reflectivity of the top mirror 114 (i.e., the reflective surface 146), so that the light leaking out of the Fabry-Perot cavity 102 is preferentially transmitted through the top mirror 114 rather than the bottom mirror 116. The back surface 144 of the top mirror 114 may be anti-reflection coated to enhance the transmission of the leakage light 326 through the top substrate 148. For the same reason, the back surface 134 of the bottom mirror 116 may also be anti-reflection coated.

[0029] The leakage light 326 is a traveling wave that propagates vertically upward away from the Fabry-Perot cavity 102. The leakage light 326 has a transverse field distribution determined by the excitation mode of the Fabry-Perot cavity 102. Specifically, each longitudinal mode of the Fabry-Perot cavity 102 has multiple transverse modes. Herein, it is assumed that only the lowest-order transverse mode is excited. This lowest-order transverse mode has a transverse intensity distribution that is approximately described by a two-dimensional Gaussian distribution (e.g., see Figure 6C As indicated by the mode profile 310, the width w of this Gaussian distribution m The lateral intensity distribution of the leakage light 326 can be expressed as its width w l is equal to the width w of the mode envelope 310 at the top mirror 114 m It is approximated by a Gaussian distribution.

[0030] Thus, the Fabry-Perot cavity 102 not only helps direct the spontaneous emission from the quantum emitter 106 into the vertical direction, but it also spatially filters this spontaneous emission into a collimated Gaussian beam that can be efficiently (i.e., with low loss) coupled into an optical fiber 150, an optical waveguide, another optical cavity, or any other type of optical component. Figure 3 , where lens 152 focuses leakage light 326 into the end face of optical fiber 150. To increase transmission, the end face of optical fiber 150 and the surface of lens 152 may be anti-reflection coated. Figure 3 Lens 152 is shown as a biconvex lens, but lens 152 may alternatively be an aspheric lens, a microscope objective, or other type of lens or lens assembly known in the art.

[0031] exist Figure 1 and Figure 3In the example of FIG. 1 , the bottom mirror 116 and the bullseye cavity 104 form part of a semiconductor heterostructure. Such integration can be used to simplify the manufacture of these components. In this example, the reflective front surface 136 can be a dielectric stack forming a distributed Bragg reflector (see, for example, Figure 5 ). However, the reflective front surface 136 may alternatively be a sub-wavelength reflector (e.g., an optical metasurface), a metallic reflector, a photonic crystal, or another type of reflector or mirror known in the art. Similarly, the reflective front surface 146 of the top mirror 114 may be a dielectric mirror, a sub-wavelength reflector, a photonic crystal, a metallic mirror, or another type of reflector or mirror.

[0032] exist Figure 1 and Figure 3 In the example of , the bottom mirror 116 is planar and the top mirror 114 is concave. The Fabry-Perot cavity 102 can have a semi-confocal geometry, where the top mirror 114 has a radius of curvature R and the cavity length L is approximately equal to R / 2. This geometry ensures that the Fabry-Perot cavity 102 is stable. However, the cavity length L does not have to be exactly equal to R / 2, as long as the Fabry-Perot cavity 102 is stable. The Fabry-Perot cavity 102 can optionally be configured as another type of geometry (e.g., fully confocal, concentric, concave-convex, etc.). In order to prevent losses due to diffraction at the edge of the center disk 122, the center disk 122 can have a width w much larger than the center disk 122. m diameter.

[0033] exist Figure 1 and 3 In the example of , the bull's-eye cavity 104 and the quantum emitter 106 are axially positioned adjacent to the bottom mirror 116. In this case, the bull's-eye cavity 104 and the bottom mirror 116 are in physical contact with each other. In addition, due to the semi-confocal geometry, the bull's-eye cavity 104 and the quantum emitter 106 are located near the waist of the Fabry-Perot cavity 102. However, the bull's-eye cavity 104 and the quantum emitter 106 can be located at other locations in the Fabry-Perot cavity 102 (e.g., near the top mirror 114 or between the mirrors 114 and 116). In these cases, the bull's-eye cavity 104 and the quantum emitter 106 do not need to directly contact the bottom mirror 116.

[0034] The quantum emitter 106 can be any kind of quantum emitter or nonlinear emitter known in the art. In some embodiments, the quantum emitter 106 is a quantum dot. The quantum dot can be a semiconductor quantum dot made of indium arsenide (InAs), indium gallium arsenide (InGaAs), gallium arsenide (GaAs), gallium nitride (GaN) or another semiconductor material. In other embodiments, the quantum emitter 106 is a point defect in the lattice. For example, a point defect can be a nitrogen vacancy (NV) center in diamond, or another color center that can act as a quantum emitter. In other embodiments, the quantum emitter 106 is a trapped neutral atom, a trapped molecule, or a trapped ion (molecule or atom). In these embodiments, the quantum emitter 106 can be trapped (e.g., using an optical dipole trap) inside the Fabry-Perot cavity 102 and the bull's eye cavity 104. In this case, the central disk 122 can be a vacuum. In other embodiments, the quantum emitter 106 is a molecule (e.g., a molecular quantum bit) embedded in the host matrix.

