Optical resonator with intracavity nonlinear optics

Abstract

An optical resonator includes a plurality of mirrors positioned to reflect light along a closed path, thereby defining an optical axis. The optical resonator also includes one or more intracavity lenses positioned along the optical axis to establish a resonator mode whose waist that is located along the optical axis. The optical resonator also includes an intracavity nonlinear optical element that implements a nonlinear frequency-mixing process within the optical resonator. When input light is coupled into the optical resonator to excite the resonator mode, the intracavity nonlinear optical element nonlinearly converts at least some of the input light into nonlinearly generated light. This nonlinearly generated light may then be coupled out of the optical resonator, such as via transmission through one of the mirrors. In some embodiments, the waist is five microns or less. In some embodiments, the finesse of the optical resonator is 100 or less.

Description

OPTICAL RESONATOR WITH INTRACAVITY NONLINEAR OPTICSRELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application No. 63 / 536,533, filed 05 September 2023, the entirety of which is incorporated herein by reference.STATEMENT REGARDING FEDERALLYSPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with Government support under contract FA9550-22- 1-0279, awarded by the Air Force Office of Scientific Research, and under contract W91 1NF- 23-1-0053 awarded by the Department of Defense. The Government has certain rights in the invention.BACKGROUND

[0003] Control of light is a critical challenge in quantum science. For example, different wavelengths of light are used for optimal coupling to different types of atoms, emitters, or qubits. Similarly, different wavelengths are optimized for transmission along different types of optical fiber. These tasks, and others, require nonlinear optical processes. These processes typically have to be introduced sequentially, incurring complexity and loss.SUMMARY

[0004] In cavity quantum electrodynamics (cQED), it is frequently ideal to engineer the single-particle cooperativity g to be as large as possible. Defined as g = g2 / id the cooperativity g quantifies the competition between (i) coherent information exchange at rate g between a cavity and an atom (e.g., a neutral atom or ion) located within the cavity and (ii) the decoherence rates T and K of the atom and cavity, respectively. Increasing g increases the photon collection probability Pc= 77 / (1 + 77) that the atom emits into (or absorbs from) a mode of the cavity as opposed to free space. Increasing 77 also reduces the failure rate 271 / 77x / 2of cavity-mediated quantum information transfer between two atoms trapped in separate optical cavities.

[0005] Another way to express the cooperativity is 77 « 0.2 T A2 / IVQ , where T is the cavity finesse, w0is the minimum diffraction-limited waist of the cavity mode, and A is the wavelength of the atomic transition and cavity resonance. The finesse T can be interpreted asthe number of round trips that light in the optical cavity makes before lost due to absorption or transmission through a cavity mirror. This alternative expression for 77 can be interpreted geometrically: the resonant cross-section that an atom presents for absorption of light is ~A2and the area of the cavity mode going past the atom is ~WQ . Therefore, for each pass of the cavity light past the atom, the absorption probability is ~ A2 / WQ . The optical cavity simply enhances this single-pass absorption probability by the number of passes ".

[0006] Prior-art optical cavities used for cQED achieve a high cooperativity 7] by employing a relatively large waist w0and very high finesse F. Such optical cavities are typically fabricated using concave mirrors having very high reflectivities, typically greater than 99.999%. The highest finesses of nearly 106have been achieved by improving superpolishing and dielectric coatings of these mirrors. Due to their high finesse F, these prior-art optical cavities are challenging to align and stabilize. Furthermore, specialized handling techniques are needed to prevent airborne particulate matter (e.g., dust) from landing on the mirror surfaces; such contamination reduces the finesse F by increasing scatter. Similarly, mounting the optical cavity inside a vacuum chamber, as needed for atom trapping, puts stringent cleanliness requirements on the vacuum system to prevent contaminants (e.g., oil) from landing on the mirrors.

