Cascade resonator photon pair source

Abstract

A photon source includes: a bus waveguide; a photon source pump laser coupled to the bus waveguide; and a plurality of optical resonators coupled to the bus waveguide. Each of the plurality of optical resonators has a corresponding resonant linewidth and a corresponding resonant frequency, wherein the bandwidth of the resonant center frequencies of the plurality of optical resonators is greater than the bandwidth of the photon source pump laser. The bus waveguide generates photons in response to receiving a laser pulse from the pump laser.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Provisional Patent Application No. 62 / 941,407 filed on November 27, 2019 and U.S. Provisional Patent Application No. 63 / 042,438 filed on June 22, 2020, the disclosures of which are incorporated herein by reference in their entirety for all purposes. Background Art

[0003] Photon pair sources can be used in a variety of technologies. For example, photonic quantum technologies benefit from photon pair sources with improved brightness, spectral purity, reproducibility, and manufacturability. Summary of the invention

[0004] In some embodiments, a photon source includes: a bus waveguide; a pump laser coupled to the bus waveguide; and a plurality of optical resonators coupled to the bus waveguide. Each of the plurality of optical resonators may have a corresponding resonant linewidth and a corresponding resonant frequency. In some embodiments, the frequency span of the resonant center frequencies of the plurality of optical resonators is greater than the bandwidth of the photon source pump laser.

[0005] In some embodiments, the photon source further comprises a plurality of dispersive elements coupled to the bus waveguide, wherein a dispersive element of the plurality of dispersive elements is positioned between respective adjacent pairs of optical resonators of the plurality of optical resonators.

[0006] In some embodiments, a variation in the resonant center frequency between adjacent optical resonators is less than a resonant linewidth of each of the plurality of optical resonators.

[0007] In some embodiments, the number of the plurality of optical resonators is two. In other embodiments, the number of the plurality of optical resonators is greater than ten.

[0008] In some embodiments, the plurality of optical resonators is a first plurality of first optical resonators, and each first optical resonator is coupled to a respective second optical resonator in a second plurality of optical resonators.

[0009] In some embodiments, a second plurality of optical resonators is coupled to a second waveguide that emits photons.

[0010] In some embodiments, the bus waveguide is an optical resonator.

[0011] In some embodiments, a photon source includes: a bus waveguide having an input region and an output region; and a plurality of optical resonators coupled to the bus waveguide in series between the input region and the output region. The output region can be configured to transmit photon pairs generated within the plurality of optical resonators in response to the input region receiving a laser pulse. In some embodiments, each optical resonator in the plurality of optical resonators has a corresponding resonant linewidth and a corresponding resonant frequency.

[0012] In some embodiments, the frequency span of the resonant center frequencies of the plurality of optical resonators is greater than a bandwidth of laser pulses received at the input region.

[0013] In some embodiments, further comprising a plurality of dispersive elements coupled to the bus waveguide, and a dispersive element of the plurality of dispersive elements is positioned between each of the plurality of optical resonators.

[0014] In some embodiments, a variation in the resonant center frequency between adjacent optical resonators is less than a resonant linewidth of each of the plurality of optical resonators.

[0015] In some embodiments, the number of the plurality of resonant optical resonators is greater than ten.

[0016] In some embodiments, the plurality of optical resonators is a first plurality of first optical resonators, and each first optical resonator is coupled to a corresponding second optical resonator in a second plurality of optical resonators.

[0017] In some embodiments, the bus waveguide is an optical resonator bus waveguide that recirculates the laser pulses. In some embodiments, the photon source further comprises a plurality of optical resonator bus waveguides, each optical resonator bus waveguide being optically coupled to a corresponding plurality of resonant optical resonators.

[0018] In some embodiments, for a resonator in the plurality of resonators, a second resonator is positioned directly adjacent to a first resonator, and a third resonator is positioned directly adjacent to the second resonator. The resonant frequency of the first resonator is greater than the resonant frequency of the second resonator. Additionally, the resonant frequency of the third resonator may be less than the resonant frequency of the first resonator.