[0035] Figure 4 is a side cross-sectional view of quantum light source 400, which is similar to Figure 1 and Figure 3 The quantum light source 100 of the embodiment of the present invention is different in that the top substrate 148 and the bottom substrate 138 are directly bonded to each other in the region surrounding the composite cavity. Specifically, the top substrate 148 forms a radially distant region 410 surrounding the reflective front face 146. The radially distant region 410 has a bottom surface 414 that can be axially located at or below the reflective front face 146 (i.e., in the -z direction). Similarly, the bottom substrate 138 has a radially distant region 416 surrounding the reflective front face 136 and a bulls-eye cavity 104. The radially distant region 416 has an upper surface 412 that can be axially located at or above the bulls-eye cavity 104 so that it directly contacts the bottom surface 414. In one embodiment, the upper surface 412 and the bottom surface 414 are in direct contact with each other continuously around the composite cavity.

[0036] The upper surface 412 and the bottom surface 414 can be bonded to each other, such as optical contact bonding or anodic bonding. Alternatively, the upper surface 412 and the bottom surface 414 can be bonded to each other using epoxy, solder, or another type of adhesive known in the art. Advantageously, the surfaces 412 and 414 can be bonded together using wafer bonding techniques known in the art. These techniques allow the quantum light source 400 to be manufactured in large quantities.

[0037] With substrates 138 and 148 directly bonded to each other, the cavity length L cannot be adjusted by axially translating mirrors 114 and 116. However, there are other ways to ensure that the spontaneous emission from quantum emitter 106 is resonant with Fabry-Perot cavity 102. For example, when quantum emitter 106 is a quantum dot, the quantum dot can be embedded in an undoped intrinsic semiconductor region of a pin junction. A voltage applied across the junction (e.g., see Figure 4 The voltage source 408 in the embodiment can be used to adjust the wavelength λ of the spontaneous emission. In another example, the front reflective surface 136 is a metal in direct contact with the quantum dots to form a Schottky barrier. The voltage applied across the Schottky barrier can also be used to change the wavelength λ.

[0038] In other embodiments, the wavelength λ of the spontaneous emission is changed via strain or pressure adjustment. Such adjustment can be achieved, for example, using a piezoelectric transducer fixed to the quantum emitter 106 or the central disk 122. In other embodiments, a piezoelectric transducer fixed to or bonded to one or both of the substrates 138 and 148 can be used to slightly change the cavity length L by applying stress to one or both of the mirrors 114 and 116. Without departing from the scope of this article, another method can be used to change the wavelength λ or change the resonant frequency of the Fabry-Perot cavity 102.

[0039] Figure 5 is a side cross-sectional view of a heterostructure 500, wherein the bull's-eye cavity 104 is located above an oblique distributed Bragg reflector (DBR) mirror 512, which in turn is located above a normal DBR mirror 514. The oblique DBR mirror 512 is formed by a stack of layers 522 and 524 having alternating refractive indices. Specifically, layer 522 is formed of a first material having a first refractive index, and layer 524 is formed of a second material having a second refractive index different from the first refractive index. Similarly, the normal DBR mirror 514 is formed by a stack of layers 532 and 534 having alternating refractive indices. Figure 5 In the example of , layer 532 is formed of a first material and layer 534 is formed of a second material. Figure 5 For the sake of clarity, not all layers 522 and 524 are shown. Similarly, not all layers 532 and 534 are shown.

[0040] Each of layers 522 and 524 has a first optical thickness t1, and each of layers 532 and 534 has a second optical thickness t2 that is less than the first optical thickness t1. The greater thickness of layers 522 and 524 compared to layers 532 and 534 means that for spontaneous emission at wavelength λ, tilted DBR mirror 512 will reflect spontaneous emission emitted from quantum emitter 106 at a tilted angle relative to optical axis 110. Such spontaneous emission is Figure 5 In contrast, spontaneous emission emitted from quantum emitter 106 at an angle closer to the normal direction of DBR mirrors 512 and 514 will mostly propagate through tilted DBR mirror 512 to reach normal DBR mirror 514, which will reflect such spontaneous emission. Such spontaneous emission is Figure 5 Identified as normal light 552 in FIG.

[0041] Using multiple DBR mirrors, each customized to reflect light at different incident angles, helps prevent the loss of oblique light 550 emitted by quantum emitter 106, compared to when only one DBR mirror is configured for normal reflection. Thus, heterostructure 500 can help improve the coupling of spontaneous emission out of Fabry-Perot cavity 102. Figure 5 Two DBR mirrors are shown, but the concept can be extended to three or more stacked DBR mirrors. In one embodiment, heterostructure 500 includes a DBR mirror structure formed of layers whose thickness varies continuously along z. In another embodiment, DBR mirrors 512 and 514 are physically separated from bullseye cavity 104, thereby forming two or more different heterostructures.