[0007] One aspect of the present embodiments is the realization that increasing the single-particle cooperativity r] places no significant restrictions on the cavity length L. The idea that cQED requires a small mode volume V is a misnomer that arose by writing the Purcell factor as FP= 3A32 / (4TT27). The Purcell factor FPquantifies how much an emitter’s spontaneous emission rate is enhanced when it is located inside a resonant cavity having quality factor Q. The expression makes small mode volume V seem advantageous to increasing the Purcell factor FP, but ignores the fact that the Q drops as the cavity length L decreases. What is relevant for cQED is actually the finesse F = Qc / 2Lfc, where fcis the resonant frequency of the cavity mode. When written in terms of the finesse F and assuming that the mode volume V~LWQ , the Purcell factor FPis identical, up to unit factors, to the single-particle cooperativity 77 and therefore only depends on F , A, and w0. Thus, for a fixed value of A there are only two independent experimental parameters that control the cooperativity 77: the finesse F and the waist w0.

[0008] The present embodiments include optical resonators that use intracavity lenses to achieve a waist w0that is smaller than that achieved with the prior-art optical cavities described above. Since 77 oc I / WQ , the smaller waist w0results in a significantly largercooperativity i] that can be used to lower the finesse F . For example, the optical cavity can generate a waist of w0« 500 nm at A = 780 nm (the D2transition for Rb), yielding a cooperativity of 77 « 9.4 for a finesse of only F = 20. This value of the cooperativity r) is so large that an atom trapped near the waist emits a photon ten times faster into the optical cavity than into free space. When the atom is implemented as a qubit, the emitted photon has a greater- than-90% chance of being collected by the optical cavity. Furthermore, due to the lower finesse F, the cavity length L only needs to be stabilized to within A / (2F) = A / 20, making the optical cavity easier to align and stabilize than prior-art optical cavities. Also due to the lower finesse F, additional optical components can be placed within the cavity without significantly degrading the finesse F. The lower finesse F also eases requirements on handling, assembly, and vacuum cleanliness since an increase in optical scatter off of surface contaminants no longer significantly degrades the finesse F .

[0009] Another aspect of the present embodiments is the realization that when an optical cavity has lower finesse F, a nonlinear optical element can be placed inside the optical cavity without degrading the finesse F, and therefore without degrading the cooperativity 77. The nonlinear optical element may be a nonlinear crystal (e.g., bulk, periodically poled, voltage-controlled, etc.) whose input and output facets are anti-reflection coated to reduce loss from reflections. The optical cavities of the present embodiments may have a relatively low finesse (e.g., F < 100), in which case residual absorption of the cavity mode by the nonlinear crystal is negligible compared to other loss mechanisms and therefore results in little, if any, reduction of the finesse F. By contrast, residual absorption inside an optical cavity with relatively high finesse (e.g., F > 105) will significantly reduce the finesse F, thereby prohibiting the use of intracavity nonlinear elements and devices in such high-finesse cavities for many applications.

[0010] The present embodiments include an optical resonator having one or more intracavity nonlinear optical elements. Such an optical resonator is particularly useful for quantum-science applications where the cooperativity can be large by making the intracavity waist small (e.g., five microns or less) and therefore the cavity finesse F relatively low. Examples of the one or more intracavity nonlinear optical elements include, but are not limited to, bulk nonlinear crystals (e.g., potassium titanyl phosphate (KTP), lithium niobate (LiNbOs), potassium niobate (KNbCh), barium borate (BBO), gallium selenide (GaSe), lithium tantalate (LiTaCh)), and periodically poled crystals (e.g., periodically poled lithium niobate (PPLN)). Any nonlinear crystal (bulk or periodically poled) may be doped (e.g., with MgO) or undoped.The one or more intracavity nonlinear optical elements may include different combinations of such elements (e.g., an EOM and a bulk nonlinear crystal).

