Optical cavity array

Abstract

The optical cavity array includes a plurality of mirrors forming an optical cavity, a first lens system located within the optical cavity, and a second lens system located within the optical cavity. The first lens system has a first output facing a first mirror of the plurality of mirrors and a second output facing a second mirror of the plurality of mirrors. The second lens system has a second input facing the first input and a second output facing the second mirror. The first lens system and the second lens system are configured such that the optical cavity supports a laterally non-degenerate longitudinal mode, forming a spatially separated waist along a focal plane located axially between the first input and the second input. When the longitudinal mode is excited, the waists may be used as an array of optical dipole traps.

Description

[0001] Related Applications

[0002] This application claims priority to U.S. Provisional Patent Application No. 63 / 364,678, filed on May 13, 2022, the entire contents of which are incorporated herein by reference. Background Art

[0003] Cavity quantum electrodynamics (cQED) is the study of the interaction between light and matter in a resonant cavity. Matter can be atoms, ions, molecules or other types of quantum particles or emitters coupled to light. Quantum particles can be trapped near the waist of the excited mode of the cavity, resulting in intracavity optical tweezers. Summary of the invention

[0004] The present embodiment includes an optical cavity array that can be used to create multiple longitudinal modes in an optical cavity. Advantageously, these longitudinal modes are laterally separated from each other and are therefore not coupled to each other. Using a lens system, each longitudinal mode forms a corresponding one of multiple foci overlapping a focal plane located in the optical cavity. Due to the lateral separation of the modes, these foci are also laterally separated. Longitudinal modes with this behavior are referred to herein as laterally non-degenerate. Each focus can be used as an optical dipole trap or optical tweezers for capturing quantum emitters (e.g., neutral atoms, atomic ions, molecules, etc.). Therefore, multiple focuses can be considered to form an optical tweezers array for capturing several quantum emitters.

[0005] The multiple foci may be separated laterally, for example by several microns. These embodiments advantageously avoid the aberration sensitivity and resonator stability limitations that exist when many foci are generated using degenerate resonators (also referred to as "imaging resonators"). Each focal point can be considered to be generated by its own optical resonator or cavity, with its own unique path. However, most, if not all, optical elements are bulky. These optical resonator paths can be formed in a one- or two-dimensional array, extending transverse to the optical axis. Each optical resonator path of the array is independently stable and can operate away from any mode degeneracy that would make it susceptible to mode mixing, aberration-induced instabilities, or both.

[0006] In an embodiment, an optical cavity array includes a plurality of mirrors forming an optical cavity, a first lens system located within the optical cavity, and a second lens system located within the optical cavity. The first lens system has a first output facing a first mirror of the plurality of mirrors and a first input facing a second mirror of the plurality of mirrors. The second lens system has a second input facing the first input and a second output facing the second mirror. The first lens system and the second lens system are configured such that the optical cavity supports transversely non-degenerate longitudinal modes. These longitudinal modes form spatially separated waists that are distributed along a focal plane axially located between the first input and the second input. When the longitudinal modes are excited, the waists can be used as an array of optical dipole traps (i.e., an optical tweezers array) or an array of optical lattices. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Figure 1 is a side view of an optical cavity array forming multiple transversely non-degenerate longitudinal modes in an embodiment.

[0008] Figure 2 yes Figure 1 Figure 4 is a side view of an optical cavity array showing in more detail how each longitudinal mode forms a corresponding one of a plurality of foci at the focal plane.

[0009] Figure 3 is a side view of the polygon mirror in the embodiment.

[0010] Figure 4 is the same as in the embodiment Figure 3 A side view of a similar polygonal mirror.

[0011] Figure 5 is a side view of a cat's eye retroreflector array in an embodiment.

[0012] Figure 6 is a side view of a convex micromirror array in an embodiment.

[0013] Figure 7 is a side view of a retroreflector array in an embodiment.

[0014] Figure 8 is the same as in the embodiment Figure 1 A side view of a similar optical cavity array.

[0015] Fig. 9 yes Figure 8 A side view of the optical cavity array showing in more detail how the focal point is located at the reflecting surface of the first mirror.

[0016] Fig.10 is the same as in the embodiment Figure 1 A side view of a similar optical cavity array.

[0017] Fig.11 yes Fig.10 A side view of the optical cavity array showing in more detail how the focal points are located at the focal plane. DETAILED DESCRIPTION

[0018] In cavity quantum electrodynamics (cQED), it is often desirable to design the single-particle cooperativity η to be as large as possible. This is defined as η≡g 2 The single-particle cooperativity η of / kΓ quantifies the competition between (i) the coherent information exchange at rate g between the cavity and the quantum emitter (e.g., neutral atoms, ions, quantum dots, etc.) located inside the cavity and (ii) the decoherence rates Γ and κ of the quantum emitter and cavity, respectively. Increasing η increases the collection probability P of a quantum emitter emitting into (or absorbing from) a mode of the cavity, as opposed to free space. c =η / (1+η). Increasing η can also reduce the failure rate of cavity-mediated quantum information transfer between two quantum emitters trapped in separate optical cavities by 2π / η 1 / 2 .

[0019] Another way to express synergy is Among them is The cavity finesse, w0 is the smallest diffraction-limited waist of the cavity mode, and λ is the wavelength of the radiative transitions of both the quantum emitter and the cavity resonance. can be interpreted as the number of round trips that the light makes in the optical cavity before disappearing due to absorption or transmission through the cavity mirrors. This alternative representation of η can be explained geometrically: the resonant cross section of the quantum emitter for absorbing light is ~λ 2 , the area of ​​the cavity mode passing through the quantum emitter is Therefore, for each time the cavity light passes through the quantum emitter, the absorption probability is Optical cavity passes through the number of To simply increase the probability of this single pass absorption.