[0042] Numerical simulation

[0043] To demonstrate the efficiency of this implementation, we used Figure 5 500 pairs of heterostructures Figure 1 A multiphysics simulation of a quantum light source 100 is performed. To simulate a quantum emitter 106, a dipole is placed at the center of the composite cavity. The cavity parameters are adjusted to maximize the transmission of the spontaneous emission emitted from the dipole through the top mirror 114. The following table lists the best values ​​found for various parameters:

[0044]

[0045] For numerical simulations, the planar bottom mirror 116 was modeled as an AlAs / GaAs DBR stack, while the top mirror 114 was modeled as a Ta2O5 / SiO2 DBR stack. To make the bullseye cavity 104 interact more efficiently with horizontally emitted photons, two tilted DBR layers were placed just below the layer containing the dipole (see, for example, Figure 5These tilted DBR layers have a greater periodicity than the DBR layers used as normal bottom mirrors (see Figure 5 Layers 522 and 524 in, relative to layers 532 and 534). Fig. 6A is a plot of Purcell factor versus wavelength, showing cavity modes with Purcell factors exceeding 5 at wavelengths around 970.04 nm. Figure 6B is the absolute value square of the electric field of this particular cavity mode (|E| 2 )’s picture.

[0046] Figure 6C is a graph of the transmission through the top mirror 114 versus the number of grooves of the bulls-eye cavity 104. For 30 grooves, this transmission increases to 0.825, compared to only 0.655 without the bulls-eye cavity 104, or a 17% enhancement. Fig.6D is a graph of the lateral intensity distribution of the output mode just above the top mirror 114. As can be seen, this lateral distribution is close to a Gaussian distribution, which can be effectively coupled to an optical waveguide (e.g., Figure 3 in the optical fiber 150).

[0047] Quantum random number generation

[0048] One application of this embodiment is quantum random number generation with low bias. Quantum-generated random numbers can be used to generate encryption keys that are more difficult to crack than alternative encryption methods. In addition, the quantum light generated by this embodiment can be tested via Bell's inequality to verify that no party other than the unique user possesses the key, which is a final level of privacy that many prior art random number generators cannot provide [1].

[0049] Biased and shared strings of random numbers lead to fragile and easily cracked cryptographic keys. Quantum random number generators (QRNGs) have several advantages over traditional pseudorandom number generators (PRNGs) [1, 2]. First, QRNGs use inherently unpredictable processes, particularly those related to quantum superposition. Second, entanglement between quantum particles interweaves these superposition states so that the generated randomness can be guaranteed to be unbiased to a degree of confidence that cannot be achieved using PRNGs. Third, tests based on Bell's inequality can be performed to verify that the random numbers generated by a QRNG are "fresh" (i.e., not pre-recorded) and that these random numbers are private only to the user. Fourth, randomness generation can be device-independent, meaning that privacy verification tests also show that the components of the QRNG do not communicate the generated numbers to third parties (e.g., eavesdroppers or hackers). QRNGs with this capability are called "certified". To date, certified QRNGs have been shown to have inefficient spontaneous entanglement generation, which limits the random number generation rate to 1000 bits per second (e.g., see reference [2]). Furthermore, to verify the privacy of randomness using current schemes, hundreds of meters of distance are required between the entanglement generation and measurement stations.

[0050] The quantum light source of the present embodiment (e.g., quantum light source 100) can be used as a single photon source (SPS) for privacy, unbiased, high-speed QRNG. Typically, a QRNG repeats an operation cycle to generate a random bit stream. For each operation cycle, the QRNG performs the following steps: (i) the SPS generates a single photon (i.e., a single photon state), (ii) the single photon is collected and routed to a detector, and (iii) the single photon is detected. When each of these three steps is performed with high probability (i.e., close to 1), the QRNG is "efficient".

[0051] With regard to step (i), quantum dots are the most efficient source for generating single photons on demand. For example, quantum dots made of indium arsenide (InAs) have been shown to generate single photons at gigahertz rates and with a probability close to 1 when excited (i.e., on demand) [3]. However, other types of quantum dots (e.g., GaAs) and quantum emitters (e.g., NV centers in diamond) can also be used for SPS.

[0052] Regarding step (ii), the quantum emitter can be placed inside the optical cavity to increase the collection probability. In free space, quantum emitters typically emit photons uniformly in all directions (i.e., 4π spherical angles), which can be challenging to collect using traditional optical devices such as lenses and mirrors. The optical cavity changes the spatial distribution of the emitted photons, thereby increasing the probability that each emitted photon is coupled to a specific well-defined mode of the optical cavity. In turn, the cavity mode can be coupled with a high probability to a useful path such as a traveling mode of a waveguide (e.g., an optical fiber) that transports photons to a detector. Placing the quantum emitter inside the optical cavity also utilizes the Purcell effect to increase the spontaneous emission rate of the quantum emitter (compared to its spontaneous emission rate in free space). Therefore, the Purcell effect increases the rate at which single photons (and therefore random numbers) can be generated.