[0011] Some of the nonlinear optical processes that can be performed using the one or more intracavity nonlinear optical elements include, but are not limited to, second-harmonic generation, third-harmonic generation, sum-frequency generation, difference-frequency generation, spontaneous parametric down-conversion, four-wave mixing, cross-phase modulation, and stimulated Brillouin scattering. The one or more intracavity optical elements are “nonlinear” in that they implement optical processes via the nonlinear susceptibility (as opposed to the linear, or first-order, susceptibility x^)- The nonlinear optical process may be a second-order effect that depends on the second-order susceptibilitya third-order effect that depends on the third-order susceptibility x^\ahigher-order effect that depends on a higher-order susceptibility, or any combination thereof. The one or more intracavity nonlinear optical elements may perform one or more different nonlinear optical processes in combination. For example, each intracavity nonlinear optical element may uniquely implement one nonlinear optical process.

[0012] The increase in photon collection probability Pcthat can be achieved with the present embodiments will substantially improve state detection of tweezer-array apparatus and cQED setups. Accordingly, the present embodiments may be used to create a photonic-matter interface that efficiently converts quantum information between photonic qubits and matterbased qubits (e.g., trapped ions, neutral atoms, defects in diamond, etc.). Two of these interfaces could be used to optically couple matter-based qubits located in spatially separated traps or even separate vacuum systems. Such an optical coupling system could increase the number of qubits in a quantum computer, thereby improving qubit scaling. For example, the optical coupling setup could be used to efficiently transfer optical information between spatially disparate ion traps, thereby enabling quantum computing beyond the melting-size limit of a single ion crystal.

[0013] Another application of the present embodiments is sensing with color centers. Here, the optical cavity improves light gathering, thereby enabling faster, more accurate readout of the color center state. Such a scanning-cavity microscope would rely upon a small waist iv0rather than high finesse, greatly relaxing material constraints. As another application, the optical cavity could be used for an orders-of-magnitude speed-up in state detection for atom-array quantum simulators and computers, thereby enabling optically-mediated non-local gates and real-time feedback-based error correction.

[0014] In embodiments, an optical resonator includes a plurality of mirrors positioned to reflect light along a closed path. The plurality of mirrors define an optical axis of the optical resonator. The optical resonator also includes one or more intracavity lenses located along the optical axis. The one or more intracavity lenses are configured such that the optical resonator has a resonator mode whose waist is located along the optical axis. The optical resonator also includes an intracavity nonlinear optical element located along the optical axis. The intracavity nonlinear optical element is configured to implement a nonlinear frequency-mixing process with light exciting the resonator mode.BRIEF DESCRIPTION OF THE FIGURES

[0015] FIG. 1 is a side view of an optical resonator, in embodiments.

[0016] FIG. 2 is a side view of an optical resonator, in embodiments.

[0017] FIG. 3 is a side view of an optical resonator, in embodiments.

[0018] FIG. 4 is a side view of an optical resonator, in embodiments.

[0019] FIG. 5 is a side view of an optical resonator, in embodiments.

[0020] FIG. 6 is a side view of an optical resonator, in embodiments.

[0021] FIG. 7 is a side view of an optical resonator, in embodiments.

[0022] FIG. 8 A is a side view of an optical resonator that is one example of the optical resonator of FIG. 1 , in embodiments.

[0023] FIG. 8B is a plot of conversion efficiency versus pump power for the optical resonator of FIG. 8A.

[0024] FIG. 8C shows two plots that illustrate the formation of an avoided crossing between modes of the optical resonator of FIG. 8A.DETAILED DESCRIPTION

[0025] FIG. 1 is a side view of an optical resonator 100, in accordance with some of the present embodiments. The optical resonator 100 includes a plurality of mirrors 102 that are positioned to reflect light along a closed path. In the case of FIG. 1 , the plurality of mirrors 102 include a first mirror 102(1 ) and a second mirror 102(2) that are counterfacing to create a Fabry- Perot cavity. As shown below, the plurality of mirrors 102 may be alternatively configured to form a ring cavity. The plurality of mirrors 102 define an optical axis 122 that, in the case of FIG. 1, is parallel to the z axis of a right-handed Cartesian coordinate system 120.

