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arXiv:2504.02980

Effective Mode Description for Macroscopic Fabry Pérot Cavities

Taylor, Michael A. D., Jonathan Soderquist, Pengfei Huo

Published Apr 3, 2025• 0 citations
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Abstract

We introduce an effective modes formalism to describe how the quasi-continuum of photonic modes in an optical cavity effectively behaves in the strong light-matter coupling regime of cavity quantum electrodynamics. By expressing these effective modes, we are able to reproduce the cavity dispersion relation while showing that the mode volumes of these effective modes are independent of the physical area of the Fabry-Pérot cavity mirrors and are instead a measure of light-matter coupling strength, dependent on cavity design parameters such as mirror reflectivity.

DOI
10.48550/arxiv.2504.02980

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We introduce an effective modes formalism to describe how the quasi-continuum of photonic modes in an optical cavity effectively behaves in the strong light-matter coupling regime of cavity quantum electrodynamics. By expressing these effective modes, we are able to reproduce the cavity dispersion relation while showing that the mode volumes of these effective modes are independent of the physical area of the Fabry-Pérot cavity mirrors and are instead a measure of light-matter coupling strength, dependent on cavity design parameters such as mirror reflectivity.
Specific forms of the travelling and trapped vector mode functions for a three-dimensional Fabry-Perot cavity are developed from the general results of the preceding paper, with parameters describing the output cavity mirror chosen for a typical high Q cavity case. Cavity and external quasi-mode functions associated with the quasi-mode theory of macroscopic canonical quantization are then obtained via an idealized choice of output mirror parameters. The coupling constants describing photon exchange processes between the single cavity quasi-mode associated with each Fabry-Perot resonance and various external quasi-modes are calculated, and their slow dependence on the external quasi-mode frequency shows that the conditions for irreversible Markovian damping of the cavity quasi-mode are satisfied. For radiative atoms placed in the cavity the coupling constants for energy exchange processes with sideways travelling external quasi-modes also vary slowely, so that Markovian spontaneous emission damping occurs for the radiative atoms. However, their coupling with the isolated cavity quasi-modes is associated with reversible photon exchanges as represented via one photon Rabi frequencies. The standard model in cavity quantum electrodynamics, in which the basic processes are described by a cavity damping rate, a radiative atom spontaneous decay rate and an atom-cavity mode coupling constant has now been justified in terms of the quasi-mode theory of macroscopic canonical quantization.
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.
In the present and the accompanying paper a justification of the standard model of cavity quantum electrodynamics is given in terms of a quasi-mode theory of macroscopic canonical quantization. The coupling of the cavity quasi-mode to external quasi-modes is treated for the representative case of the three-dimensional Fabry-Perot cavity. The general form of the travelling and trapped mode functions for this cavity are derived in this paper and the mode-mode coupling constants are calculated in the accompanying paper. The slow dependence of the coupling constants with the mode frequency difference demonstrates that the conditions for Markovian damping of the cavity quasimode are satisfied. As also discussed in the accompanying paper, the interaction of radiative atoms with cavity quasi-modes is associated with reversible energy exchanges between atom and cavity and represented by Rabi coupling constants. The interaction of radiative atoms located within the cavity with sideways travelling external quasi-modes involves slowly varying coupling constants and is associated with irreversible spontaneous emission dampling. The basic processes represented in the standard cavity quantum electrodynamics model and the associated coupling constant and decay rates thereby follow from the quasi-mode theory.
We characterize a high-finesse Fabry-Perot resonator for coupling with single neutral atoms. Our cavity consists of two mirrors with different reflectivities: One has minimal optical loss, and the other high transmission loss where more than 90% of the intracavity photons would be emitted. Cavity finesse, birefringent effects, and mechanical resonances are measured using the lasers at 780, 782, and 795 nm. In order to obtain cavity geometric parameters, we drive the adjacent longitudinal or transverse modes with two lasers simultaneously, and measure those frequencies using a precision wavelength meter (WLM). A major novelty of this method is that the parameters' uncertainty is solely determined by the resolution of the WLM, eliminating all of the temporal environment fluctuations. Moreover, the technique with two lasers consists of a vital approach for determining geometric parameters of a short cavity, with a free spectral range on the order of THz. Our system operates in the strong atom-cavity coupling regime that allows us to explore fundamental quantum optics and implement quantum network protocols.
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, where they typically require precise stabilization of their optical resonances. Here, we study two different approaches to construct fiber Fabry–Perot resonators and stabilize their length for experiments in cavity quantum electrodynamics with neutral atoms. A piezo-mechanically actuated cavity with feedback based on the Pound–Drever–Hall locking technique is compared to a novel rigid cavity design that makes use of the high passive stability of a monolithic cavity spacer and employs thermal self-locking and external temperature tuning. Furthermore, we present a general analysis of the mode matching problem in fiber Fabry–Perot cavities, which explains the asymmetry in their reflective line shapes and has important implications for the optimal alignment of the fiber resonators. Finally, we discuss the issue of fiber-generated background photons. We expect that our results contribute toward the integration of high-finesse fiber Fabry–Perot cavities into compact and robust quantum-enabled devices in the future.