[0053] Regarding step (iii), superconducting nanowire single-photon detectors are the most efficient detectors of single photons [4].

[0054] The present embodiment improves the QRNG efficiency by increasing the collection probability of step (ii). Specifically, the composite cavity of the present embodiment (i.e., the spatially overlapping Fabry-Perot cavity 102 and the bull's-eye cavity 104) guides single photons from quantum dots or another type of emitter into a single-mode fiber more efficiently than other SPS (>75% vs. 57%). The efficiency of the resulting QRNG can exceed the threshold for generating private randomness with low bias through quantum routing and the laws of quantum mechanics (e.g., superposition and entanglement).

[0055] Private randomness generation with low bias has been demonstrated previously using probabilistic sources, albeit at low rates and requiring bulky setups over distances of up to hundreds of meters [1]. The present implementation overcomes these obstacles using a tabletop QRNG device that can generate private randomness at rates useful for cryptographic protocols. Not only does this technique result in a source of randomness with unique properties, but it can also be used as a long-range link for quantum networks and connect quantum computers to exponentially increase their processing power.

[0056] An efficient SPS can create superposition states on the beam splitter, which can be measured at different stations using homodyne detection [6]. This homodyne detection can be used to perform Bell tests with the SPS, generating private randomness at a rate significantly faster than current schemes, at least 100 times faster. Furthermore, the high speed of such a device enables both the entanglement source and the measurement station to be housed in a single desktop box, or even on a single integrated device (i.e., a chip-scale certified QRNG) [7].

[0057] Such a QD-cavity system is not only a deterministic SPS, but it can also be used as an on-demand entangled photon pair source [8]. On-demand single photon and entangled photon sources are the backbone of quantum networking, used to connect and entangle distant quantum processors to each other or to perform secure quantum communication protocols [9, 10]. Therefore, the quantum light source of this embodiment can be used in the quantum internet

[11] .

[0058] To create a high-speed SPS, two approaches have been explored in the prior art. The first approach is to use a heralded spontaneous down-conversion process

[12] to generate pairs of photons (called signal photons and idler photons). Each idler photon is sent to a single-photon detector to herald the presence of a signal photon when the detector is clicked. In order to suppress multiphoton generation, the probability of generating a heralded single photon using this approach must be small (e.g., <0.1). Multiple sources can be used simultaneously to increase the probability of generating a heralded single photon. The output of the source that caused the photon generation can then be switched to the output of the device. However, the switching losses and complexity caused by using multiple sources that generate photons with similar characteristics limit the ability of these sources to effectively generate single photons while maintaining suppression of multiphoton processes.

[0059] The second approach is to excite a two-level system, which then decays and emits a photon [3]. Such systems emit only a single photon upon excitation. Therefore, multiphoton generation is easily suppressed. Trapped atoms

[13] , ions

[14] , and defect centers in materials such as diamond

[15] and silicon

[16] have been proposed for this approach. However, these systems are too slow to decay, which results in low single-photon rates. In the case of defect centers, their decay does not always result in the generation of optical photons.

[0060] Some of the present embodiments utilize quantum dots as a two-level system that results in high-speed and efficient photon emission upon excitation [3]. For example, InAs quantum dots can be grown on GaAs substrates using molecular beam epitaxy, resulting in quantum dot wafers with low defect counts [9]. Such quantum dots are the most efficient SPS, capable of emitting photons within nanoseconds of excitation with a probability of up to 96% [3].

[0061] Deterministically preparing the charge state of a quantum dot is an important task for achieving high emission probability at a single emission frequency / wavelength

[17] . One way to deterministically control the charge state is to create a Schottky barrier around the quantum dot. For certain values ​​of the voltage applied across this Schottky barrier, the quantum dot is deterministically initialized to one of several charge states. This Figure 7 It is shown in Figure 7 is the photoluminescence spectrum of a quantum dot measured for different voltages applied across the Schottky barrier. Each bright horizontal line represents a different charge state. Figure 7It shows that quantum dots can be initialized to a specific charge state. In addition, the slope of the horizontal line indicates that the emission frequency of the quantum dots can be adjusted in a small range (e.g., less than 1 nm) by changing the voltage. Another method of initializing quantum dots to a specific charge state and changing their emission frequency is to electrically control the pin junction in which the quantum dots are embedded.

[0062] In order to use these quantum dots for on-demand SPS, photons must be generated with a single polarization, single frequency, and spatial mode that can be efficiently coupled into a single-mode fiber. This coupling is performed using the composite optical cavity of the present embodiment.

[0063] Bull's-eye cavity (see, for example, Figure 1 and 2 The bullseye cavity 104 can be formed by circular grooves of varying radius etched into the sample surface, with the quantum dot at the center [5]. These grooves ensure that light emitted horizontally to the sample surface is directed upward. Top-down cavities (e.g., see Figure 1 The Fabry-Perot cavity 102 is formed by a DBR mirror below the quantum dots and a concave mirror on top. The concave mirror can be made on a fused silica substrate with the DBR on top [3]. Figure 4 As shown, the two substrates can be wafer bonded together. Although this results in the loss of the ability to tune the cavity frequency, the quantum dots can instead be tuned to resonate with the cavity, for example using a Schottky barrier.