[0020] The existing optical cavity for cQED uses a relatively large waist w0 and very high finesse. A high cooperativity η is achieved. Such optical cavities (see, for example, Figure 1 and Figure 2 ) are typically manufactured using concave mirrors with very high reflectivity (typically greater than 99.999%). By improving the super-polishing and dielectric coatings of these mirrors, nearly 10 6 Due to their high precision These prior art optical cavities are difficult to align and stabilize. In addition, specialized handling techniques are required to prevent airborne particles, such as dust, from settling on the mirror surfaces; such contamination reduces finesse by increasing scattering. Similarly, mounting the optical cavity within a vacuum chamber (as required for atom trapping) places stringent cleanliness requirements on the vacuum system to prevent contaminants (such as oil) from settling on the mirrors.

[0021] One aspect of this embodiment is the realization that increasing the single-particle cooperativity η does not impose a significant limit on the cavity length L. The idea that cQED requires a small mode volume V is incorrect, since the Purcell factor can be written as F P =3λ 3 Q / (4π 2 V). Purcell Factor F P quantifies how much the spontaneous emission rate of a quantum emitter is enhanced when it is located inside a resonant cavity with a quality factor Q. This expression shows that a small mode volume V appears to be beneficial for increasing the Purcell factor F P , but ignores the fact that Q decreases with decreasing cavity length L. Related to cQED is the finesse where f c is the resonant frequency of the cavity mode. Denote and assume the mode volume When the Purcell factor F P is identical to the single-particle cooperativity η at a unity factor and therefore depends only on λ and w0. Therefore, for a fixed value of λ, the fineness and waist w0 are two independent experimental parameters for determining the cooperativity η.

[0022] This embodiment uses an intracavity lens to achieve a smaller waist w0 than the optical cavity of the prior art. The smaller waist w0 leads to significantly greater synergy η, which can be used to reduce the fineness For example, an optical cavity can generate a waist of w0≈500nm at λ=780nm (D2 transition of Rb) and The finesse of η≈9.4 produces a cooperativity of η≈9.4. This value of cooperativity η is so large that atoms trapped near the waist can emit photons into the optical cavity ten times faster than into free space. When the atoms are implemented as qubits, the probability that the emitted photons are collected by the optical cavity exceeds 90%. In addition, due to the lower finesse The cavity length L only needs to be stabilized at The optical cavity is easier to align and stabilize than the optical cavity of the prior art. Additional optical elements can be placed inside the cavity without significantly reducing finesse Lower precision The requirements for handling, assembly and vacuum cleanliness are also relaxed, as the increase in light scattering from surface contaminants no longer significantly reduces the fineness.

[0023] Photon collection probability P c The increase in will significantly improve the state detection of cQED devices and other systems using optical tweezers arrays. Therefore, this embodiment can be used to create a photon-matter interface that can efficiently convert quantum information between photonic qubits and matter-based qubits (e.g., trapped ions, neutral atoms, defects in diamond, quantum dots, etc.). Such optically coupled systems can increase the number of qubits in a quantum computer, thereby improving the scaling of qubits. For example, optically coupled devices can be used to efficiently transfer optical information between spatially different ion traps, thereby enabling quantum computing beyond the melting size limit of a single ion crystal.

[0024] Another application of this embodiment is sensing using color centers. Here, the optical cavity improves light focusing, allowing faster and more accurate readout of the color center state. This scanning cavity microscope will rely on a small waist w0 instead of high finesse, greatly relaxing material constraints. As another application, the optical cavity can be used to accelerate the state detection of atomic array quantum simulators and computers by orders of magnitude, thereby achieving optically mediated non-local division and error correction based on real-time feedback.

[0025] Figure 1 is a side view of an optical cavity array 100 forming a plurality of laterally non-degenerate longitudinal modes 140 in an embodiment. Figure 2 yes Figure 1 1 is a side view of the optical cavity array 100 showing in greater detail how each longitudinal mode 140 forms a corresponding one of the plurality of focal points 130 at the focal plane 108. Figure 1 and Figure 2 Best viewed in conjunction with the following description.

[0026] The optical cavity array 100 includes a first mirror 102 and a second mirror 116 facing each other to form a Fabry-Perot cavity. The mirrors 102 and 116 are opposed retroreflectors whose positions define an optical axis 118 parallel to the z-axis (see right coordinate system 120). For clarity, the directions along x and y are also referred to as "lateral", while the direction along z is referred to as "longitudinal" or "axial". Figure 1 In the example of FIG. 1 , the first mirror 102 is a plane mirror perpendicular to the optical axis 118. However, the first mirror 102 can have a different geometry, as described in more detail below. Figures 3 to 7 The geometry of the second mirror 116 is described in detail.

[0027] The optical cavity array 100 also includes a first lens system 122 axially located between the mirrors 102 and 118. The first lens system 122 has a first input facing in the +z direction (i.e., toward the second mirror 116) and a first output facing in the -z direction (i.e., toward the first mirror 102). Figure 1 In the example of , the first lens 106 defines a first input and the second lens 104 defines a first output. The optical cavity array 100 also includes a second lens system 124 axially located between the first lens system 122 and the second mirror 116. The second lens system 124 has a second input facing the first input (i.e., the first lens 106) and a second output facing the second mirror 116. Figure 1 In the example of FIG. 1 , the third lens 110 defines a second input and the fourth lens 112 defines a second output.