[0019] In order to better understand the nature and advantages of the present invention, reference should be made to the following description and drawings. However, it should be understood that the various drawings are provided for illustrative purposes only and are not intended as a definition of the limitations of the scope of the present invention. Moreover, as a general rule, and unless otherwise apparent from the description, where the same reference numerals are used for elements in different drawings, the elements are generally the same or at least similar in function or purpose. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1A is a diagram of a cascaded resonator photon pair source using a single bus according to an embodiment of the present invention;

[0021] Figure 1B is a diagram of a series of resonant spectral enhancements according to an embodiment of the present invention;

[0022] FIG. 2A to FIG. 2B illustrates an approximate graphical depiction of the joint spectral amplitude of photons generated from a cascaded resonator photon pair source in accordance with an embodiment of the present invention;

[0023] Figure 3 is a diagram of a cascaded resonator photon pair source including separate pump and photon buses with coupled optical resonators according to an embodiment of the present invention;

[0024] Figure 4 A simplified diagram illustrating a pump recycling design for a cascaded resonator photon pair source according to an embodiment of the present invention; and

[0025] Figure 5 A frequency conversion system employing a cascaded resonant structure according to some embodiments is illustrated. DETAILED DESCRIPTION

[0026] The technology disclosed herein generally relates to a photon pair source. Such a source produces correlated photon pairs, each photon pair including a photon commonly referred to as a signal photon and a herald photon. By detecting the herald photon, the presence of the signal photon is announced for use.

[0027] In some embodiments, the photon pair source is composed of an integrated waveguide structure in a third-order or second-order nonlinear optical material (e.g., silicon, silicon nitride, silicon-rich silicon nitride, germanium compounds, silicon-rich germanium, chalcogenide glass, organic compounds, PZT, BTO, LiNb, etc.). The pump laser is coupled to these waveguide structures so that spontaneous four-wave mixing (SFWM) or spontaneous parametric down conversion (SPDC) can occur. During the SFWM process, two pump laser photons can be converted into a pair of daughter photons (e.g., a signal photon and a proclamation photon) in the nonlinear optical material. Due to energy conservation, the generated signal photons and proclamation photons can be at frequencies symmetrically distributed around the pump frequency. Typically, due to this spectral correlation, the proclamation signal photon can be in a mixed state, in which case the source does not produce the same photon in subsequent experiments. The frequency distribution of the generated pairs (defined by the joint spectral amplitude (JSA)) is controlled by the interaction between energy conservation and momentum conservation in the spontaneous pair generation process.

[0028] Some embodiments employ optical resonators. In such embodiments, the optical resonator shapes the spectral density of states (defined by spectral resonance enhancement) so that photon pair generation is enhanced near the resonant frequency. The optical resonator can be implemented as a traveling wave resonant structure. One implementation is a loop in a waveguide shaped as a ring, a racetrack, or other closed curve coupled to a bus waveguide. Another implementation uses a reflector and a semi-transparent reflector to form a closed beam path. The optical resonator can also be implemented as a standing wave resonant structure, such as a distributed Bragg grating of a Fabry-Perot cavity or a photonic crystal cavity.

[0029] Photon pair sources using optical resonators in integrated optical devices can be used to increase the brightness of SFWM photon pair generation compared to non-resonator forms, where brightness is the probability of generating a photon pair per pump photon. The brightness increase is caused by the enhanced resonance of the pump, signal, and announced spectra near the resonant frequency. To increase the brightness, the following resonant condition can be satisfied: ν p =v res M ,ν s =v res M-n ,ν h =v res M+n Here, ν p , ν s , ν h are the frequencies of the pump field, signal field, and announcement field, respectively. Moreover, at ν res In the above equation, the superscript indicates the number of resonances. M is a positive integer and n is an arbitrary integer. The resonance condition for the Mth order is Among them, l eff is the effective optical round trip length of the resonator, and c is the speed of light. An optical resonator has multiple resonant frequencies. The frequency difference between two adjacent resonances M&M+1 is the free spectral range (FSR). The resonant enhancement is a Lorentzian distribution of the spectral density of states, centered at the resonant frequency and with a bandwidth defined by the full width at half maximum (FWHM) of the distribution (also referred to herein as the resonant linewidth). The ratio of FSR / FWHM is the finesse of the resonator. The brightness of a photon pair source using an optical resonator increases with increasing finesse.

[0030] In some embodiments based on a single optical resonator, the brightness of the source can be traded off against the bandwidth of the source. However, many systems employing many single photon sources, such as for linear optical quantum computing, require that the announced photons from different sources interfere at a beam splitter to produce entangled states of photons. However, in order for the announced photons produced by two sources to interfere well, each source must be nearly identical to the other (e.g., the resonance must be nearly identical). If only a single resonator is used, this imposes severe restrictions on the alignment of the resonant frequencies of each resonator source.