[0026] The optical resonator 100 includes a first intracavity lens 110(1) and a second intracavity lens 110(2) that are located along the optical axis 122. The optical resonator 100has a mode 124 whose waist iv0lies between the lenses 110(1) and 110(2). The waist iv0is the smallest 1 / e radius of the mode 124 (where the mode 124 is assumed to have a Gaussian transverse profile). Accordingly, the mode 124 has a 1 / e diameter of 2iv0at the waist. The mode 124 may be excited with excitation light 130 that is coupled into the optical resonator 100 via transmission through one or both of the mirrors 102(1) and 102(2).

[0027] The optical resonator 100 includes one or more intracavity nonlinear optical elements 104. In the example of FIG. 1, the one or more intracavity nonlinear optical elements 104 is a periodically poled crystal that implements frequency / wavelength-dependent outcoupling through the first mirror 102(1). The periodically poled crystal is pumped with a pump beam 132 that is coupled into the optical resonator 100 with an intracavity dichroic mirror 106. Alternatively, the pump beam 132 may be coupled into the optical resonator 100 via transmission through the first mirror 102(1) or the second mirror 102(2). One or more surfaces of the mirrors 102(1) and 102(2) may be anti-reflection coated at the wavelength of the pump beam 132 so that residual pump light (i.e., a portion of the pump beam 132 that is not absorbed by the periodically poled crystal) couples out of the optical resonator 100 via transmission through one or both of the mirrors 102(1) and 102(2).

[0028] In FIG. 1, the periodically poled crystal is configured to perform nonlinear frequency mixing (also referred to as frequency generation). As shown, mixing of the pump beam 132 with the cavity mode 124 produces a photon 134 at a wavelength that does not resonate in the optical resonator 100. One or both of the mirrors 102(1) and 102(2) may be antireflection coated at the wavelength of the photon 134 to facilitate coupling of the photon 134 out of the optical resonator 100. Alternatively, the mirrors 102(1) and 102(2) may be coated for high reflectivity at the wavelength of the photon 134 to facilitate excitation of a corresponding mode of the optical resonator 100.

[0029] In general, each of the intracavity lenses 110(1) and 110(2) may be any type of lens or lens assembly known in the art. Examples include, but are not limited to, biconvex lenses, plano-convex lenses, doublets (e.g., achromats), triplets, and Fresnel lenses. The lenses 110(1) and 110(2) may be of the same type or different types. Where the lenses 110(1) and 110(2) are of the same type, they may have different parameters (e.g., numerical aperture, focal length, clear aperture, etc.), similar parameters, or a combination thereof.

[0030] FIG. 2 is a side view of an optical resonator 200, in accordance with some of the present embodiments. The optical resonator 200 is similar to the optical resonator 100 of FIG. 1 except that it uses a curved mirror in place of one of the intracavity lenses 110.Specifically, the optical resonator 200 includes a first mirror 202(1) and a second mirror 202(2) that form a Fabry-Perot cavity. The second mirror 202(2) is concave (e.g., spherical). The optical resonator 200 includes an intracavity lens 210 that cooperates with the second mirror 202(2) to form the waist w0therebetween. The optical resonator 200 may be excited with the pump beam 130, which couples into the cavity via transmission through the first mirror 202(1).

[0031] FIG. 3 is a side view of an optical resonator 300, in accordance with some of the present embodiments. The optical resonator 300 is similar to the optical resonator 100 of FIG. 1 except that it uses a planar mirror at the waist w0. Specifically, the optical resonator 300 includes a first mirror 302(1) and a second mirror 302(2) that is planar. The optical resonator 100 includes an intracavity lens 310 that cooperates with the second mirror 302(2) to form the waist w0at the surface of the second mirror 302(2). Affixed to the front surface of the second mirror 302(2) is a sample 314 containing nonlinear quantum emitters (e.g., nitrogen-vacancy centers in diamond, quantum dots, etc.).

[0032] FIG. 4 is a side view of a optical resonator 400, in accordance with some of the present embodiments. The optical resonator 400 is similar to the optical resonator 100 of FIG. 1 except that it forms a ring cavity instead of a Fabry-Perot cavity. Specifically, the optical resonator 400 includes a first mirror 402(1), a second mirror 402(2), and a third mirror 402(3) that form a triangular- shaped ring cavity. The optical resonator 400 also includes a first intracavity lens 410(1) and a second intracavity lens 410(2) that cooperate to form the waist w0therebetween. A traveling- wave resonant mode of the optical resonator 400 may be excited by transmitting pump light 130 through any of the mirrors 402. The photon 134 generated by the nonlinear optical element 104 may be coupled out of the optical resonator 400 via transmission through any of the mirrors 402.