[0028] The first input and the second input (i.e., lenses 106 and 110) are axially separated, forming a focal plane 108 therebetween. The first lens 106 has a first focal length f1, and the second lens 104 has a second focal length f2. Figure 1 In the example of , the second focal length f2 is greater than the first focal length f1. The surface of the first lens 106 closest to the focal plane 108 is located at a first working distance WD1 from the focal plane 108. Generally, the first working distance WD1 is not equal to the first focal length f1, but may depend on other parameters such as the focal lengths f1 and f2 and the first lens spacing D1 between the lenses 104 and 106. The first lens system 122 has a first back distance B1. Figure 1 In the example of , the first mirror 102 is located at the first back distance B1 behind the second lens 104, or near the first back distance B1 behind the second lens 104. However, the first mirror 102 does not have to be located exactly at this position. Generally, the first back distance B1 is not equal to the second focal length f2. However, for the case where f2>>f1 and D1=f1+f2, the first back distance B1 can have a value close to the second focal length f2.

[0029] Despite Figure 1 The second lens system 124 is similar to the first lens system 122, but not identical. The third lens 110 has a third focal length f3, and the fourth lens 112 has a fourth focal length f4. Figure 2 In the example of FIG. 1 , the fourth focal length f4 is greater than the third focal length f3. The surface of the third lens 110 closest to the focal plane 108 is located at a second working distance WD2 from the focal plane 108. The lenses 110 and 112 are axially separated by a second lens spacing D2. The second lens system 124 has a second back distance B2 between the fourth lens 112 and the second mirror 116.

[0030] exist Figure 1, lenses 106 and 104 are separated by a distance approximately equal to the sum of their focal lengths, i.e., D1 ~ f1 + f2. However, lenses 106 and 104 may be separated by different values ​​of D1. Similarly, lenses 110 and 112 are separated by a distance approximately equal to the sum of their focal lengths, i.e., D2 ~ f3 + f4. However, lenses 110 and 112 may be separated by different values ​​of D2. Similarly, in Figure 1 , the first lens 106 has a higher NA than the second lens 104, and the third lens 110 has a higher NA than the fourth lens 112. It can be seen that the clear aperture of the second lens 104 can be larger than the clear aperture of the first lens 106, especially when the first focal length f1 is larger than the second focal length f2. Similarly, the clear aperture of the fourth lens 112 can be larger than the clear aperture of the third lens 110.

[0031] Although Figure 1 The lens systems 122 and 124 shown in FIG. 1 each have two plano-convex lenses, but one or both of the lens systems 122 and 124 can have more than two lens elements, or other types of lens elements, or both. As is known to those skilled in the art, such multi-lens systems can be used to correct aberrations (e.g., chromatic aberration, spherical aberration, coma, astigmatism, etc.). In addition, the lens systems 122 and 124 are not limited to thin lenses, but can alternatively or additionally include thick lenses, composite lenses, objective lenses, GRIN lenses, aspherical lenses, etc. Thus, one or both of the lens systems 122 and 124 can be configured to be similar to Figure 1 Different forms may be shown without departing from the scope of the invention.

[0032] One or both of lens systems 122 and 124 may have a finite conjugate ratio, and therefore a magnification. For example, when second lens system 124 has a finite conjugate ratio, it may be configured to image focal plane 108 onto image plane 114. Second mirror 116 may be located at or near image plane 114. However, second mirror 116 need not be located exactly at image plane 114. In fact, it may be advantageous to intentionally position second mirror 116 away from image plane 114, for example, to improve cavity stability, correct aberrations, or achieve certain design specifications.

[0033] Figure 1An optical cavity array 100 supporting three laterally non-degenerate longitudinal modes 140 is shown. Each longitudinal mode 140 corresponds to a standing wave resonating with a Fabry-Perot cavity. Specifically, a first longitudinal mode 140(1) spatially overlaps with an optical axis 118 at all axial positions between mirrors 102 and 116, a second longitudinal mode 140(2) is laterally above the optical axis 118 between the first mirror 102 and the focal plane 108 (i.e., in the +x direction), and a third longitudinal mode 140(3) is laterally below the optical axis 118 between the first mirror 102 and the focal plane 108 (i.e., in the -x direction). Between the focal plane 108 and the second mirror 116, the second longitudinal mode 140(2) and the third longitudinal mode 140(3) are flipped, with the second longitudinal mode 140(2) being below the optical axis 118 and the third longitudinal mode 140(3) being above the optical axis 118.

[0034] exist Figure 1 and Figure 2 In FIG. 1 , each longitudinal mode 140 is represented by a shaded area, which indicates how its spot size (i.e., the lateral dimension along x) varies with the axial position z. Assume that each longitudinal mode 140 is in the TEM 00 Therefore, the transverse intensity distribution of each longitudinal mode 140 is a Gaussian distribution, and the spot size can be 1 / e of the Gaussian intensity distribution. 2 Strength Radius or Diameter.

[0035] Figure 2 1 shows how each longitudinal pattern 140 forms a focus 130 on or near the focal plane 108. Specifically, the first longitudinal pattern 140(1) forms a first focus 130(1) that coincides with the optical axis 118, the second longitudinal pattern 140(2) forms a second focus 130(2) that is laterally above the optical axis 118, and the third longitudinal pattern 140(3) forms a third focus 130(3) that is laterally below the optical axis 118. Thus, the foci 130(1), 130(2), and 130(3) are laterally separated. Figure 2 For clarity, each focus 130 is surrounded by a small circle.