[0031] If the JSA can be expressed as the product of the declared spectral distribution and the signal spectral distribution (the JSA is separable), then the source is spectrally pure. In some embodiments of the photon pair source based on a single optical resonator, the spectral purity can be optimized by tailoring the resonant bandwidth of the system at the declared resonance, signal resonance, and pump resonance.

[0032] The technology disclosed herein relates to cascaded resonator sources, where photon pairs generated in several optical resonators are coherently added together, which can result in enhanced spectral purity and brightness. By cascading multiple resonator sources on a single bus and coherently combining them, the typical tradeoff between brightness and resonance bandwidth can be improved. In some embodiments, cascaded sources are disclosed that can generate substantially identical photons even if the resonators that make up the cascaded source have offset resonance frequencies.

[0033] Cascaded resonator sources as described and disclosed herein may be used in any optical device including, but not limited to, quantum computing, quantum communication, quantum metrology, spectroscopy, LiDAR, and other applications.

[0034] In order to better understand the features and aspects of a source that coherently combines multiple resonators on a single bus, further context of the invention is provided by discussing the implementation of a cascaded source according to an embodiment of the invention. These embodiments are exemplary only, and other embodiments may be employed in other photon sources and photon devices.

[0035] Figure 1A A cascaded resonator photon pair source 100 according to an embodiment of the present invention is illustrated. The cascaded resonator photon pair source 100 may include a waveguide 105 and a series of optical resonators 110_1, 110_2, ..., 110_n, each optical resonator having a different resonant frequency. Pump light (e.g., from a laser pump 122) may be coupled to an input region 130 of the waveguide 105 and may be coupled into each ring resonator 110_1, 110_2, ..., 110n. The pump laser may have a programmed power spectral density and spectral chirp. Each optical resonator 110_1, 110_2, ..., 110_n may include a waveguide loop so that when the optical path length of the ring resonator is an integer multiple of the wavelength of the light, resonance for light having a specific wavelength may occur. Each optical resonator may support multiple resonances of multiple wavelengths that meet the resonance condition.

[0036] Figure 1BA graph of the resonance enhancement and wavelength function of the spectral density of states of multiple resonators according to some embodiments is shown. Each of the distributions shown (also referred to herein as resonance curves, or simply resonances) is centered at the "resonance frequency" of the corresponding resonator, and these curves are referred to herein as "resonator resonances". Each resonator resonance has a spectral width, which is defined as the full width at half maximum (FWHM) of the distribution. This width is referred to herein as the "resonance linewidth". The pump, signal, and announced resonant frequencies are given by v p, , ν s, , ν h, Given, where j denotes the resonator structure itself, e.g. Figure 1A However, it is important to note that the index j (in Figure 1B The resonant frequencies of the resonators need not increase monotonically or even increase (or decrease in order) when traveling from the input to the output. Figure 1B , resonator resonances (for any of the three fields) are illustrated for five optical resonators (which can be positioned anywhere along the bus), where the index j is from 1 to 5, corresponding to 150a-150e. The shift in the resonant frequency between different resonators (also referred to herein as resonance shift) can be obtained by small changes in the optical resonator waveguide width or the optical resonator length or another resonator characteristic.

[0037] Return to Figure 1A , a series of optical resonators are optically coupled to the bus, and the individual resonant frequencies of the series of resonators can be selected to improve the brightness and purity of the photon pairs generated by the source. In the figure, the resonators are labeled 110_1, 110_2, ..., 110_n, where the index n indicates the physical position of the resonator relative to the input side of the device (where 110_1 is the first input resonator, 110_2 is the second resonator positioned directly adjacent to resonator 110_1, and so on). In some embodiments, the series of resonant frequencies of the series of resonators along the device (from input to output, or vice versa) can be ordered (increasing, decreasing) and equally spaced. In other embodiments, the resonant frequencies of the resonators indexed by n may not be a monotonically increasing or decreasing function of n when moving down the device, that is, the resonant frequency of the first resonator may be greater than the resonant frequency of the second resonator (where the second resonator is positioned directly adjacent to the first resonator), and the resonant frequency of the third resonator (where the third resonator is positioned directly adjacent to the second resonator) may be less than the resonant frequency of the first resonator. In some embodiments, making the second resonant frequency less than the first resonant frequency and making the third resonant frequency greater than the first resonant frequency can improve the spectral purity of the source. As used herein, the term "frequency span" of the resonant frequencies is the difference between the largest and smallest of these frequencies.