[0064] Top-down cavities have previously been used to achieve a record SPS efficiency of 57% [3]. However, 14% of the light in this experiment was not coupled into the desired mode due to the horizontal emission of the quantum dots. The bullseye cavity reduces this lost light by suppressing spontaneous emission in the lateral (i.e. radial) direction. The composite cavity of the present embodiment combines the advantages of the top-down Fabry-Perot cavity and the bullseye cavity, thereby further enhancing the emission of photons into optical modes that are perfectly matched to the single-mode fiber.

[0065] By directing photons emitted vertically into the substrate (see, for example, Figure 5 ), as well as better mode matching with the fiber, the bullseye cavity has improved photon collection from the quantum dots (by a factor of ten)

[18] . Unlike previous demonstrations [5], these cavities do not require a suspended structure, but instead use a carefully designed DBR below the quantum dots that is compatible with top-down cavities. This improved photon collection can be achieved in Figure 8 As seen in Figure 8 Two measured photoluminescence spectra of an ensemble of quantum dots are shown. Figure 8 In the left figure, the ensemble is outside the bullseye cavity (i.e., photon collection is not enhanced). Figure 8In the right image of the image, the ensemble is inside the bullseye cavity. Note that the left image is multiplied by a factor of ten. Photoluminescence was measured with a CCD camera, not a superconducting nanowire single-photon detector.

[0066] There are many methods for making concave mirrors with top-down cavities (i.e. Figure 1 Top mirror 114 in the figure). One method is CO2 laser ablation[3]. In this case, a concave mirror is made by irradiating a CO2 laser onto a silicon dioxide substrate to melt the surface with a curvature as small as 10μm. Another method is photoresist pattern transfer

[19] . In this method, a circular photoresist is patterned on a silicon dioxide substrate. The photoresist is then reflowed by baking it to form a concave shape. Finally, the surface is etched to transfer the shape of the photoresist to the silicon dioxide and remove the remaining photoresist. Using this method, mirror curvatures as small as 100μm have been demonstrated.

[0067] An efficient SPS can be used to generate authentic quantum random numbers. The simplest way to generate random numbers via a quantum process is to send a single photon into a 50 / 50 beam splitter. Two single-photon detectors are located at the output of this beam splitter. The clicks registered by the detectors produce a sequence of random bits based on which detectors click at each cycle

[20] . The deviation of this QRNG depends on how close the transmission / reflection of the beam splitter is to 50%, and whether the transmission varies with fluctuations in the photon mode (such as its wavelength or polarization).

[0068] The use of quantum entanglement can further enhance this protocol by exploiting non-classical correlations between quantum states, thereby significantly reducing bias and adding privacy tests to the generated random numbers. The simplest photon entangled state has two photons, each of which can exist in two modes |0> or |1>. The overall state of the two photons is |ψ>∝|00>+|11>, which means that measurement of the first photon immediately reveals the state of the second photon. However, these photons can be measured on bases other than {|0>,|1>}, such as {|+>,|->}, where and In this basis, the two-photon state can be rewritten as |ψ>∝|++>+|-->, which again shows strong correlations. If the two photons are spatially separated, and the measurement basis is chosen randomly, then a Bell test can show that the outcome of the measurement shows true quantum correlations (i.e., nonlocality). If the outcome is measured faster than information about the chosen basis can travel between the two measurement stations (i.e., the speed of light), then a flawless Bell test can lead to a probability with as low as 10 -20To put this number in perspective, using a classic RNG to achieve a similar deviation requires the device to first generate 10 40 This low deviation leads to more secure cryptographic key generation. In addition, the Bell test shows that the joint state measured between the two stations is a pure quantum state, meaning it has no correlation with anything outside the stations. This leads to confirmation that the random numbers generated are private to the user and that they are freshly generated.

[0069] There are two challenges associated with certified QRNGs. The first is a strict photon transmission threshold throughout the experiment, which should exceed ~75% [1]. Second, certified QRNGs demonstrated to date have low rates of at most 1000 bits per second, due to the fact that they use a source of spontaneously entangled photons that only result in photon pairs with a probability of less than 5% per cycle in order to suppress multi-photon pair events [2].

[0070] As an alternative to two-photon entangled states, a loophole-free Bell test can be performed using a single-photon state incident on a beam splitter [6]. The state of the two output ports can then be written as |ψ>∝|01>+|10>. Here, |0> represents the absence of a photon in the port, and |1> represents a single photon. Writing the state in this form simply means that the photon is in a superposition of the two output ports. This state can be used as a single-photon entangled state, for which the measurement basis is more complex and non-locality is shown using homodyne detection [6].