[0036] exist Figure 1 and Figure 2 For clarity, the lateral center (i.e., the point of highest intensity) of each longitudinal mode 140(1), 140(2), and 140(3) is identified by a dashed line. These dashed lines are also referred to as the central axis of the longitudinal mode 140. Figure 2As can be seen, these central axes do not intersect at focal plane 108. Instead, the point at which they intersect is located at a distance Δz from focal plane 108. It is believed that this feature arises from the different configurations of lens systems 122 and 124 and is related to the ability of optical cavity array 100 to form transversely non-degenerate longitudinal modes. Therefore, if lens systems 122 and 124 were configured identically, Δz would be zero and optical cavity array 100 would no longer be able to support transversely non-degenerate longitudinal modes (i.e., longitudinal modes 140 would all "collapse" into one degenerate mode, similar to prior art Fabry-Perot cavities).

[0037] The lens systems 122 and 124 can be configured differently in many ways. For example, the lenses 104, 106, 110, and 112 can be selected so that D1≠D2, WD1≠WD2, B1≠B2, or a combination thereof. In another example, the first mirror 102 is axially positioned a distance B1 away from the back of the second lens 104. Similarly, the second mirror 116 can be axially positioned away from the back distance B2. In another example, the lenses 104 and 106 are positioned so that D1≠f1+f2. Similarly, the lenses 110 and 112 can be positioned so that D2≠f3+f4.

[0038] For the sake of clarity, Figure 2 Only three focal points 130(1), 130(2) and 130(3) are shown in FIG. However, the optical cavity array 100 may alternatively form only two focal points 130 or more than three focal points 130. Although the focal points 130 are Figure 1 and Figure 2 1 and 2. Although shown as extending along x, the focus 130 may alternatively or additionally extend along y. The number of focus 130 formed by the optical cavity array 100 may be as high as hundreds, or even more.

[0039] In order to locate the waist (i.e., minimum spot size) of each longitudinal mode 140 at the corresponding focus 130 in the focal plane 108, each of the lenses 106 and 110 may have a high NA (e.g., 0.5 or greater). Figure 1 As can be seen in FIG. 1 , the spot size of each longitudinal mode 140 is also small at mirrors 102 and 116. However, due to the relationship between the NAs of lenses 104, 106, 110, and 112, the spot size of longitudinal mode 140 may be larger at mirrors 102 and 116 than at focal plane 108. In general, one or both of lenses 106 and 110 may have an NA less than 0.5 without departing from the scope of this disclosure.

[0040] As in Figure 1As can be seen in , the lateral spacing of the longitudinal modes 140 at the mirrors 102 and 116 is greater than the lateral spacing at the focal plane 108. The lateral spacing is measured between the central axes of adjacent longitudinal modes 140 (i.e., between the dashed lines). It is believed that this effect is caused by the magnification of the lens systems 122 and 124. Specifically, the first lens system 122 has a first magnification M1>1 for light propagating in the -z direction. Similarly, the second lens system 122 has a second magnification M2>1 for light propagating in the +z direction. The longitudinal modes 140 have a first lateral spacing d1 at the first mirror 102 and a second lateral spacing d2 at the second mirror 116. Figure 1 In the example, d1>d2, which may occur when M1>M2. However, lens systems 122 and 124 may alternatively be configured such that d2 <d1。

[0041] One advantage of having a larger lateral spacing at the mirrors 102 and 116 compared to the focal plane 108 is that it is easier to couple light into the optical cavity array 100. For example, the longitudinal mode 140 can be excited by transmitting light through one of the mirrors 102 and 116. The light can be a single monochromatic laser beam with a large enough spot size to cover all longitudinal modes. Alternatively, the light can be several smaller monochromatic laser beams that are laterally spaced from each other. Each of the several laser beams can be individually controlled (e.g., intensity, propagation direction, etc.) for coupling to a corresponding one of the longitudinal modes 140. Such individual control may be easier to achieve when the several laser beams are spaced from each other by a larger lateral spacing.

[0042] Another advantage of having a larger lateral spacing at the mirrors 102 and 116 is the handling of light leaking from the optical cavity array 100. The leaking light may come from a longitudinal mode 140, or from fluorescence emitted into the longitudinal mode 140 by a quantum emitter located at the waist or trapped at the waist. The leaking light leaves the optical cavity array 100 via transmission through one or both of the mirrors 102 and 116. Alternatively or additionally, the light may be coupled out of the optical cavity array 100 using an intracavity beam sampler. To minimize aberrations, the beam sampler may be placed in a low NA region of the optical cavity array 100 (e.g., between the fourth lens 112 and the second mirror 116, or between the second lens 104 and the first mirror 102). In any case, it may be desirable to handle the leaking light differently depending on which longitudinal mode 140 it comes from. This different handling may be facilitated by spatially separating the leaking light, which is easier to do when the lateral spacing is larger.

[0043] Although Figure 1An optical cavity array 100 is shown with mirrors 102 and 116 forming a Fabry-Perot cavity, but the optical cavity array 100 may alternatively have three or more mirrors positioned and oriented to form a ring cavity. In this case, each of the three or more mirrors may be a turning mirror rather than a retroreflector. The ring cavity also supports multiple longitudinal modes. However, in this case, each longitudinal mode corresponds to a traveling wave rather than a standing wave.

