Cascaded resonators photon pair source

Abstract

SOLUTION: A method includes: coupling a pump laser to a bus waveguide; coupling a plurality of optical resonators to the bus waveguide, wherein each optical resonator of the plurality of optical resonators has a respective resonance line width and a respective resonance center frequency, and the frequency span of the resonance center frequencies of the plurality of optical resonators is greater than a bandwidth of the pump laser; generating photon pairs in the plurality of optical resonators; and actuating the pump laser.EFFECT: A typical trade-off between the luminance and the bandwidth of resonance can be improved.SELECTED DRAWING: Figure 1A

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 62 / 941,407, filed November 27, 2019, and U.S. Provisional Patent Application No. 63 / 042,438, filed June 22, 2020, the disclosures of which are incorporated by reference in their entireties herein for all purposes. [Background technology]

[0002]

[0002] Photon pair sources are useful in a variety of technologies. For example, photonic quantum technologies would benefit from photon pair sources with improved brightness, spectral purity, reproducibility, and manufacturability. Summary of the Invention

[0003] In some embodiments, the 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 optical resonator of the plurality of optical resonators may have a respective resonance linewidth and a respective resonance frequency. In some embodiments, a frequency span of the resonance center frequencies of the plurality of optical resonators is greater than the bandwidth of the photon source pump laser.

[0004]

[0004] In some embodiments, the photon source further includes a plurality of dispersive elements coupled to the bus waveguide, one dispersive element of the plurality of dispersive elements being positioned between each adjacent pair of optical resonators of the plurality of optical resonators.

[0005] In some embodiments, the change in resonant center frequency between adjacent optical resonators is less than the resonant linewidth of each of the plurality of optical resonators.

[0006] In some embodiments, the number of the plurality of optical resonators is 2. In other embodiments, the number of the plurality of optical resonators is greater than 10.

[0007]

[0007] In some embodiments, the plurality of optical resonators is a first plurality of first optical resonators, each of which is coupled to a respective second optical resonator of a second plurality of optical resonators.

[0008] In some embodiments, the second plurality of optical resonators is coupled to a second waveguide that radiates photons.

[0009] In some embodiments, the bus waveguide is an optical resonator.

[0010] In some embodiments, the photon source includes a bus waveguide having an input region and an output region, and a plurality of optical resonators coupled in series to the bus waveguide between the input region and the output region. The output region can be configured to transmit photon pairs generated in the plurality of optical resonators in response to the input region receiving a laser pulse. In some embodiments, each optical resonator of the plurality of optical resonators has a respective resonance linewidth and a respective resonance frequency.

[0011] In some embodiments, the frequency span of the resonant center frequencies of the multiple optical resonators is greater than the bandwidth of the laser pulse received at the input region.

[0012]

[0012] In some embodiments, the optical fiber further includes a plurality of dispersion elements coupled to the bus waveguide, one dispersion element of the plurality of dispersion elements being positioned between each optical resonator of the plurality of optical resonators.

[0013] In some embodiments, the change in resonant center frequency between adjacent optical resonators is less than the resonant linewidth of each of the plurality of optical resonators.

[0014] In some embodiments, the number of the plurality of resonant optical cavities is greater than ten.

[0015]

[0015] In some embodiments, the plurality of optical resonators are a first plurality of first optical resonators, each of which is coupled to a respective second optical resonator of a second plurality of optical resonators.

[0016] In some embodiments, the bus waveguide is an optical resonator bus waveguide that recirculates the laser pulses. In some embodiments, the photon source further includes a plurality of optical resonator bus waveguides each optically coupled to a respective one of the plurality of resonant optical resonators.

[0017] In some embodiments, for a resonator in the plurality of resonators, a second resonator is positioned immediately adjacent to the first resonator and a third resonator is positioned immediately 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.