[0038] Some embodiments may use an additional optional dispersive element that adjusts the optical phase between the pump, signal, and idle between two optical resonators. FIG. 1 illustrates such a device 100, where Δk 115a is the momentum mismatch between the pump, signal, and idle. In some embodiments, the dispersive element may be implemented using any type of dispersive structure, including but not limited to waveguides with different geometries, chirped gratings through multimode dispersion engineering, or chirped mirrors. The dispersive element may be coupled to the bus in any manner, for example, may be formed directly from and / or integrated into the bus waveguide, or optically coupled to the bus (via direct coupling or evanescent coupling, etc.).

[0039] According to some embodiments, the resonator resonances of the resonators may overlap, such as Figure 1B That is, if the resonator resonances are plotted as a function of wavelength (or equivalently, frequency), the areas under the curves are approximately overlapping. In some embodiments, two resonator resonances are defined as overlapping if the difference between their respective resonant frequencies is less than twice the resonant linewidth of one of the two resonances. In some embodiments, the difference between the resonant frequencies defined as overlapping can be several hundred picometers (e.g., 100 picometers), or in the range of 50 picometers to 400 picometers (5 GHz-50 GHz when frequency units are used).

[0040] In some embodiments, the pump pulse spectrum is a Gaussian spectrum with a controlled bandwidth. Here, the term bandwidth refers to the FWHM of the pump power spectral density. In some embodiments, the pump spectrum has a controlled spectral chirp (non-zero quadratic spectral phase). The FWHM of the pump spectrum can be less than the frequency span of the resonance.

[0041] Figure 2AA diagram 200 of a JSA of a cascaded resonator photon pair source 100 is illustrated. Region 205 illustrates a pump function, which illustrates the energy conservation of generating photon pairs from a pump pulse. Region 210 illustrates the common spectral resonant enhancement due to multiple resonators in the cascaded resonator source. When the pump, signal, and announced spectral enhancement are shifted together from one resonator to another, the region is approximately orthogonal to the pump function. The interaction of the pump function and the common spectral enhancement can result in a JSA that is approximately a 2D Gaussian distribution, illustrated by region 215. The JSA can be made approximately separable, which results in high spectral purity. The cascaded resonator source 100 can be a relatively bright, spectrally pure source of photon pairs. High purity means >99%, while low purity or standard purity is approximately 90%. In some embodiments, for example, the purity of the JSA illustrated by region 215 can be 99.9%, while in other embodiments, the purity can be different.

[0042] The cascade resonator source 100 is robust to long-range process variations. More specifically, manufacturing defects often cause all v p,j , ν s,j , ν h,j If all the resonant frequencies of the cascaded resonator source are shifted together, the pump "selects" a subset of the resonators 110_1, ..., 110_n to interact with. The resulting JSA may be almost identical to that of the nominal source.

[0043] Figure 2B A diagram of a cascaded resonator source is illustrated, showing the effect of process variability on the JSA. Figure 2A illustrates the common spectral enhancement of a nominal source, Figure 2B A source is shown that is affected by a shift in all resonant frequencies due to process variations (e.g., waveguide film thickness variations). In this configuration, the result of the process variations is simply a shift of the common spectral resonance enhancement to a new position 210'. However, because the frequency span of the common spectral resonance enhancement is larger than the shift caused by the process variations, region 215 is largely unaffected. This enables the system to be robust to variability in the manufacturing process.

[0044] The above explanations of characteristics and operations may be considered approximations and / or simplifications, and the present disclosure is not limited by these explanations.In some embodiments, the infrastructure is fully simulated including pump propagation, dispersion, nonlinearity, losses, multiphotons, non-perturbative effects, and other considerations.

[0045] Figure 3An embodiment of a cascade source 300 according to an embodiment of the present invention is illustrated. In this embodiment, a series of optical resonators 303 includes a row of optical resonators 310a...310n and another row of optical resonators 320a...320n, however in other embodiments the series of optical resonators may have other suitable shapes different from the illustration. The series of optical resonators 303 is disposed between a first waveguide 305 and a second waveguide 325. A laser pump source is coupled to the first waveguide 305, which is positioned to couple light into each optical resonator 320a...320n. Each optical resonator 320a...320n is separated by a corresponding phase shift 315a...315n (labeled as φ). Each optical resonator 320a...320n is positioned to couple light into a corresponding optical resonator 310a...310n, which couples light into the second waveguide 325.

[0046] In other embodiments, coupled optical resonators may be used instead of a single optical resonator. In further embodiments, quasi-phase matching techniques may be used, where the nonlinear properties of spatial modulation are used to engineer momentum matching during the pair generation process.

