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Physical Review A

Antiresonant Fabry-Pérot cavity with ultralow finesse

Tiantian Shi, Jianxiang Miao, Jia Zhang, Jingbiao Chen

Published Feb 22, 2023• 6 citations
Publisher

Abstract

The exact expressions of finesse and full width at half maximum (FWHM) of the Airy distribution of a Fabry-P\'erot (FP) resonator are derived, which solves the breakdown problem at ultralow reflectivity in traditional formulas. We demonstrate that, when the cavity-mirror reflectivity $R\ensuremath{\rightarrow}0$, the FWHM approaches half of the free spectral range rather than infinity; moreover, the cavity finesse $\mathcal{F}$ approaches 2 rather than zero. These expressions are useful for the development of bad-cavity lasers, such as the four-level active optical clock based on the strong atomic transition of cesium. Also, the exact expressions of the FWHM and finesse of the reflection distribution composed of reflected mode profiles are derived, which separately intersect with that of the Airy one at $R=0$. In addition, the characteristics of an antiresonant cavity, the frequency of which is exactly at the center of two adjacent resonant cavity modes, are analyzed. It is demonstrated that at the resonant and antiresonant frequencies the enhancement and inhibition of intracavity light intensity caused by the FP cavity are symmetrical in the logarithmic view. Furthermore, we provide a universal expression of the cavity-enhancement factor rather than the classical representation of ``$\text{2}\mathcal{F}/\phantom{\text{2}\mathcal{F}\ensuremath{\pi}}\phantom{\rule{0.0pt}{0ex}}\ensuremath{\pi}$,'' which is inadequate for the high-loss cavity because the cavity-enhancement factor should naturally reach 1 when $R\ensuremath{\rightarrow}0$. Finally, we extend the application of the antiresonant cavity to an inhibited laser, the frequency of which has a stronger suppression effect on the cavity-length thermal noise than the traditional resonant laser.

DOI
10.1103/physreva.107.023517

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The exact expressions of finesse and full width at half maximum (FWHM) of the Airy distribution of a Fabry-P'erot (FP) resonator are derived, which solves the breakdown problem at ultralow reflectivity in traditional formulas. We demonstrate that, when the cavity-mirror reflectivity R\ensuremath→0R\ensuremath{\rightarrow}0R\ensuremath→0, the FWHM approaches half of the free spectral range rather than infinity; moreover, the cavity finesse F\mathcal{F}F approaches 2 rather than zero. These expressions are useful for the development of bad-cavity lasers, such as the four-level active optical clock based on the strong atomic transition of cesium. Also, the exact expressions of the FWHM and finesse of the reflection distribution composed of reflected mode profiles are derived, which separately intersect with that of the Airy one at R=0R=0R=0. In addition, the characteristics of an antiresonant cavity, the frequency of which is exactly at the center of two adjacent resonant cavity modes, are analyzed. It is demonstrated that at the resonant and antiresonant frequencies the enhancement and inhibition of intracavity light intensity caused by the FP cavity are symmetrical in the logarithmic view. Furthermore, we provide a universal expression of the cavity-enhancement factor rather than the classical representation of ``2F/2F\ensuremathπ\ensuremathπ\text{2}\mathcal{F}/\phantom{\text{2}\mathcal{F}\ensuremath{\pi}}\phantom{\rule{0.0pt}{0ex}}\ensuremath{\pi}2F/2F\ensuremathπ\ensuremathπ,'' which is inadequate for the high-loss cavity because the cavity-enhancement factor should naturally reach 1 when R\ensuremath→0R\ensuremath{\rightarrow}0R\ensuremath→0. Finally, we extend the application of the antiresonant cavity to an inhibited laser, the frequency of which has a stronger suppression effect on the cavity-length thermal noise than the traditional resonant laser.
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.
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.
Cavity-based quantum node is a competitive platform for distributed quantum networks. Here, we characterize a high-finesse Fabry-Pérot optical resonator for coupling single or few atomic quantum registers. 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’ uncertainties are solely determined by the resolution of the WLM, eliminating all of the temporal environment fluctuations. Our scheme makes it possible to quantify the atom-cavity coupling constant up to four significant figures, the most precise and accurate estimation so far, which would become a key ingredient for benchmarking a cavity-based quantum node. Furthermore, the distortion of polarized photonic qubits would be minimized owing to the small birefringent splitting, below 4.9% of the cavity linewidth. Our system should operate in the intermediate atom-cavity coupling regime that would allow us to implement various quantum network protocols.
Traditional lasers function using resonant cavities, in which the round-trip optical path is exactly equal to an integer multiple of the intracavity wavelengths to constructively enhance the spontaneous emission rate. By taking advantage of the enhancement from the resonant cavity, the narrowest sub-10-mHz-linewidth laser and a 10−1610^{-16}10−16-fractional-frequency-stability superradiant active optical clock (AOC) have been achieved. However, a laser with atomic spontaneous radiation being destructively inhibited in an anti-resonant cavity, where the atomic resonance is exactly between two adjacent cavity resonances, has not been reported. Herein, we experimentally demonstrate inhibited stimulated emission and termed it an inhibited laser. Compared with traditional superradiant AOCs, which exhibit superiority in terms of the high suppression of cavity noise, the suppression of the cavity-pulling effect of an inhibited laser can be further improved by a factor of (2F/pi)2(2F/pi)^2(2F/pi)2, i.e., 2.07 in this work, which was improved from 26 to 53 times. This study will guide further development of AOCs with better stability, and thus, it is significant for quantum metrology and may lead to new research in the laser physics and cavity quantum electrodynamics fields.
SummaryActive optical atomic clocks are emerging as a new promising tool for time and frequency metrology. Such clocks have the potential to reach a fractional frequency instability in the 10-18range at one second [1]. These references are based on the superradiant emission of an ensemble of atoms coupled to a single mode of the electromagnetic field [2]. For optical references, this coupling is achieved through a resonant high-finesse Fabry-Perot cavity that therefore plays a crucial role to reach superradiant lasing. Specific characteristics are required to permit superradiant emission in a metrologically relevant regime: tunability of the cavity resonant frequency, ability to accommodate atoms and low fractional length fluctuations, in the order of 10-13. This work shows the conception, through simulation, assembly and preliminary characterization of this Fabry Perot cavity.