[0033] FIG. 5 is a side view of an optical resonator 500, in accordance with some of the present embodiments. The optical resonator 500 is similar to the optical resonator 400 of FIG. 4 except that it uses a pair of off-axis parabolic resonators to form the ring cavity. Specifically, the optical resonator 500 includes a first mirror 502(1), a second mirror 502(2), a third mirror 502(3), and a fourth mirror 502(4) that form a rectangular- shaped ring cavity. Instead of using intracavity lenses, the first mirror 502(1) and second mirror 502(2) are off- axis parabolic mirrors positioned such that the waist w0is formed therebetween. A travelingwave resonant mode of the optical resonator 500 may be excited by transmitting pump light 130 through any of the mirrors 502. The photon 134 generated by the nonlinear optical element104 may be coupled out of the optical resonator 500 via transmission through any of the mirrors 502.

[0034] FIG. 6 is a side view of an optical resonator 600, in accordance with some of the present embodiments. The optical resonator 600 is similar to the optical resonator 100 of FIG. 1 except that it uses a pair of off-axis parabolic resonators to form the waist iv0. Specifically, the optical resonator 600 includes a first mirror 602(1), a second mirror 602(2), a third mirror 602(3), and a fourth mirror 602(4) that form a multi-leg Fabry-Perot cavity. The first mirror 602(1) and second mirror 602(2) are off-axis parabolic mirrors that are positioned to form the waist w0therebetween. A standing-wave resonant mode of the optical resonator 600 may be excited by transmitting pump light 130 through the third mirror 602(3) or fourth mirror 602(4). Similarly, the photon 134 generated by the nonlinear optical element 104 may be coupled out of the optical resonator 600 via transmission through the third mirror 602(3) or fourth mirror 602(4).

[0035] FIG. 7 is a side view of an optical resonator 700, in accordance with some of the present embodiments. The optical resonator 700 is similar to the optical resonator 600 of FIG. 6 except that it uses only one off-axis parabolic resonator to form the waist iv0. Specifically, the optical resonator 700 includes a first mirror 702(1), a second mirror 702(2), and a third mirror 702(3) form a multi-leg Fabry-Perot cavity. The first mirror 702(1) is planar, being located near the waist iv0. The second mirror 702(2) is an off-axis parabolic mirror that cooperates with the first mirror 702(1) to form the waist iv0near the reflective surface of the first mirror 702(1). A standing-wave resonant mode of the optical resonator 700 may be excited by transmitting pump light 130 through the third mirror 702(3). Similarly, the photon 134 generated by the nonlinear optical element 104 may be coupled out of the optical resonator 700 via transmission through the third mirror 702(3).

[0036] In any of the embodiments described herein, the optical resonator may further include an intracavity EOM used to rapidly tune the resonance frequencies of the optical resonator. The intracavity EOM may also be used to perform rapid cavity dumping, finesse tuning, and mode conversion via a frequency-dependent outcoupling mirror (e.g., realized as a pair of mirrors).

[0037] In some embodiments, the effective resonator finesse T is adjusted by outcoupling at a secondary wavelength. For example, the optical cavity may be constructed (e.g., with high-reflectivity coatings) to resonate at a primary wavelength near= 780 nm. One of the cavity mirrors may be anti-reflection coated at 1530 nm. A pump beam at 1530 nmapplied to the nonlinear optical element (e.g., a periodically poled crystal) converts some of the light at 780 nm to light at 1530 nm that is transmitted through the AR-coated mirror on each roundtrip.