[0018]

[0018] For a better understanding of the nature and advantages of the present disclosure, reference should be made to the following description and the accompanying drawings. It should be understood, however, that each figure is provided for illustrative purposes only and is not intended as a definition of the limits of the scope of the present disclosure. Furthermore, as a general rule, unless otherwise clear from the description, when elements in different figures use the same reference numerals, the elements are generally identical or at least similar in function or purpose. [Brief explanation of the drawings]

[0019] [Figure 1A] FIG. 1 is a diagram of a cascaded resonator photon pair source using a single bus, according to an embodiment of the present disclosure. [Figure 1B] 1A-1C are diagrams of a series of resonant spectral enhancements according to embodiments of the present disclosure. [Figure 2A] FIG. 1 is a schematic diagram of the joint spectral amplitude of photons generated from a cascaded resonator photon pair source, according to an embodiment of the present disclosure. [Figure 2B]FIG. 1 is a schematic diagram of the joint spectral amplitude of photons generated from a cascaded resonator photon pair source, according to an embodiment of the present disclosure. [Figure 3] FIG. 1 is a diagram of a cascaded resonator photon pair source including separate pumps and photon buses with coupled optical resonators, according to an embodiment of the present disclosure. [Figure 4] 1 shows a simplified diagram of a pump recycling design for a cascaded resonator photon pair source according to an embodiment of the present disclosure. [Figure 5] 1 illustrates a frequency conversion system employing a cascaded resonant structure according to some embodiments. DETAILED DESCRIPTION OF THE INVENTION

[0020]

[0025] The technology disclosed herein generally relates to photon pair sources. Such sources create correlated photon pairs, each containing a photon generally referred to as a signal photon and a herald photon. Detecting the herald photon signals the presence of the signal photon for use.

[0021]

[0026] In some embodiments, photon pair sources are constructed from integrated waveguide structures of third- or second-order nonlinear optical materials (e.g., silicon, silicon nitride, silicon-rich silicon nitride, germanides, silicon-rich germanium, chalcogenide glasses, organic compounds, PZT, BTO, LiNb, etc.). Pump lasers are coupled to these waveguide structures, which can cause spontaneous four-wave mixing (SFWM) or spontaneous parametric down-conversion (SPDC). In the SFWM process, two pump laser photons can be converted into a pair of daughter photons (e.g., a signal photon and a herald photon) within the nonlinear optical material. Due to energy conservation, the generated signal and herald photons can be at frequencies symmetrically distributed around the pump frequency. In general, such spectral correlation can cause the heralded signal photon to become mixed, in which case the light source does not create identical photons on subsequent attempts. The frequency distribution of the generated pairs (defined by the joint spectral amplitude (JSA)) is controlled by the interplay between energy and momentum conservation in the spontaneous pair production process.

[0022]

[0027] Some embodiments use an optical resonator. In such embodiments, the optical resonator reshapes the spectral density of states (defined by the spectral resonance enhancement) so that photon pair generation is enhanced near the resonance frequency. The optical resonator may be implemented as a traveling-wave resonant structure. One implementation is a loop in a waveguide shaped as a ring, racetrack, or other closed curve coupled to a bus waveguide. Another implementation uses mirrors and semitransparent mirrors to form a closed beam path. The optical resonator may also be implemented as a standing-wave resonant structure, such as a Fabry-Perot cavity, a distributed Bragg grating in a photonic crystal cavity, etc.

[0023]

[0028] Photon pair sources using optical resonators in integrated optics can be used to increase the brightness of SFWM photon pair generation compared to non-resonator versions, where brightness is the probability of generating a photon pair per pump photon. The increase in brightness is caused by a spectral resonance enhancement of the pump, signal, and readout near the resonant frequency. To increase the brightness, v p =v res M , v s =v res M-n , v h =v res M+n The resonance condition can be satisfied. p , v s , v h are the frequencies of the pump, signal, and herald fields, respectively. Also, v res In the above, the upper script indicates the resonance number. M is a positive integer, and n is an arbitrary integer. The resonance condition of order M is

number

[0024]

[0029] 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 using many single-photon sources, for example for linear optical quantum computing, require heralded photons from different sources to interfere with a beam splitter to create an entangled state of photons. However, for the heralded photons created by two sources to interfere sufficiently, each source must be nearly identical to the other (e.g., the resonances must be nearly identical). This imposes strict constraints on the alignment of the resonant frequencies of each resonator source when only a single resonator is used.

[0025]

[0030] A source is spectrally pure (the JSA is separable) if the JSA can be expressed as the product of the herald spectral distribution and the signal spectral distribution. In some embodiments of a photon pair source based on a single optical resonator, spectral purity can be optimized by tuning the resonant bandwidth of the system at the herald, signal, and pump resonances.