[0047] The above-described photon pair sources can lead to numerous improvements in performance, including but not limited to the following. First, the disclosed structure can decouple the bandwidth of the announced photons from the source brightness. In contrast, previous optical resonator photon pair sources achieve higher brightness by narrowing the resonant frequency. In the cascaded resonator source disclosed herein, this limitation is eliminated, thereby significantly increasing the design space. For example, the bandwidth can be selected given other system considerations.

[0048] A second improvement of the photon pair sources described herein is that if the two photon pair sources share approximately the same pump, then two separate photon pair sources can produce approximately the same annunciation photon, regardless of the resonant frequency offset imparted to all optical resonators by long-distance process variations. This feature allows different photon pair sources to produce approximately the same annunciation photon. This can reduce the required adjustments and / or adjustments by several orders of magnitude to achieve frequency alignment of different photon pair sources.

[0049] A third improvement is that the photon pair sources described herein can generate Gaussian photons. In some embodiments, a Gaussian distribution is a desired single photon wave packet shape because it is robust to dispersion, timing jitter, etc. In contrast, a typical single optical resonator source does not generate Gaussian photons.

[0050] Another advantage is that the photon pair source described herein can achieve high spectral purity.

[0051] Figure 4A simplified diagram of one embodiment of a compact pump-recirculating cascade source 400 is illustrated. Figure 4 As shown, the recirculating cascade resonator source 400 includes a plurality of recirculating resonant structures 405a...405n, each of which includes a plurality of loops 410 coupled to a corresponding resonant bus 415. In some embodiments, the cascade source 400 provides an additional benefit: when the pump leaves the source, it is not spectrally altered, but only delayed. If the bus waveguide becomes a resonator, this additional delay caused by the cascade resonator source can allow the cavity length to be matched so as to pump the sources synchronously. More specifically, when the pump laser repetition rate is matched to the accumulated delay in the cascade resonator source, the pump pulses can be enhanced by the cavity, thus significantly reducing the required external pump power. In some embodiments, when critically coupled, further enhancements of up to a multiple of two orders of magnitude can be generated.

[0052] Although cascade sources are described and illustrated as one particular type of source, embodiments of the present invention are suitable for use with a variety of systems, including but not limited to quantum computers and LiDAR systems. The common spectral enhancement produced via cascaded resonators can be used by any parametric wave mixing process (e.g., for single harmonic generation, difference frequency generation (DFG), and / or optical parametric oscillation), but is not limited thereto.

[0053] Figure 5 A frequency conversion system 500 based on a cascaded resonator structure according to some embodiments is shown. The structure is similar to the photon pair source structure described in detail above with respect to FIG. 1, and for the sake of clarity, repeated elements are not described here. In some embodiments, the input of the cascaded resonator frequency conversion system may include two lasers, FREQ.2 and FREQ.1, each with a different frequency. These lasers can be input to an optical combining device (e.g., a wavelength division multiplexing device, shown here as WDM 505). In this case, the cascaded resonator structure can generate mixing between the inputs, such as difference frequency or sum frequency generation. In some embodiments, the output WDM 515 can be used to separate the converted frequencies (e.g., sum frequency and / or difference frequency) from the input lasers generated by lasers FREQ.2 and FREQ.1. When FREQ.2 and FREQ.1 may not be as useful as the converted frequencies, this frequency conversion can be used to generate new frequencies from FREQ.2 and FREQ.1. For example, it may be that FREQ.2 and FREQ.1 are not easily detected, but the converted frequencies are easily detected by available detectors. The cascaded resonator frequency conversion structure can improve the brightness of frequency mixing when compared to other approaches for frequency conversion including waveguides or single optical resonators.

[0054] In the foregoing description, embodiments of the present invention have been described with reference to many specific details that may vary from implementation to implementation. Therefore, the description and drawings should be regarded as illustrative rather than restrictive. The sole and exclusive indication of the scope of the present invention and what the applicant intends as an indication of the scope of the present disclosure is the literal and equivalent range of such claims issued from this application in the specific form in which the claims are issued, including any subsequent amendments. The specific details of a particular embodiment may be combined in any appropriate manner without departing from the spirit and scope of the embodiments of the present disclosure.

[0055] In addition, spatially relative terms such as "bottom" or "top" may be used to describe the relationship of an element and / or feature to another one or more elements and / or features, such as illustrated in the accompanying drawings. It should be understood that spatially relative terms are intended to include different orientations of the device in use and / or operation in addition to the orientations described in the accompanying drawings. For example, if the device in the figure is turned over, the element described as the "bottom" surface can then be oriented as "above" other elements or features. The device can be oriented in other ways (e.g., rotated 90 degrees or in other orientations), and the spatially relative descriptions used herein are interpreted accordingly.