[0038] In some embodiments, an optical resonator generates a single cavity mode that operates simultaneously at multiple wavelengths to directly, coherently, and optically control and couple atoms of different species (e.g., 780 nm for rubidium and 852 nm for cesium). The optical resonator may generate small waists (at each of the multiple wavelengths) in different vacuum chambers, thereby coupling atoms of different species within one and the same cavity mode.

[0039] In some embodiments, the nonlinear optical element is used to hybridize different resonator modes at different frequencies (or corresponding wavelengths). This hybridization may be implemented via sum-frequency generation by pumping a nonlinear crystal with a pump beam having a pump frequency that is at or near the difference frequency of the two resonator modes, (see section “Experimental Demonstration” below). Furthermore, this resonator-mode hybridization may be implemented with a laser field that is not spatially uniform so as to break the orthogonality between the spatial profiles of the resonator modes.

[0040] In some embodiments, the optical resonator uses the intracavity nonlinear optical element to generate squeezed states of light via degenerate parametric down conversion. These squeezed states may be mapped within the same cavity onto an atomic ensemble for sensing and metrological applications.Experimental Demonstration

[0041] As an example of cavity-mode hybridization, FIG. 8A is a side view of an optical resonator 800 that is one example of the optical resonator 100 of FIG. 1. For clarity in FIG. 8A, the optical resonator 800 is shown without any intracavity lens (e.g., the intracavity lenses 110(1) and 110(2) of FIG. 1). The optical resonator 800 includes a first mirror 802(1) and a second mirror 802(2) that face each other to form a Fabry-Perot cavity having longitudinal standing-wave resonances or modes. The optical resonator 800 also includes a periodically poled crystal 804 (e.g., periodically poled lithium niobate) that is one example of the nonlinear optical element 104 of FIG. 1. Coupled into the optical resonator 800, via transmission through the first mirror 802(1), is a probe beam 810 having a probe frequency and a pump beam 812 having a pump frequency. Coupled out of the optical resonator 800, via transmission through the second mirror 802(2), is a generated beam 814 whose frequency equals the sum of the probe and pump frequencies. Also coupled out of the optical resonator800, via transmission through the second mirror 802(2), is an unabsorbed pump beam 812’ that represents the portion of the pump beam 812 that is not absorbed by the periodically poled crystal 804.

[0042] The periodically poled crystal 804 implements sum-frequency generation within the optical resonator 800. Specifically, the periodically poled crystal 804 absorbs one photon of the probe beam 810 and one photon of the pump beam 812 to generate one photon of the generated beam 814. For the experimental demonstration described herein, the wavelength of the probe beam 810 is 780 nm, the wavelength of the pump beams 812 and 812’ is 1525 nm, and the wavelength of the generated beam 814 is 516 nm.

[0043] The mirrors 802(1) and 802(2) have high-reflectivity coatings at both the wavelength of the probe beam 810 (i.e., 780 nm) and the wavelength of the generated beam 814 (i.e., 516 nm). The mode of the optical resonator 800 that is resonant with the probe beam 810 is referred to herein as the “probe mode” while the mode of the optical resonator 800 that is resonant with the generated beam 814 is referred to as the “sum-frequency mode.”

[0044] In the absence of the periodically poled crystal 804, the probe and sumfrequency modes are uncoupled. In this case, the quantum state of the optical resonator 800 may be expressed as a direct product of the individual quantum states of the probe and sumfrequency modes. However, with the periodically poled crystal 804 included in the optical resonator 800, the probe and sum-frequency modes are coupled together. This coupling modifies the eigenstates of the optical resonator 800, giving rise to an avoided crossing (see FIG. 8C below).

[0045] FIG. 8B is a plot of conversion efficiency versus pump power (in mW) for the optical resonator 800 of FIG. 8A. Here, the probe frequency was selected to be resonant with the probe mode. The power of the probe beam 810 was fixed while the power of the pump beam 812 was varied across several values up 175 mW. The data points in the plot represent measured values of the conversion efficiency and are based on measurements of the power of the generated beam 814 (as measured outside of the optical resonator 800). The solid line in the plot is a theoretical calculation of the predicted conversion efficiency. The highest conversion efficiency measured was approximately 17% (at a pump power of 125 mW). The optical resonator 800 was controlled so that the frequency of the generated beam 814 was slightly detuned from the sum-frequency resonance; this detuning prevents the optical resonator 800 from operating at an avoided crossing, where generation of the generated beam 814 is suppressed (see FIG. 8C).