[0026]

[0031] The technology disclosed herein relates to cascaded resonator sources in which photon pairs generated in several optical resonators are coherently added, resulting in improved spectral purity and brightness. By cascading multiple resonator sources on a single bus and coherently combining them, the typical tradeoff between resonance brightness and bandwidth can be improved. In some embodiments, cascaded sources are disclosed that can create substantially identical photons even when the resonators they are composed of have shifted resonance frequencies.

[0027]

[0032] The cascaded resonator sources described and disclosed herein can be used in any optical device, including but not limited to quantum computing, quantum communications, quantum metrology, spectroscopy, LiDAR, and other applications.

[0028]

[0033] To better understand the features and aspects of a light source that coherently combines multiple resonators on a single bus, further context for the present disclosure is provided by describing implementations of cascaded light sources according to embodiments of the present disclosure. These embodiments are, for example, merely examples, and other embodiments may be used for other photon sources and photonic devices.

[0029]

[0034] FIG. 1A illustrates a cascaded-cavity photon pair source 100 according to an embodiment of the present disclosure. The cascaded-cavity photon pair source 100 can include a waveguide 105 and a series of optical resonators 110_1, 110_2, ..., 110_n, each having a different resonant frequency. For example, pumping light from a laser pump 122 can be coupled to an input region 130 of the waveguide 105 and into each of the ring resonators 110_1, 110_2, ..., 110_n. The pump laser can have a programmed power spectral density and spectral chirp. Each optical resonator 110_1, 110_2, ..., 110_n can include a waveguide loop such that a resonance for light having a certain wavelength can occur when the optical path length of the ring resonator is an integer number of wavelengths of light. Each optical resonator can support multiple resonances at multiple wavelengths that satisfy the resonance condition.

[0030]

[0035] 1B shows a plot of the spectral density of states and resonance enhancement as a function of wavelength for multiple resonators, according to some embodiments. Each distribution shown (also referred to herein as a resonance curve, or simply resonance) is centered at the "resonance frequency" of the respective resonator, and the curves are referred to herein as "resonator resonances." Each resonator resonance has a spectral width defined to be the full width at half maximum (FWHM) of the distribution. This width is referred to herein as the "resonance linewidth." The pump, signal, and herald resonance frequencies are expressed as v p、j , v s、j , v h、jwhere j labels the resonator structure itself, e.g., the ring shown in FIG. 1A. However, it is important to note that the index j (counting the resonances in FIG. 1B from lowest to highest resonant frequency) is not tied to the index n (representing the physical location of the resonator on the bus) above; i.e., the resonator frequencies do not have to monotonically increase or even ascending (or descending) as one moves from the input end to the output end. In FIG. 1B, the resonator resonances (for any of the three fields) of five optical resonators (which may be positioned anywhere along the bus) are shown, with the index j ranging from 1 to 5, corresponding to 150a to 150e. A shift in resonant frequency between different resonators (also referred to herein as a resonance shift) can be obtained by slight changes in the optical resonator waveguide width or optical resonator length or another resonator characteristic.

[0031]

[0036] Returning to FIG. 1A , a series of optical resonators are optionally 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 paired photons generated by the light source. In the figure, the resonators are labeled 110_1, 110_2, ..., 110_n, where index n indicates the physical location of the resonator relative to the input side of the device (110_1 is the first input resonator, 110_2 is the second resonator positioned immediately adjacent to resonator 110_1, etc.). 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 (low to high) and evenly spaced. In other embodiments, the resonant frequencies of the resonators indexed by n may not be monotonically increasing or decreasing functions of n as one moves down the device; i.e., the resonant frequency of a first resonator may be greater than the resonant frequency of a second resonator (where the second resonator is positioned immediately adjacent to the first resonator), and the resonant frequency of a third resonator (where the third resonator is positioned immediately adjacent to the second resonator) may be less than the resonant frequency of the first resonator. In some embodiments, having a second resonant frequency less than the first resonant frequency and a third resonant frequency greater than the first can improve the spectral purity of the light source. As used herein, resonant frequency

number

[0032]