[0071] Combination of features

[0072] The above features and the features claimed below can be combined in various ways without departing from the scope of the present invention. The following examples illustrate possible non-limiting combinations of the above features and embodiments. It should be clear that other changes and modifications can be made to this embodiment without departing from the spirit and scope of the present invention:

[0073] (A1) A quantum light source includes a bull's-eye cavity, a Fabry-Perot cavity, and a quantum emitter located in both the bull's-eye cavity and the Fabry-Perot cavity.

[0074] (A2) In the quantum light source represented by (A1), the Fabry-Perot cavity includes a first mirror and a second mirror facing each other, the Fabry-Perot cavity defines an optical axis extending between the first mirror and the second mirror, and the bull's-eye cavity is located in a plane perpendicular to the optical axis.

[0075] (A3) In the quantum light source represented by (A2), the quantum light source also includes a substrate located between the first mirror and the second mirror, and the quantum emitter is embedded in the substrate.

[0076] (A4) In any quantum light source represented by (A2) and (A3), the second mirror is a dielectric mirror.

[0077] (A5) In any quantum light source represented by (A2) and (A3), the second mirror is a metal mirror.

[0078] (A6) In any quantum light source represented by (A2) to (A5), the second mirror is planar.

[0079] (A7) In any quantum light source represented by (A2) to (A6), the first mirror is concave.

[0080] (A8) In the quantum light source represented by (A7), the radius of curvature of the first mirror is 100 microns or less.

[0081] (A9) In any of the quantum light sources denoted as (A2) to (A8), the quantum light source further comprises an optical fiber having a tip positioned to receive photons that exit the Fabry-Perot cavity via the second mirror.

[0082] (A10) In any of the quantum light sources represented by (A1) to (A9), the bullseye cavity includes a central disk formed of a first material having a first refractive index. The bullseye cavity also includes an alternating sequence of concentric rings surrounding the central disk. Each of a first subset of the alternating sequence of concentric rings is formed of the first material, each of a second subset of the alternating sequence of concentric rings is formed of a second material having a second refractive index different from the first refractive index, and an innermost ring of the alternating sequence of concentric rings is formed of the second material.

[0083] (A11) In the quantum light source represented by (A10), the second material is air or vacuum.

[0084] (A12) In any of the quantum light sources represented by (A10) and (A11), the quantum emitter is embedded in the central disk.

[0085] (A13) In any of the quantum light sources represented by (A10) to (A13), the bull's eye cavity includes a lower substrate of the first material. The second subset of the alternating sequence of concentric rings is a groove etched downward from the top surface of the lower substrate, so that the lower substrate forms the first subset of the alternating sequence of concentric rings after etching.

[0086] (A14) In the quantum light source represented by (A13), the Fabry-Perot cavity includes a first mirror and a second mirror facing each other. The first mirror is a plane mirror located below the lower substrate. The second mirror is a concave mirror formed on an upper substrate located above the lower substrate.

[0087] (A15) In the quantum light source represented by (A14), the upper substrate is directly bonded to the lower substrate.

[0088] (A16) In the quantum light source represented by (A15), the upper substrate is directly bonded to the lower substrate continuously along a line surrounding the first mirror and the second mirror.

[0089] (A17) In any quantum light source represented by (A1) to (A16), the quantum emitter is a point defect in the crystal.

[0090] (A18) In the quantum light source represented by (A17), the point defect is a nitrogen vacancy center in diamond.

[0091] (A19) In any quantum light source represented by (A1) to (A16), the quantum emitter is a quantum dot.

[0092] (A20) In the quantum light source represented by (A19), the quantum dots are semiconductor quantum dots.

[0093] (A21) In the quantum light source represented by (A20), semiconductor quantum dots are embedded in a pin junction.

[0094] (A22) In the quantum light source represented by (A20), the semiconductor quantum dots form part of the Schottky barrier.

[0095] (A23) In any quantum light source represented by (A20) to (A22), the quantum dots are formed of (InAs), indium gallium arsenide (InGaAs), gallium arsenide (GaAs) or gallium nitride (GaN).

[0096] (B1) A method comprising optically pumping any quantum light source represented by (A1) to (A23) to generate a single photon.

[0097] (B2) In the method represented by (B1), the optical pumping includes exciting the quantum emitter using light that resonates with a single-photon transition of the quantum dot.

[0098] (B3) In the method represented by (B2), the quantum emitter is a quantum dot, and the method also includes controlling the quantum dot before the optical pumping so that the quantum dot is in a negatively charged ground state.

[0099] (B4) In the method represented by (B2), the quantum emitter is a quantum dot, and the method also includes controlling the quantum dot before the optical pumping so that the quantum dot is in a neutral ground state.

[0100] (B5) In the method represented by (B4), the optical pumping includes exciting the quantum dots from a neutral ground state to a lowest energy biexciton state.

[0101] (B6) In the method represented by (B5), the method also includes optically driving the quantum dot to induce stimulated emission of the quantum dot from the lowest energy biexciton state to the exciton state.