Claims

1. A photon source, comprising: Bus waveguide; a pump laser coupled to the bus waveguide; as well as A plurality of optical resonators arranged in sequence are coupled to the bus waveguide, wherein each optical resonator of the plurality of optical resonators has a corresponding resonant linewidth and a corresponding resonant center frequency, wherein a frequency span of the resonant center frequencies of the plurality of optical resonators is greater than a bandwidth of the pump laser, and wherein the resonant linewidth of each corresponding optical resonator of the plurality of optical resonators overlaps a resonant linewidth of at least one adjacent optical resonator of the plurality of optical resonators.

2. The photon source of claim 1 , further comprising a plurality of dispersive elements coupled to the bus waveguide, wherein a dispersive element of the plurality of dispersive elements is positioned between respective adjacent pairs of optical resonators in the plurality of optical resonators.

3. The photon source according to claim 1, wherein: A variation in resonance center frequency between adjacent optical resonators is less than a resonance linewidth of each of the plurality of optical resonators.

4. The photon source according to claim 1, wherein: The number of the plurality of optical resonators is two.

5. The photon source according to claim 1, wherein: The number of the plurality of optical resonators is greater than ten.

6. The photon source according to claim 1, wherein: The plurality of optical resonators is a first plurality of first optical resonators, and each first optical resonator is coupled to a corresponding second optical resonator in a second plurality of optical resonators.

7. The photon source according to claim 6, wherein: The second plurality of optical resonators is coupled to a second waveguide that emits photons.

8. The photon source according to claim 1, wherein: The bus waveguide is an optical resonator.

9. The photon source according to claim 1, wherein: For a resonator in the plurality of optical resonators, The resonant frequency of the first resonator is greater than the resonant frequency of the second resonator, and wherein the resonant frequency of the third resonator is less than the resonant frequency of the first resonator, and wherein the second resonator is positioned directly adjacent to the first resonator, and the third resonator is positioned directly adjacent to the second resonator.

10. A photon source comprising: a bus waveguide having an input region and an output region; as well as a plurality of optical resonators coupled in series to the bus waveguide between the input region and the output region, wherein the output region is configured to transmit photon pairs generated within the plurality of optical resonators in response to the input region receiving a laser pulse, and wherein a resonant linewidth of each respective optical resonator of the plurality of optical resonators overlaps a resonant linewidth of at least one adjacent optical resonator of the plurality of optical resonators.

11. The photon source according to claim 10, wherein Each optical resonator of the plurality of optical resonators has a corresponding resonance linewidth and a corresponding resonance center frequency.

12. The photon source according to claim 11, wherein The frequency span of the resonant center frequencies of the plurality of optical resonators is greater than a bandwidth of the laser pulses received at the input region.

13. The photon source of claim 12, further comprising a plurality of dispersive elements coupled to the bus waveguide, wherein a dispersive element of the plurality of dispersive elements is positioned between respective adjacent pairs of optical resonators of the plurality of optical resonators.

14. The photon source according to claim 13, wherein A variation in resonance center frequency between adjacent optical resonators is less than a resonance linewidth of each of the plurality of optical resonators.

15. The photon source according to claim 11, wherein For a resonator in the plurality of optical resonators, The resonant frequency of the first resonator is greater than the resonant frequency of the second resonator, and wherein the resonant frequency of the third resonator is less than the resonant frequency of the first resonator, and wherein the second resonator is positioned directly adjacent to the first resonator, and the third resonator is positioned directly adjacent to the second resonator.

16. The photon source according to claim 10, wherein: The number of the plurality of optical resonators is greater than ten.

17. The photon source according to claim 10, wherein: The plurality of optical resonators is a first plurality of first optical resonators, and each first optical resonator is coupled to a corresponding second optical resonator in a second plurality of optical resonators.

18. The photon source according to claim 10, wherein: The bus waveguide is an optical resonator bus waveguide that recirculates the laser pulses.

19. The photon source of claim 18, further comprising a plurality of optical resonator bus waveguides, each optical resonator bus waveguide being optically coupled to a corresponding plurality of optical resonators.

20. The photon source of claim 11, wherein: A difference between resonance center frequencies of any two resonators of the plurality of optical resonators is less than or equal to twice the resonance line width of one of the two resonators.

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