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arXiv:2201.10493 · New Journal of Physics

Evolutionary algorithm to design high-cooperativity optical cavities

D. V. Karpov, Péter Horák

Published Jul 1, 2022• 6 citations
arXivHTMLPDF

Abstract

Abstract Using an evolutionary algorithm combined with a gradient descent (GD) method we design optical cavities with significantly enhanced strong coupling rates between cavity photons and a single quantum emitter. Our approach allows us to find specially designed non-spherical mirrors which lead to high-finesse cavity eigenmodes with large field enhancement at the center of the cavity. The method is based on adding consecutive perturbations to an initial spherical mirror shape using the GD method for optimization. We present mirror profiles which demonstrate higher cavity cooperativity than any spherical cavity of the same size. Finally, we demonstrate numerically how such a cavity enhances the operation frequency and purity of coupling a Ca+ ion to an optical fiber photon.

DOI
10.1088/1367-2630/ac7e66

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Abstract Using an evolutionary algorithm combined with a gradient descent (GD) method we design optical cavities with significantly enhanced strong coupling rates between cavity photons and a single quantum emitter. Our approach allows us to find specially designed non-spherical mirrors which lead to high-finesse cavity eigenmodes with large field enhancement at the center of the cavity. The method is based on adding consecutive perturbations to an initial spherical mirror shape using the GD method for optimization. We present mirror profiles which demonstrate higher cavity cooperativity than any spherical cavity of the same size. Finally, we demonstrate numerically how such a cavity enhances the operation frequency and purity of coupling a Ca+ ion to an optical fiber photon.
We propose a procedure for the significant enhancement of the strong coupling rate between photons in an optical cavity and a single quantum emitter, such as an atom, quantum dot or trapped ion. We show that specially designed, non-spherical mirrors can lead to cavity eigenmodes that exhibit a large field enhancement at the center of the cavity while inducing significantly less beam divergence, and therefore smaller round trip losses and higher cooperativity, than can be achieved by operating a spherical-mirror cavity in the near-concentric regime. We verify our designs using mode matching theory and discuss their robustness relative to different kinds of manufacturing deviations.
We propose a procedure for the significant enhancement of the strong-coupling rate between photons in an optical cavity and a single quantum emitter, such as an atom, quantum dot, or trapped ion. We show that specially designed, nonspherical mirrors can lead to cavity eigenmodes that exhibit a large field enhancement at the center of the cavity while inducing significantly less beam divergence and therefore smaller round trip losses and higher cooperativity than can be achieved by operating a spherical-mirror cavity in the near-concentric regime. We verify our designs using mode matching theory and discuss their robustness relative to different kinds of manufacturing deviations.
Coupling an emitter to a Fabry-Pérot optical cavity can provide a coherent and strong light-matter interface whose performance in a variety of applications depends critically on the emitter-photon coupling strength. Altering the typically spherical profiles of the cavity mirrors can improve this coupling strength, but directly optimizing the mirror shape is numerically challenging as the multidimensional parameter space features many local optima. Here we develop a two-step method to optimize mirror surface profiles while avoiding these issues. First, we optimize the target cavity eigenmode for the chosen application directly, and, second, we construct the mirror surfaces to retroreflect this optimized target mode at both ends of the cavity. We apply our procedure to different emitter-cavity coupling scenarios. We show that mirror shaping can increase the cooperativity of coupling to a central emitter by a factor of approximately 3 across a wide range of geometries and that, for coupling two or more emitters to a single cavity mode, the improvement factors can far exceed an order of magnitude.
Optical Fabry-Pérot resonators are traditionally formed by spherical mirrors. However, we have shown that by allowing for more general mirror shapes, the eigenmodes of a resonator can be designed and optimised for specific applications, e.g., for maximised coupling to a quantum emitter for quantum information processing. We discuss the general concepts, the numerical methods for optimising the mirror shapes, and the main results of our simulations. For example, we find that in plano-concave resonators the cooperativity can be enhanced by one order of magnitude. Finally, we compare the theoretically optimum solutions with those obtained for more easily manufacturable mirror shapes.
Optical cavities are frequently used in quantum technologies to enhance light matter interactions, with applications including single photon generation and entanglement of distant emitters. The Fabry-Pérot resonator is a popular choice for its high optical access and large emitter-mirror separation. A typical configuration, particularly for emitters that should not be placed close to the mirror surface like trapped ions and Rydberg atoms, features two spherical mirrors placed around a central emitter, but this arrangement can put demanding requirements on the mirror alignment. In contrast, plano-concave cavities are tolerant to mirror misalignment and only require the manufacture of one curved mirror, but have limited ability to focus light in the centre of the cavity. Here we show how mirror shaping can overcome this limitation of plano-concave cavities while preserving the key advantages. We demonstrate through numerical simulations that simple mirror shaping can increase coupling between a plano-concave cavity and a central emitter by an order of magnitude, even rivalling misalignment-sensitive concave-concave counterparts for achievable interaction strength. We use these observations to establish the conditions under which plano-concave cavities with shaped mirrors could improve the performance and practicality of emitter-cavity systems.
Abstract We present a systematic numerical study of Fabry–Pérot optical cavities with Gaussian-shape mirrors formed between tips of optical fibers. Such cavities can be fabricated by laser machining of fiber tips and are promising systems for achieving strong coupling between atomic particles and an optical field as required for quantum information applications. Using a mode mixing matrix method, we analyze the cavity optical eigenmodes and corresponding losses depending on a range of cavity-shape parameters, such as mirror radius of curvature, indentation depth and cavity length. The Gaussian shape of the mirrors causes mixing of optical modes in the cavity. We investigate the effect of the mode mixing on the coherent atom-cavity coupling as well as the mode matching between the cavity and a single-mode optical fiber. While the mode mixing is associated with increased cavity losses, it can also lead to an enhancement of the local optical field. We demonstrate that around the resonance between the fundamental and 2nd order Laguerre–Gaussian modes of the cavity it is possible to obtain 50% enhancement of the atom-cavity coupling at the cavity center while still maintaining low cavity losses and high cavity-fiber optical coupling.