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.
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.
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.
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.
In recent years there has been rapid progress into realising a working universal quantum computer, in particular with the development of chip-based radio frequency ion traps. The next significant leap will come with successfully integrating optical cavities into these ion traps to allow for interaction between remote ions via photons as required for more efficient and scalable quantum networking schemes. Fibre-tip cavities are especially interesting for such applications as they enable highly efficient coupling of photons from the cavity into optical fibres for onward transmission. Here we analyse theoretically and numerically the effects of parallel off-axial misalignment in millimetre scale optical Fabry-Perot cavities. While near-concentric cavity configurations produce the smallest mode waist and thus strongest coupling to a trapped ion, their mode is extremely sensitive to misalignment. Shorter cavities exhibit more robust modes, but at the cost of larger mode waists. For example, for typical experimental parameters (mirror radius of curvature 0.7 mm, mirror diameter 0.140 mm, operation wavelength 850 nm) we find that the cavity lifetime is reduced by a factor 1/e for a misalignment of 0.95 nm for a beam waist of 2.91 um (cavity length of 1.397 mm), which increases to 11.0 nm for a waist of 4.33 um (length of 1.386 mm), and 3.12 um for a waist of 7.38 um (length of 1.273 mm). In the parameter regimes of interest, we derive a simple relation between cavity length, mirror radius, and misalignment sensitivity. Finally, we also consider the effect of mode matching of the misaligned cavity mode with the optical mode of the fibre for efficient cavity to fibre coupling. In conclusion, our model allows us to optimise photon-ion coupling in fibre-tip resonators for quantum information processing in the presence of finite fabrication and alignment tolerances.
Fiber Fabry-Perot cavities, formed by micro-machined mirrors on the end-facets of optical fibers, are used in an increasing number of technical and scientific applications. Some of the most promising areas of application of these optical micro-resonators with high finesse and small mode volume are in the field of quantum communication and information. The resonator-enhanced light-matter interaction, for instance, provide basis for the realization of efficient optical interfaces between stationary matter-based quantum nodes and flying single-photon qubits. To date fiber Fabry-Perot cavities have been successfully applied in experiments interfacing single photons with a wide range of quantum systems, including cold atoms, ions and solid state emitters as well as quantum optomechanical experiments. Here we address some important practical questions that arise during the experimental implementation of high finesse fiber Fabry-Perot cavities: How can optimal fiber cavity alignment be achieved and how can the efficiency of coupling light from the optical fibers to the cavity mode and vice versa be characterized? How should optical fiber cavities be constructed and stabilized to fulfill their potential for miniaturization and integration into robust scientific and technological devices that can operate outside of dedicated laboratory environments in the future? The first two questions we answer with an analytic mode matching calculation that relates the alignment dependent fiber-to-cavity mode-matching efficiency to the easily measurable dip in the reflected light power at the cavity resonance. Our general analysis provides a simple recipe for the optimal alignment of fiber Fabry-Perot cavities and moreover for the first time explains the asymmetry in their reflective line shapes. The latter question we explore by investigating a novel, intrinsically rigid fiber cavity design that makes use of the high passive stability of a monolithic cavity spacer and employs thermal self-locking and external temperature tuning. The performance of this novel approach is compared to a more traditional, piezomechanically-actuated resonator that is feedback stabilized to a reference laser based on the Pound-Drever-Hall locking technique. Finally, with the application of single photon interfacing in mind we discuss the issue of fiber-generated background photons in Fiber Fabry-Perot cavities. We believe that, due to their simplicity, compactness and robustness, rigid fiber cavities could be a promising solution for miniaturized, integratable and scalable cavity quantum electrodynamic devices and further applications of FFPC with similar requirements.
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.
Abstract Optical cavities are one of the best ways to increase atom-light coupling and will be a key ingredient for future quantum technologies that rely on light–matter interfaces. We demonstrate that traveling-wave ‘ring’ cavities can achieve small mode waists w (i.e. large atom-cavity coupling) while maintaining stability to fluctuations and large mirror separation. Additionally, our ring cavity design can achieve arbitrary transverse-mode spacing simultaneously with the large mode-waist reductions. Following these principles, we build a parabolic atom-ring cavity system that achieves strong collective coupling NC = 15(1) between N = 10 3 Rb atoms and a ring cavity with a single-atom cooperativity C that is significantly larger than what could be achieved with a near-confocal two-mirror cavity with the same mirror separation and finesse. By using parabolic mirrors, we eliminate astigmatism–which can otherwise preclude stable operation–and increase optical access to the atoms. Cavities based on these principles, with enhanced coupling and large mirror separation, will be particularly useful for achieving strong coupling with ions, Rydberg atoms, or other strongly interacting particles, which often have undesirable interactions with nearby surfaces.