[0044] Figure 3 is a side view of the polygon mirror 300, as Figure 1 The polygonal mirror 300 is an example of a second mirror 116 of the embodiment of the present invention. The polygonal mirror 300 has a first face 304 that forms a first oblique angle with the optical axis 118, a second face 302 that is perpendicular to the optical axis 118, and a third face 306 that forms a second oblique angle with the optical axis 118. Faces 302, 304, and 306 are positioned to reflect light back onto themselves. More specifically, the first oblique angle is selected so that the third longitudinal mode 140 (3) is reflected back from the first face 304. Similarly, the second oblique angle is selected so that the second longitudinal mode 140 (2) is reflected back from the third face 306. When there are more than three longitudinal modes 140, the polygonal mirror 300 can be molded with additional faces. The second face 302 is a portion of the polygonal mirror 300 that cooperates with the first mirror 102 to define the optical axis 118.

[0045] Figure 4 is a side view of the polygon mirror 400, which is similar to Figure 3 The polygon mirror 300 has no axial depression except for its second face 302. Specifically, the second face 302 in the polygon mirror 400 is located further in the -z direction than the polygon mirror 300. Due to the absence of the depression, the polygon mirror 400 may be easier to manufacture than the polygon mirror 300.

[0046] Figure 5 is a side view of the cat's eye retroreflector array 500, as Figure 1 1. Another example of a second mirror 116 of the cat's eye retroreflector array 500. The cat's eye retroreflector array 500 includes a microlens array 502 extending in one or both of the two lateral dimensions (i.e., x and y). Each longitudinal pattern 140 interacts uniquely with one microlens in the array 502. The microlens array 502 focuses the longitudinal patterns 140 so that their central axes are all parallel to the optical axis 118. Therefore, a plane mirror 504 located behind the microlens array 502 (i.e., in the +z direction) and oriented perpendicular to the optical axis 118 can be used to reflect the longitudinal patterns 140.

[0047] Figure 6 is a side view of the convex micromirror array 600, as Figure 1Another example of the second mirror 116. The micromirror array 600 is a one-dimensional or two-dimensional convex mirror array, which can be, for example, formed by a microlens array (e.g. Figure 5 The microlens array 502 is manufactured by depositing a high reflectivity coating on the convex surface of the microlens array 502. Figure 6 As can be seen in FIG. 6 , the micromirror array 600 is configured to retroreflect the longitudinal patterns 140 regardless of their different incident angles.

[0048] Figure 7 is a side view of the retroreflector array 700, as Figure 1 Another example of a second mirror 116. The retroreflector array 700 includes a microlens array 702, which is similar to Figure 5 The microlens array 702 is similar to the microlens array 502, except that it is located axially behind the image plane 114 in the +z direction. The microlens array 702 collimates the longitudinal patterns 140 and deflects the longitudinal patterns 140 so that their central axes are parallel to the optical axis 118. In this case, the longitudinal patterns 140 are retroreflected using a plane mirror 704 oriented perpendicular to the optical axis 118.

[0049] Depending on the quality of the optics, it may be necessary to tune the resonant frequency of each longitudinal mode 140 individually. For example, such tuning may be used to ensure that the atoms emit fluorescence that is resonant with the longitudinal mode 140 in which they are trapped. This may be accomplished, for example, by placing a phase-only spatial light modulator in a low NA region of the optical cavity array 100 (e.g., between the fourth lens 112 and the second mirror 116 or between the second lens 104 and the first mirror 102). Alternatively, once the necessary phase shift is determined, a custom anti-reflection coated phase mask may be installed within the optical cavity array 100, which may advantageously yield lower optical insertion losses than a spatial light modulator.

[0050] When the optical cavity array 100 is optically excited (as described above), an optical dipole trap is formed at each of the focal points 130. The optical dipole trap can be a standing wave optical lattice or a traveling wave optical tweezer. The multiple optical dipole traps thus produced can be used to capture cold atoms or ultracold atoms, or to capture other types of optically trappable quantum emitters. Advantageously, these optical dipole traps are located far enough away from nearby physical surfaces (such as lenses 106 and 110) to ensure that the trapped atoms are not ejected when colliding with such surfaces. Once the atoms are trapped, they can be driven, measured, coupled, detected, or otherwise manipulated as required by the current application. For example, fluorescence can be collected from at least one atom trapped in one of the optical dipole traps. As described above, the fluorescence can be coupled to one of the longitudinal modes 140, from which the fluorescence can be transmitted through one of the mirrors 102 and 116.

[0051] To further facilitate the trapping of cold atoms, the optical cavity array 100 can be arranged so that the array of focal points 130 is located within an ultra-high vacuum environment. However, some conventional vacuum chambers are so large that lenses 106 and 110 cannot be placed outside the vacuum chamber because they are too far apart from each other to produce focal points 130 (i.e., waists) that are tight enough for the current application. In this case, by mounting one or both of lenses 106 and 110 within the vacuum chamber, they can be brought closer to each other (see, for example, FIG. 1 ). Fig.10 ). Additional components of the optical cavity array 100 can be mounted within the vacuum chamber. A vacuum window can be used in a vacuum system to allow light to pass through it.

[0052] Figure 8 is a side view of the optical cavity array 800, which is similar to Figure 1 1. The optical cavity array 100 is shown in FIG. 1, except that the first lens system 122 is excluded and the first mirror 102 is located at or near the focal plane 108. Fig. 9 yes Figure 8 800 , showing in greater detail how the focal point 830 is located near the first mirror 102 . Figure 8 and Fig. 9 Best viewed in conjunction with the following description.