[0102] (B7) In any of the methods represented by (B1) to (B6), the method also includes coupling the single photon into an optical fiber.

[0103] (C1) A method comprising optically pumping any quantum light source represented by (A1) to (A23) to generate entangled photon pairs.

[0104] (C2) In the method represented by (C1), the quantum emitter is a quantum dot, and the method also includes controlling the quantum dot so that the quantum dot is in a neutral ground state before the optical pumping.

[0105] (C3) In the method represented by (C2), the optical pumping includes exciting the quantum dots from a neutral ground state to a lowest energy biexciton state.

[0106] (C4) In any of the methods represented by (C1) to (C3), the method also includes coupling one or both of the entangled photon pairs into an optical fiber.

[0107] Changes may be made to the above methods and systems without departing from the scope of this document. It should be noted, therefore, that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. The appended claims are intended to cover all general and specific features described herein, as well as all statements of the scope of the present methods and systems, which, by language, can be said to fall within the above scope.

[0108] References

[0109] [1] P. Bierhorst et al., “Experimentally generated randomness certified by the impossibility of superluminal signals,” Nature 556, 223–226 (2018).

[0110] [2] L.K. Shalm et al., “Device-independent randomness expansion with entangled photons,” Nat. Phys. 17, 452–456 (2021).

[0111] [3] N. Tomm et al., “A bright and fast source of coherent single photons,” Nat. Nanotechnol. 16, 399–403 (2021).

[0112] [4] DvReddy, DvReddy, RRNerem, SW Nam, RPMirin, and VBVerma, “Superconducting nanowire single-photon detectors with 98% system detection efficiency at 1550 nm,” Optica 7, 1649–1653 (2020).

[0113] [5] L. Sapienza, A. Badolato and K. Srinivasan, “Nanoscale optical positioning of single quantum dots for bright and pure single-photon emission,” Nat. Commun. 6, 7833 (2015).

[0114] [6] and N. Brunner, “Self-testing nonlocality without entanglement,” arXiv 2203.13171 (2022).

[0115] [7] C. McDonald, G. Moody, S. W. Nam, R. P. Mirin, J. M. Shainline, A. McCaughan, S. Buckley, and K. L. Silverman, “III-V photonic integrated circuit with waveguide-coupled light-emitting diodes and WSi superconducting single-photon detectors,” Appl. Phys. Lett. 115, 081105 (2019).

[0116] [8] J. Liu et al., “A solid-state source of strongly entangled photon pairs with high brightness and indistinguishability,” Nat. Nanotechnol, 14, 586–593 (2019).

[0117] [9] P. Imany et al., “Quantum phase modulation with acoustic cavities and quantum dots,” Optica 9, 501-504 (2022).

[0118]

[10] Y. Tsuchimoto, Z. Sun, E. Togan, W.Wegscheider, A.Wallraff, K.Ensslin, and M. Kroner, “Large-bandwidth transduction between an optical single quantum-dot molecule and a superconducting resonator,” arXiv 2110.03230v1 (2021).

[0119]

[11] HJ Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).

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[12] F. Kaneda and P.G. Kwiat, “High-efficiency single-photon generation via large-scale active time multiplexing,” Sci. Adv. 5 (2019).

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[13] F. Ripka, H. Kübler, and T. Pfau, “A room-temperature single-photon source based on strongly interacting Rydberg atoms,” Science 362, 446-449 (2018).

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[14] HG Barros, A. Stute, TE Northup, C. Russo, P O Schmidt, and R. Blatt, “Deterministic single-photon source from a single ion,” New J. Phys. 11, 103004 (2009).

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[15] ENKnall et al., “Efficient Source of Shaped Single Photons Based on an Integrated Diamond Nanophotonic System,” arXiv 2201.02731 (2022).

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[16] S. Castelletto, “Silicon carbide single-photon sources: challenges and prospects,” Mater. Quantum. Tech. 1, 023001 (2021).

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[17] Av Kuhlmann, J. Houel, D. Brunner, A. Ludwig, D. Reuter, A. D. Wieck, and R. J. Warburton, “A dark-field microscope for background-free detection of resonance fluorescence from single semiconductor quantum dots operating in a set-and-forget mode,” Rev. Sci. Instrum. 84, 073905 (2013).

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[18] R. A. DeCrescent, Z. Wang, P. Imany, R. C. Boutelle, R. P. Mirin, and K. L. Silverman, “Semicircular dielectric gratings for strongly polarized and enhanced emission from GaAs / InAs quantum dots,” 2022 Conference on Lasers and Electro-Optics (CLEO), San Jose, CA, USA, pp. 1–2 (2022).

[0127]

[19] N. Jin, C. A. McLemore, D. Mason, J. P. Hendrie, Y. Luo, M. L. Kelleher, P. Kharel, F. Quinlan, S. A. Diddams, and P. T. Rakich, “Scalable fabrication of ultrahigh-finesse micromirrors with variable geometry,” arXiv 2203.15931 (2022).