[0037] Some embodiments may use additional, optional dispersive elements to adjust the optical phase between the pump, signal, and idler between the two optical resonators. FIG. 1 illustrates device 100 in which Δk 115a is the momentum mismatch between the pump, signal, and idler. In some embodiments, the dispersive elements may be implemented using any type of dispersive structure, including, but not limited to, waveguides with different geometries, multimode dispersion-engineered chirped gratings, or chirped mirrors. The dispersive elements may be coupled to the bus in any manner, for example, formed directly from and / or integrated into the bus waveguide, or optionally optically coupled to the bus (e.g., via direct or evanescent coupling).

[0033]

[0038] According to some embodiments, the resonator resonances of a resonator can overlap, as shown in FIG. 1B. That is, when the resonator resonances are plotted as a function of wavelength (or equivalently, frequency), the areas under the curves substantially overlap. 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 in the range of a few hundred picometers, e.g., 100 picometers, or 50-400 picometers (5-50 GHz, if using units of frequency).

[0034]

[0039] In some embodiments, the pump pulse spectrum is Gaussian 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 second-order spectral phase). The FWHM of the pump spectrum is determined by the frequency span of the resonance.

number

[0035]

[0040] FIG. 2A shows a graph 200 of the JSA of the cascaded resonator photon pair source 100. Region 205 shows the pump function, illustrating the energy conservation of photon pair generation from a pump pulse. Region 210 shows the collective spectral resonance enhancement due to the multiple resonators in the cascaded resonator source. This region is nearly orthogonal to the pump function when the pump, signal, and Held spectral enhancements are shifted together from one resonator to another. The interaction of the pump function and the collective spectral enhancement can result in a JSA that is approximately two-dimensional Gaussian, as shown by region 215. This JSA can be nearly separable, resulting in high spectral purity. The cascaded resonator source 100 can be a relatively bright, spectrally pure photon pair source. High purity means >99%, while low or typical purity is approximately 90%. In some embodiments, for example, the JSA purity shown in region 215 can be 99.9%, although in other embodiments, the purity can be different.

[0036]

[0041] The cascaded resonator source 100 can be robust to long-range process variations. More specifically, due to manufacturing imperfections, all v p、j , v s、j , v h、j are often shifted together. If all the resonant frequencies of a cascaded resonator source are shifted together, the pumps "select" a subset of the resonators 110_1, ..., 110_n with which to interact. The resulting JSA can be nearly identical to that of the nominal source.

[0037]

[0042] FIG. 2B shows a graph of a cascaded resonator source illustrating the effect of process variations on the JSA. FIG. 2A shows the collective spectral enhancement of a nominal source, while FIG. 2B shows a source affected by process variations, such as a shift in all resonant frequencies due to changes in waveguide film thickness. In this configuration, the result of process variations simply shifts the collective spectral resonance enhancement to a new position 210'. However, because the frequency span of the collective spectral resonance enhancement is larger than the shift caused by process variations, region 215 is largely unaffected. This allows the system to be robust to variations in the manufacturing process.

[0038]

[0043] The above descriptions of properties and operation may be considered approximations and / or simplifications, and the present disclosure is in no way limited by these descriptions. In some embodiments, the complete simulation infrastructure includes pump propagation, dispersion, nonlinearity, loss, multi-photon, non-perturbative effects, and other considerations.

[0039]

[0044] FIG. 3 illustrates one embodiment of a cascaded light source 300 in accordance with embodiments of the present disclosure. In this embodiment, the series of optical resonators 303 includes one row of optical resonators 310a...310n and another row of optical resonators 320a...320n, although in other embodiments, the series of optical resonators can have other suitable shapes beyond this 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 positioned to couple light into each optical resonator 320a...320n. Each optical resonator 320a...320n is separated by a respective phase shift 315a...315n (labeled φ). Each optical resonator 320a...320n is positioned to couple light into its respective optical resonator 310a...310n, which couples the light into the second waveguide 325.

[0040]

[0045] In other embodiments, coupled optical resonators can be used instead of a single optical resonator. In further embodiments, quasi-phase matching techniques can be used that use spatially modulated nonlinear properties to manipulate momentum matching in the pair creation process.