[0053] The optical cavity array 800 is advantageous for quantum emitters that are solid-state and therefore do not need to be trapped magnetically or optically. Figure 8 and Fig. 9 In the embodiment of the present invention, a sample (e.g., a wafer or substrate) of a nonlinear emitter 802 is fixed to the front side of the first mirror 102. Examples of such nonlinear emitters 802 include, but are not limited to, rare earth ions, quantum dots, solid color centers (e.g., silicon vacancy centers in diamond, nitrogen vacancy centers in diamond, etc.), and molecules embedded in a host matrix.

[0054] Optical cavity array 800 includes a lens system 824 that projects focal plane 108 onto image plane 114 . Figure 8 and Fig. 9 A first longitudinal mode 840(1) having a first focus 830(1), a second longitudinal mode 840 having a second focus 830(2), and a third longitudinal mode 840 having a third focus 830(3) are shown. The longitudinal modes 840(1), 840(2), and 840(3) are laterally non-degenerate and therefore uncoupled from each other. Thus, as Fig. 9 As shown, focal points 830(1), 830(2), and 830(2) are spatially separated.

[0055] The lens system 824 includes a first lens 810 closer to the focal plane 108 and a second lens 812 closer to the image plane 114. Figure 1The second lens system 124 is different from Figure 8 The lens system 824 is configured such that the central axes of the longitudinal patterns 840(1), 840(2), and 840(3) are parallel to the optical axis 118. Thus, the first mirror 102 retroreflects the longitudinal pattern 840 at the focal plane 108. Figure 8 and Fig. 9 Only three longitudinal modes 840 are shown, but the optical cavity array 800 can be configured to support different numbers of transverse non-generated longitudinal modes.

[0056] exist Figure 8 and Fig. 9 In the example of , the first lens 810 has a large NA (e.g., 0.5 or greater), which helps achieve a small waist at the focal plane 108. The second lens 812 has a smaller NA than the first lens 810, but has a larger clear aperture. In addition, the second lens 812 has a larger focal length than the first lens 810. Lenses 810 and 812 are separated by a lens spacing D3, which can have a value equal to or close to the sum of their respective focal lengths. However, the lens spacing D3 can be a different value from this sum to ensure that the central axis is parallel to the optical axis 118 at the focal plane 108 and that all longitudinal modes 840 are stable. Therefore, without departing from the scope of the present invention, the lens system 824 can be connected to Figure 8 Different configurations are shown.

[0057] Figure 8 and Fig. 9 It also shows how the longitudinal pattern 840 has a smaller lateral spacing d near the image plane 114 than near the focal plane 108. f Large lateral spacing d i . Figure 1 and Figure 2 Similar to what has been described, it is believed that these different lateral spacings are caused by the magnification of lens system 824. Thus, lens system 824 can be configured with a magnification to achieve this effect.

[0058] Although Figure 8 A lens system 824 is shown having two plano-convex lenses, but the lens system 824 may alternatively have more than two lenses, different types of lenses, or both. Such a multi-lens system may be used to correct aberrations. Furthermore, the lens system 824 is not limited to thin lenses, but may alternatively or additionally include thick lenses, composite lenses, objective lenses, GRIN lenses, aspherical lenses, etc.

[0059] Fig.10 is a side view of the optical cavity array 1000, which is similar to Figure 1The optical cavity array 100 is shown in FIG. 1 , except that the first lens system 122 and the first mirror 102 are replaced by a curved mirror 1010 . Fig.11 yes Fig.10 1000 , showing in greater detail how the focal point 1030 is located at the focal plane 108 . Fig.10 and Fig.11 Best viewed in conjunction with the following description.

[0060] exist Fig.10 , the curved mirror 1010 is a concave spherical mirror having a radius of curvature R. The curved mirror 1010 is axially located at or near a distance R from the focal plane 108. However, in order to ensure stability and the formation of a laterally non-degenerate longitudinal mode, the curved mirror 1010 does not need to be located at the exact distance R from the focal plane 108.

[0061] Fig.10 and 11 An optical cavity array 1000 is shown supporting a first longitudinal mode 1040(1) that is laterally centered on the optical axis 118. Near the focal plane 108, the first longitudinal mode 1040(1) has a first focus 1030(1) located at the intersection of the focal plane 108 and the optical axis 118. The optical cavity array 1000 also supports a second longitudinal mode 1040(2) having an upper standoff 1140(1) and a lower standoff 1140(2). Near the focal plane 108, the upper standoff 1140(1) is located laterally above the optical axis 118 (i.e., in the +x direction), where it forms a second focus 1030(2) that is laterally separated from the first focus 1030(1). Also near focal plane 108, lower standoff 1140(2) is located laterally below optical axis 118 (ie, in the -x direction), where it forms a third focus 1030(3) that is also laterally separated from first focus 1030(1).

[0062] exist Fig.11 , the central axis of the first longitudinal mode 1040(1) coincides with the optical axis 118 and is therefore parallel to the optical axis 118. However, the central axes of the legs 1140(1) and 1140(2) are not parallel to the optical axis 118. As shown, the central axes are located at a point behind the curved mirror 1010 (i.e., in the -z direction relative to the curved mirror 1010). The curved mirror 1010 reflects the upper leg 1140(1) downward (i.e., in the -x direction) for a short distance and then reflects it again to form the lower leg 1140(2). Therefore, the curved mirror 1010 does not completely retroreflect the second longitudinal mode 1040(2), but rather translates it along the x direction such that the upper leg 1140(1) and the lower leg 1140(2) are laterally separated from each other. Therefore, the upper leg 1140(1) and the lower leg 1140(2) exhibit mirror symmetry about the optical axis 118.