[0128]

[20] Q. Luo et al., “Quantum random number generator based on single-photonemitter in gallium nitride,” Opt. Lett. 45, 4224-4227 (2020).

Claims

1. A quantum light source, comprising: Bullseye cavity; Fabry-Perot cavity; as well as A quantum emitter is located within both the bullseye cavity and the Fabry-Perot cavity.

2. The quantum light source according to claim 1, wherein: The Fabry-Perot cavity includes a first mirror and a second mirror facing each other, the Fabry-Perot cavity defining an optical axis extending between the first mirror and the second mirror; and The bull's-eye cavity lies in a plane perpendicular to the optical axis.

3. The quantum light source of claim 2, further comprising a substrate located between the first mirror and the second mirror, the quantum emitter being embedded in the substrate.

4. The quantum light source of claim 2, wherein the second mirror comprises a dielectric mirror.

5. The quantum light source of claim 2, wherein the second mirror comprises a metal mirror.

6. The quantum light source of claim 2, wherein the second mirror is planar.

7. The quantum light source of claim 2, wherein the first mirror is concave.

8. The quantum light source according to claim 7, wherein the radius of curvature of the first mirror is 100 micrometers or less.

9. The quantum light source of claim 2, further comprising an optical fiber having a tip positioned to receive photons exiting the Fabry-Perot cavity via the second mirror.

10. The quantum light source according to claim 1, wherein the bull's eye cavity comprises: a central disk formed of a first material having a first refractive index; and an alternating sequence of concentric rings surrounding the central disk, each of a first subset of the alternating sequence of concentric rings being formed of the first material, each of a second subset of the alternating sequence of concentric rings being formed of a second material having a second refractive index different from the first refractive index, an innermost ring of the alternating sequence of concentric rings being formed of the second material. The quantum light source of claim 10 , wherein the second material comprises air.

12. The quantum light source of claim 10, wherein the quantum emitter is embedded within the central disk.

13. The quantum light source according to claim 10, wherein: The bull's-eye cavity includes a lower substrate of the first material; and The second subset of the alternating sequence of concentric rings is a trench etched downward from a top surface of the lower substrate such that the lower substrate after etching includes the first subset of the alternating sequence of concentric rings.

14. The quantum light source according to claim 13, wherein the Fabry-Perot cavity comprises a first mirror and a second mirror facing each other, the first mirror comprises a plane mirror located below the lower substrate, and the second mirror comprises a concave mirror formed on an upper substrate located above the lower substrate. The quantum light source according to claim 14 , wherein the upper substrate is directly bonded to the lower substrate.

16. The quantum light source of claim 15, the upper substrate being directly bonded to the lower substrate continuously along a line surrounding the first mirror and the second mirror.

17. The quantum light source of claim 1, wherein the quantum emitter comprises a point defect in a crystal.

18. A quantum light source according to claim 17, the point defects comprising nitrogen vacancy centres in diamond.

19. The quantum light source of claim 1, wherein the quantum light emitters comprise quantum dots.

20. The quantum light source of claim 19, wherein the quantum dots comprise semiconductor quantum dots.

21. The quantum light source of claim 20, wherein the semiconductor quantum dots are embedded in a pin junction.

22. The quantum light source of claim 20, wherein the semiconductor quantum dots form part of a Schottky barrier.

23. The quantum light source of claim 20, wherein the semiconductor quantum dots comprise indium arsenide (InAs), indium gallium arsenide (InGaAs), gallium arsenide (GaAs), or gallium nitride (GaN).

24. A method comprising optically pumping the quantum light source of claim 1 to produce a single photon.

25. The method of claim 24, wherein the optical pumping comprises exciting the quantum emitter with light resonant with a single photon transition of the quantum emitter.

26. The method of claim 25, wherein: The quantum emitters are quantum dots; and The method also includes controlling the quantum dots prior to the optical pumping so that the quantum dots are in a negatively charged ground state.

27. The method of claim 25, wherein: The quantum emitters are quantum dots; and The method also includes controlling the quantum dot prior to the optical pumping so that the quantum dot is in a neutral ground state.

28. The method of claim 27, wherein the optical pumping comprises exciting the quantum dots from the neutral ground state to a lowest energy biexciton state.

29. The method of claim 28, further comprising optically driving the quantum dot to induce stimulated emission of the quantum dot from the lowest energy biexciton state to an exciton state.

30. The method of claim 24, further comprising coupling the single photon into an optical fiber.

31. A method comprising optically pumping the quantum light source according to claim 1 to produce entangled photon pairs.

32. The method of claim 31, wherein: The quantum emitters are quantum dots; and The method also includes controlling the quantum dot prior to the optical pumping so that the quantum dot is in a neutral ground state.

33. The method of claim 32, wherein the optical pumping comprises exciting the quantum dots from the neutral ground state to a lowest energy biexciton state.

34. The method of claim 31 further comprising coupling one or both of the entangled photon pairs into an optical fiber.

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