[0041]

[0046] The above-described photon pair sources may offer myriad improvements in performance, including, but not limited to, the following. First, the disclosed structure can decouple the bandwidth of the heralded photons from the source brightness. In comparison, previous optical resonator photon pair sources achieve higher brightness by narrowing the resonant frequency. The cascaded resonator source disclosed herein removes this constraint, thereby significantly increasing the design space. For example, the bandwidth may be selected taking into account other system considerations.

[0042]

[0047] A second improvement provided by the photon pair sources described herein is that two separate photon pair sources can produce substantially identical heralded photons, independent of the resonant frequency shifts imparted to any optical cavity by long-range process variations, when the two photon pair sources share substantially identical pumps. This feature allows different photon pair sources to produce substantially identical heralded photons, thereby reducing by orders of magnitude the trimming and / or tuning required to achieve frequency alignment of the different photon pair sources.

[0043]

[0048] A third improvement is that the photon pair sources described herein can create Gaussian photons. In some embodiments, a Gaussian distribution is a desirable single-photon wave packet shape because it is robust to dispersion, timing jitter, etc. In comparison, typical single optical resonator sources do not create Gaussian photons.

[0044]

[0049] Another advantage is that the photon pair sources described herein can achieve high spectral purity.

[0045]

[0050] FIG. 4 shows a simplified diagram of one embodiment of a miniature pump recycling cascaded light source 400. As shown in FIG. 4, the recycling cascaded resonator source 400 includes multiple recycling resonator structures 405a...405n, each including multiple rings 410 coupled to a respective resonator bus 415. In some embodiments, the cascaded light source 400 offers the additional advantage that the pump is spectrally unchanged as it exits the light source, but is simply delayed. If the bus waveguide is converted into a resonator, this additional delay induced by the cascaded resonator source can enable matching the cavity length for synchronously pumping the light source. More specifically, if the pump laser repetition rate is matched to the delay accumulated in the cascaded resonator source, the pump pulse can be enhanced by the cavity, thus significantly reducing the required external pump power. In some embodiments, when critically coupled, further enhancement by a factor of up to two orders of magnitude can be generated.

[0046]

[0051] Although cascaded light sources are described and illustrated as one particular type of light source, embodiments of the present disclosure are suitable for use with numerous systems, including, but not limited to, quantum computers and LiDAR systems. The collective spectral enhancement created via cascaded resonators can be used by any parametric wave mixing process (e.g., but not limited to, single harmonic generation, difference frequency generation (DFG), and / or optical parametric oscillation).

[0047]

[0052] FIG. 5 illustrates a frequency conversion system 500 based on a cascaded resonator structure according to some embodiments. The structure is similar to the photon pair source structure described in detail above with respect to FIG. 1, and for clarity, elements will not be repeated here. In some embodiments, the input to the cascaded resonator frequency conversion system may include two lasers, FREQ.2 and FREQ.1, each having a different frequency. These lasers may be input to an optical combining device, such as a wavelength division multiplexing device, shown here as WDM 505. In this case, the cascaded resonator structure may generate frequency mixing between the inputs, such as difference or sum frequency generation. In some embodiments, an output WDM 515 may be used to separate the converted frequencies (e.g., sum and / or difference frequencies) from the input laser light generated by lasers FREQ.2 and FREQ.1. This frequency conversion may be useful for generating new frequencies from FREQ.2 and FREQ.1 when FREQ.2 and FREQ.1 are not as useful as the converted frequencies. For example, perhaps FREQ.2 and FREQ.1 are not easily detected, but the converted frequencies are fairly or easily detected by available detectors. Cascaded resonator frequency conversion structures can improve the brightness of frequency mixing when compared to other methods for frequency conversion, including waveguides or single optical resonators.

[0048]

[0053] In the foregoing specification, embodiments of the present disclosure have been described with reference to numerous specific details that may vary from implementation to implementation. Accordingly, the specification and drawings should be considered in an illustrative rather than a restrictive sense. The sole and exclusive indication of the scope of the present disclosure, and what is intended by the applicant to be the scope of the present disclosure, is the literal equivalents of the claims issuing from this application in the specific form in which such claims issue, including any subsequent amendments. The specific details of particular embodiments can be combined in any suitable manner without departing from the spirit and scope of the embodiments of the present disclosure.