[0063] Since both foci 1030(2) and 1030(3) are part of the second longitudinal mode 1040(2), atoms trapped at these two foci will couple with each other. To avoid this coupling, atoms should not be trapped at one of the two foci. Fig.11 , the third focus 1030(3) is shown with an "x" to indicate that it can be excluded from trapping. Alternatively, the first focus 1030(1) can be excluded. Therefore, of the three focuses 1030(1), 1030(2), and 1030(3), at most two can be used for atom trapping without coupling. Extending this to N transverse non-degenerate longitudinal modes 1040, the optical cavity array 1000 forms 2N-1 focuses 1030, of which at most N can be used for atom trapping without coupling between traps.

[0064] exist Fig.10 In the embodiment, the central axis of the longitudinal mode 1040 does not need to be parallel to the optical axis 118 near the second mirror 116. Therefore, the second mirror 116 can be Figure 3 Polyhedron 300, Figure 4 Polyhedron 400, Figure 5 Cat's eye retroreflector array 500, Figure 6 Micromirror array 600, Figure 7 1040 or another type of retroreflector known in the art. In addition, since the curved mirror 1010 does not retroreflect any longitudinal modes 1040 that are laterally offset from the optical axis 118, the second mirror 116 retroreflects each of these off-axis longitudinal modes 1040 twice (instead of once). Figure 1 once in the optical cavity array 100).

[0065] Fig.10 Also shown is how this embodiment can be mounted within a vacuum chamber 1004. In this example, the curved mirror 1010 and the third lens 110 are located within the vacuum chamber 1004, where they can be placed close (e.g., within millimeters) to the focal plane 108 to ensure the formation of a high NA waist and fluorescence collection. The fourth lens 112 and the second mirror 116 are located outside the vacuum chamber 1004. The vacuum window 1008 provides optical access between those components within the vacuum chamber 1004 and those components outside the vacuum chamber 1004. The vacuum window 1008 can be located in a low NA region of the optical cavity array 1000. For example, in Fig.10 In the embodiment shown in FIG. 1 , vacuum window 1008 is located between lenses 110 and 112. Alternatively, vacuum window 1008 may be located between lens 112 and second mirror 116, in which case lens 112 would be located within vacuum chamber 1004.

[0066] Alternatively, the lens 112 and the second mirror 116 may also be located within the vacuum chamber 1004, in which case the vacuum window 1008 is not located within the optical cavity array 1000. In fact, in this case, for example, when the light used to be coupled into the optical cavity array 1000 is guided into the vacuum chamber 1004 via an optical fiber, the vacuum window 1008 may not be needed. However, the vacuum window 1008 may still be used, for example, to couple a free-space beam into the optical cavity array 1000, to collect light from the optical cavity array 1000, or both.

[0067] Feature combination

[0068] The above features and the features claimed below may be combined in various ways without departing from the scope of this document. The following examples illustrate possible non-limiting combinations of the above features and embodiments. It should be clear that other changes and modifications may be made to the present embodiment without departing from the spirit and scope of the present invention:

[0069] (A1) An optical cavity array includes a plurality of mirrors positioned and oriented to form an optical cavity. The optical cavity array also includes a first lens system located within the optical cavity. The first lens system has a first output facing a first mirror among the plurality of mirrors and a first input facing a second mirror among the plurality of mirrors. The optical cavity array also includes a second lens system located within the optical cavity. The second lens system has a second input facing the first input of the first lens system and a second output facing the second mirror. The optical cavity supports a plurality of longitudinal modes that are transversely non-degenerate and form a corresponding plurality of focal points that are distributed along a focal plane axially located between the first input of the first lens system and the second input of the second lens system.

[0070] (A2) In the optical cavity array denoted as (A1), the plurality of mirrors include three or more mirrors forming a ring cavity. Each of the plurality of longitudinal modes corresponds to a traveling wave propagating in the ring cavity.

[0071] (A3) In the optical cavity array denoted as (A1), the first mirror and the second mirror are first and second reflectors, respectively, facing each other to form a Fabry-Perot cavity. Each of the plurality of longitudinal modes corresponds to a standing wave resonating with the Fabry-Perot cavity.

[0072] (A4) In the optical cavity array denoted as (A3), the second lens system images the focal plane onto an imaging plane. The second retroreflector is axially located near the imaging plane.

[0073] (A5) In any of the optical cavity arrays represented as (A3) and (A4), the second reflector is a polygonal mirror, a cat's eye array, or a convex mirror array.

[0074] (A6) In any of the optical cavity arrays denoted as (A3) to (A5), the first retroreflector is a plane mirror oriented perpendicular to the optical axis of the optical cavity.

[0075] (A7) In any of the optical cavity arrays denoted as (A3) to (A6), the first lens system includes a first lens having a first focal length f1 and a second lens having a second focal length f2. The second lens is axially located at f1+f2 behind the first lens.

[0076] (A8) In the optical cavity array represented as (A7), the second focal length f2 is greater than the first focal length f1.

[0077] (A9) In any of the optical cavity arrays denoted as (A7) and (A8), the first lens has a numerical aperture greater than that of the second lens.

[0078] (A10) In any of the optical cavity arrays denoted as (A7) to (A9), the second lens system includes a third lens having a third focal length f3 and a fourth lens having a fourth focal length f4. The fourth lens is axially located at f3+f4 behind the third lens.