[0046] FIG. 8C shows two plots that illustrate the formation of an avoided crossing between modes of the optical resonator 800 of FIG. 8A. In the left plot, the unabsorbed power of the probe beam 810 was measured for various detunings of the probe frequency from the resonant frequency of the probe mode (along the x axis) and various cavity detunings of the optical resonator 800. In the right plot, the power of the generated beam 814 was measured for the same probe detunings and cavity detunings as in the left plot. In both plots, the darker data corresponds to greater measured power.Combinations of Features

[0047] Features described above as well as those claimed below may be combined in various ways without departing from the scope hereof. The following examples illustrate possible, non-limiting combinations of features and embodiments described above. It should be clear that other changes and modifications may be made to the present embodiments without departing from the spirit and scope of this invention:

[0048] (Al) An optical resonator includes a plurality of mirrors positioned to reflect light along a closed path. The plurality of mirrors define an optical axis of the optical resonator. The optical resonator also includes one or more intracavity lenses located along the optical axis. The one or more intracavity lenses are configured such that the optical resonator has a resonator mode whose waist is located along the optical axis. The optical resonator also includes an intracavity nonlinear optical element located along the optical axis. The intracavity nonlinear optical element is configured to implement a nonlinear frequency-mixing process with light exciting the resonator mode.

[0049] (A2) In the optical resonator denoted (Al), the optical resonator has a finesse of 100 or less.

[0050] (A3) In either of the optical resonators denoted (Al) and (A2), the waist is five microns or less.

[0051] (A4) In any of the optical resonators denoted (Al) to (A3), the one or more intracavity lenses include first and second intracavity lenses positioned along the cavity axis such that the waist is located between the first and second intracavity lenses.

[0052] (A5) In the optical resonator denoted (A4), the first and second intracavity lenses having the same numerical aperture.

[0053] (A6) In either of the optical resonators denoted (A4) and (A5), each of the first and second intracavity lenses has a numerical aperture of 0.5 or higher.

[0054] (A7) In any of the optical resonators denoted (Al) to (A6), the intracavity nonlinear optical element includes a bulk nonlinear crystal or a periodically poled nonlinear crystal.

[0055] (A8) In any of the optical resonators denoted (Al) to (A7), the optical resonator further includes an intracavity dichroic mirror positioned to couple pump light into the optical resonator.

[0056] (A9) In any of the optical resonators denoted (Al) to (A8), one of the plurality of mirrors is anti-reflection coated to couple light generated by the intracavity nonlinear optical element out of the optical resonator via transmission through said one of the plurality of mirrors.

[0057] (A10) In any of the optical resonators denoted (Al) to (A9), the plurality of mirrors form a Fabry-Perot cavity.

[0058] (Al l) In any of the optical resonators denoted (Al) to (A9), the plurality of mirrors form a ring cavity.

[0059] (A12) In any of the optical resonators denoted (Al) to (Al l), the plurality of mirrors include one or more off-axis parabolic mirrors.

[0060] (Al 3) In any of the optical resonators denoted (Al) to (A12), the nonlinear frequency-mixing process includes a second-order effect that depends on a second-order susceptibility of the intracavity nonlinear optical element, a third-order effect that depends on a third-order susceptibility of the intracavity nonlinear optical element, or a combination thereof.

[0061] (Bl) A method includes coupling input light into any of the optical resonators denoted (Al) to (A 13) to excite the resonator mode of the optical resonator. The intracavity nonlinear optical element of the optical resonator nonlinearly converts at least a portion of the input light into nonlinearly generated light.

[0062] (B2) In the method denoted (Bl), said coupling the input light includes transmitting the input light through one of the plurality of mirrors of the optical resonator.

[0063] (B3) In the method denoted (B l), said coupling the input light includes coupling, into the optical resonator, light emitted by one or more nonlinear quantum emitters.