[0049]

[0054] Additionally, spatially relative terms such as "bottom or top" may be used to describe the relationship of an element and / or feature to another element(s) and / or feature(s), as shown, for example, in the figures. It will be understood that spatially relative terms are intended to encompass different orientations of the device during use and / or operation in addition to the orientation shown in the figures. For example, if the device in the figures is turned upside down, an element described as being on the "bottom" surface may be oriented "above" the other element or feature. The device may be oriented in other ways (e.g., rotated 90 degrees or to other orientations), and the spatially relative descriptors used herein will be interpreted accordingly.

Claims

1. a bus waveguide; a pump laser coupled to the bus waveguide; a plurality of optical resonators coupled to the bus waveguide, each optical resonator of the plurality of optical resonators having a respective resonance linewidth and a respective resonance frequency, wherein a frequency span of resonance center frequencies of the plurality of optical resonators is greater than a bandwidth of the pump laser, the pump laser being a photon source pump laser; A photon source comprising:

2. 10. The photon source of claim 1, further comprising a plurality of dispersive elements coupled to said bus waveguide, one dispersive element of said plurality of dispersive elements positioned between each adjacent pair of optical resonators of said plurality of optical resonators.

3. 10. The photon source of claim 1, wherein the change in resonance center frequency between adjacent optical resonators is less than the resonance linewidth of each of said plurality of optical resonators.

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

5. The photon source of claim 1 wherein the number of said plurality of optical resonators is greater than ten.

6. 10. The photon source of claim 1, wherein the plurality of optical resonators is a first plurality of first optical resonators, each first optical resonator coupled to a respective second optical resonator of a second plurality of optical resonators.

7. The photon source of claim 6 wherein the second plurality of optical resonators are coupled to a second waveguide that radiates photons.

8. The photon source of claim 1 wherein said bus waveguide is an optical resonator.

9. For a resonator within the plurality of optical resonators, the resonant frequency of the first resonator is greater than the resonant frequency of the second resonator, and the resonant frequency of the third resonator is less than the resonant frequency of the first resonator; 10. The photon source of claim 1, wherein the second resonator is positioned immediately adjacent to the first resonator and the third resonator is positioned immediately adjacent to the second resonator.

10. a bus waveguide having an input region and an output region; a plurality of optical resonators coupled in series to the bus waveguide between the input region and the output region, the output region configured to transmit photon pairs generated in the plurality of optical resonators in response to the input region receiving a laser pulse; A photon source comprising:

11. The photon source of claim 10 , wherein each optical resonator of said plurality of optical resonators has a respective resonant linewidth and a respective resonant frequency.

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

13. 13. The photon source of claim 12, further comprising a plurality of dispersive elements coupled to said bus waveguide, one dispersive element of said plurality of dispersive elements positioned between each adjacent pair of optical resonators of said plurality of optical resonators.

14. 14. The photon source of claim 13, wherein the change in resonant center frequency between adjacent optical resonators is less than the resonant linewidth of each of said plurality of optical resonators.

15. For a resonator within the plurality of optical resonators, the resonant frequency of the first resonator is greater than the resonant frequency of the second resonator, and the resonant frequency of the third resonator is less than the resonant frequency of the first resonator; 12. The photon source of claim 11, wherein the second resonator is positioned immediately adjacent to the first resonator and the third resonator is positioned immediately adjacent to the second resonator.

16. The photon source of claim 10 wherein the number of said plurality of optical resonators is greater than ten.

17. 11. The photon source of claim 10, wherein the plurality of optical resonators is a first plurality of first optical resonators, each first optical resonator coupled to a respective second optical resonator of a second plurality of optical resonators.

18. The photon source of claim 10 wherein said bus waveguide is an optical resonator bus waveguide that recirculates said laser pulses.

19. 20. The photon source of claim 18, further comprising a plurality of optical resonator bus waveguides each optically coupled to a respective one of the plurality of resonant optical cavities.

20. 11. The photon source of claim 10, wherein the difference in the resonant frequencies of any two of the plurality of optical resonators is less than or equal to twice the resonant linewidth of one of the two resonators.

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