[0079] (A11) In the optical cavity array represented as (A10), the fourth focal length f4 is greater than the third focal length f3.

[0080] (A12) In either of the optical cavity arrays denoted as (A10) and (A11), the third lens has a numerical aperture greater than that of the fourth lens.

[0081] (A13) In any of the optical cavity arrays represented as (A1) to (A12), each of the first lens system and the second lens system has a finite conjugate ratio.

[0082] (A14) In any of the optical cavity arrays denoted as (A1) to (A13), the optical cavity array further includes a vacuum chamber. The focal plane is located within the vacuum chamber.

[0083] (A15) In the optical cavity array represented as (A14), one or both of the first mirror and the second mirror are located within the vacuum chamber.

[0084] (A16) In any of the optical cavity arrays represented as (A1) to (A15), the optical cavity array also includes a phase plate or a phase modulator located within the optical cavity.

[0085] (B1) A method comprising coupling laser light into any one of the optical cavity arrays represented as (A1) to (A16) to excite multiple longitudinal modes.

[0086] (B2) In the method denoted as (B1), when excited, each of the plurality of longitudinal modes forms a corresponding one of a plurality of optical dipole traps located at the focal plane. The method further includes trapping at least one atom in each of one or more of the plurality of optical dipole traps.

[0087] (B3) In the method denoted as (B2), the method further includes collecting fluorescence emitted by at least one atom trapped in one of the plurality of optical dipole traps, the fluorescence being transmitted through one of a first mirror and a second mirror of the optical cavity array.

[0088] (B4) In any of the methods denoted as (B1) to (B3), the method further includes changing an optical path length of only one longitudinal mode among the plurality of longitudinal modes.

[0089] Changes may be made to the above methods and systems without departing from the scope of this document. It should be noted, therefore, that the matter contained in the above description or shown in the accompanying drawings is to be interpreted as illustrative and not restrictive. 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 methods and systems that, by definition, can be said to fall within the scope of the present invention.

Claims

1. An optical cavity array, comprising: a plurality of mirrors positioned and oriented to form an optical cavity; a first lens system within the optical cavity, the first lens system having a first output facing a first mirror of the plurality of mirrors, the first lens system having a first input facing a second mirror of the plurality of mirrors; as well as a second lens system within the optical cavity, the second lens system having a second input facing the first input of the first lens system and a second output facing the second mirror; wherein the optical cavity supports a plurality of longitudinal modes that are transversely non-degenerate and form a corresponding plurality of foci distributed along a focal plane axially located between the first input of the first lens system and the second input of the second lens system.

2. The optical cavity array according to claim 1, wherein: The plurality of mirrors includes three or more mirrors forming an annular cavity; and Each of the plurality of longitudinal modes corresponds to a traveling wave propagating in the ring cavity.

3. The optical cavity array according to claim 1, wherein: The first mirror and the second mirror are respectively a first retroreflector and a second retroreflector facing each other to form a Fabry-Perot cavity; and Each of the plurality of longitudinal modes corresponds to a standing wave resonating with the Fabry-Perot cavity.

4. The optical cavity array according to claim 3, wherein: The second lens system images the focal plane onto an imaging plane; and The second retroreflector is located axially proximate to the imaging plane.

5. The optical cavity array according to claim 3, wherein the second retroreflector comprises a polygonal mirror, a cat's eye array or a convex mirror array.

6. The optical cavity array of claim 3, the first retroreflector comprising a plane mirror oriented perpendicular to an optical axis of the optical cavity.

7. The optical cavity array according to claim 3, wherein the first lens system comprises: a first lens having a first focal length f1; as well as A second lens having a second focal length f2 is axially located behind the first lens at f1+f2. The optical cavity array according to claim 7 , wherein the second focal length f2 is greater than the first focal length f1 .

9. The optical cavity array of claim 7, wherein the first lens has a larger numerical aperture than the second lens.

10. The optical cavity array according to claim 7, wherein the second lens system comprises: a third lens having a third focal length f3; as well as A fourth lens having a fourth focal length f4, the fourth lens being axially located at f3+f4 behind the third lens. The optical cavity array according to claim 10 , wherein the fourth focal length f4 is greater than the third focal length f3 . 12 . The optical cavity array of claim 10 , wherein the third lens has a larger numerical aperture than the fourth lens.

13. The optical cavity array of claim 1, each of the first lens system and the second lens system having a finite conjugate ratio.

14. The optical cavity array according to claim 1 further comprises a vacuum chamber, wherein the focal plane is located within the vacuum chamber.

15. The optical cavity array of claim 14, wherein one or both of the first mirror and the second mirror are located within the vacuum chamber.

16. The optical cavity array of claim 1, further comprising a phase plate or a phase modulator located within the optical cavity.

17. A method comprising coupling laser light into the optical cavity array of claim 1 to excite the plurality of longitudinal modes.

18. The method of claim 17, wherein: When excited, each of the plurality of longitudinal modes forms a corresponding one of a plurality of optical dipole wells located at the focal plane; as well as The method also includes trapping at least one atom in each of one or more optical dipole wells of the plurality of optical dipole wells.

19. The method of claim 18, further comprising collecting fluorescent light emitted by at least one atom trapped in one of the plurality of optical dipole traps, the fluorescent light being transmitted through one of the first mirror and the second mirror of the optical cavity array.

20. The method of claim 17, further comprising varying an optical path length of only one longitudinal mode of the plurality of longitudinal modes.

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