[0064] (B4) In any of the methods denoted (Bl) to (B3), the method further includes coupling pump light into the optical resonator such that the intracavity nonlinear optical element uses the pump light to nonlinearly convert the portion of the input light into the nonlinearly generated light.

[0065] (B5) In any of the methods denoted (Bl) to (B4), the method further includes coupling the nonlinearly generated light out of the optical resonator.

[0066] (B6) In the method denoted (B5), said coupling the nonlinearly generated light includes transmitting the nonlinearly generated light through one of the plurality of mirrors.

[0067] (B7) In any of the methods denoted (Bl) to (B6), the method further includes driving one or more nonlinear quantum emitters with the nonlinearly generated light.

[0068] Changes may he made in the above methods and systems without departing from the scope hereof. It should thus be noted 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 following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present method and system, which, as a matter of language, might be said to fall therebetween.

Claims

CLAIMSWhat is claimed is:

1. An optical resonator, comprising: a plurality of mirrors positioned to reflect light along a closed path, the plurality of mirrors defining an optical axis of the optical resonator; one or more intracavity lenses positioned along the optical axis, the one or more intracavity lenses being configured such that the optical resonator has a resonator mode whose waist is located along the optical axis; and an intracavity nonlinear optical element positioned along the optical axis, the intracavity nonlinear optical element being configured to implement a nonlinear frequency-mixing process with light exciting the resonator mode.

2. The optical resonator of claim 1, having a finesse of 100 or less.

3. The optical resonator of claim 1, the waist being five microns or less.

4. The optical resonator of claim 1, the one or more intracavity lenses comprising first and second intracavity lenses positioned along the cavity axis such that the waist is located between the first and second intracavity lenses.

5. The optical resonator of claim 4, the first and second intracavity lenses having the same numerical aperture.

6. The optical resonator of claim 4, each of the first and second intracavity lenses having a numerical aperture of 0.5 or higher.

7. The optical resonator of claim 1, the intracavity nonlinear optical element comprising a bulk nonlinear crystal or a periodically poled nonlinear crystal.

8. The optical resonator of claim 1, further comprising an intracavity dichroic mirror positioned to couple pump light into the optical resonator.

9. The optical resonator of claim 1, one of the plurality of mirrors being anti-reflection coated to couple light generated by the intracavity nonlinear optical element out of the optical resonator via transmission through said one of the plurality of mirrors.

10. The optical resonator of claim 1, the plurality of mirrors forming a Fabry-Perot cavity.

11. The optical resonator of claim 1, the plurality of mirrors forming a ring cavity.

12. The optical resonator of claim 1, the plurality of mirrors comprising one or more off- axis parabolic mirrors.

13. The optical resonator of claim 1, the nonlinear frequency-mixing process comprising a second-order effect that depends on a second-order susceptibility of the intracavity nonlinear optical element, a third-order effect that depends on a third-order susceptibility of the intracavity nonlinear optical element, or a combination thereof.

14. A method comprising coupling input light into the optical resonator of claim 1 to excite the resonator mode of the optical resonator, wherein the intracavity nonlinear optical element of the optical resonator nonlinearly converts at least a portion of the input light into nonlinearly generated light.

15. The method of claim 14, wherein said coupling the input light comprises transmitting the input light through one of the plurality of mirrors of the optical resonator.

16. The method of claim 14, wherein said coupling the input light comprises coupling, into the optical resonator, light emitted by one or more nonlinear quantum emitters.

17. The method of claim 14, further comprising coupling pump light into the optical resonator such that the intracavity nonlinear optical element uses the pump light to nonlinearly convert the portion of the input light into the nonlinearly generated light.

18. The method of claim 14, further comprising coupling the nonlinearly generated light out of the optical resonator.

19. The method of claim 18, wherein said coupling the nonlinearly converted light comprises transmitting the nonlinearly generated light through one of the plurality of mirrors.

20. The method of claim 14, further comprising driving one or more nonlinear quantum emitters with the nonlinearly generated light.

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