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Physical Review A

Active whispering-gallery microclock in pulsed-operation mode

Deshui Yu, Jingbiao Chen, Shougang Zhang

Published Apr 26, 2023• 4 citations
Publisher

Abstract

A whispering-gallery-mode microlaser in the bad-cavity limit serves as an active optical clock. In this clock scheme, an ensemble of two-level atoms is trapped in a two-color ring-shaped optical lattice, i.e., Lamb-Dicke regime, and evanescently interacts with an optical microcavity. The microclock is operated in the pulsed mode, where the atoms are periodically pumped into the upper state of the electric-dipole-forbidden clock transition, providing the optical gain. The numerical simulation shows that the fractional frequency instability of the microclock reaches $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ at ${10}^{3}$ s of averaging, mainly limited by the lattice-induced frequency shifts. This miniature optical clock owns the high integration and can be potentially used to supply the time standard in a photonic network, paving the way towards the on-chip metrology.

DOI
10.1103/physreva.107.043712

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A whispering-gallery-mode microlaser in the bad-cavity limit serves as an active optical clock. In this clock scheme, an ensemble of two-level atoms is trapped in a two-color ring-shaped optical lattice, i.e., Lamb-Dicke regime, and evanescently interacts with an optical microcavity. The microclock is operated in the pulsed mode, where the atoms are periodically pumped into the upper state of the electric-dipole-forbidden clock transition, providing the optical gain. The numerical simulation shows that the fractional frequency instability of the microclock reaches 5\ifmmode×\else\texttimes\fi10\ensuremath−145\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}5\ifmmode×\else\texttimes\fi10\ensuremath−14 at 103{10}^{3}103 s of averaging, mainly limited by the lattice-induced frequency shifts. This miniature optical clock owns the high integration and can be potentially used to supply the time standard in a photonic network, paving the way towards the on-chip metrology.
Abstract Optical atomic clocks with compact size, reduced weight and low power consumption have broad out-of-the-lab applications such as satellite-based geo-positioning and communication engineering. Here, we propose an active optical microclock based on the lattice-trapped atoms evanescently interacting with a whispering-gallery-mode microcavity. Unlike the conventional passive clock scheme, the active operation directly produces the optical frequency standard without the need of extra laser stabilization, substantially simplifying the clock configuration. The numerical simulation illustrates that the microclock’s frequency stability reaches 1.5 × 10 − 14 at 1 s of averaging, over one order of magnitude better than the recently demonstrated chip-scale optical clock that is built upon rubidium vapor cell and also more stable than current cesium fountain clocks and hydrogen masers. Our work extends the chip-scale clocks to the active fashion, paving the way towards the on-chip quantum micro-metrology, for example, the optical frequency comparison and synchronization between multiple microclocks through frequency microcombs.
Microlasers, relying on the strong coupling between active particles and optical microcavity, exhibit fundamental differences from conventional lasers, such as multi-threshold/thresholdless behavior and nonclassical photon emission. As light sources, microlasers possess extensive applications in precision measurement, quantum information processing, and biochemical sensing. Here we propose a whispering-gallery-mode microlaser scheme, where ultracold alkaline-earth metal atoms, i.e., gain medium, are tightly confined in a two-color evanescent lattice that is in the ring shape and formed around a microsphere. To suppress the influence of the lattice-induced ac Stark shift on the moderately-narrow-linewidth laser transition, the red-detuned trapping beams operate at a magic wavelength while the wavelength of the blue-detuned trapping beam is set close to the other magic wavelength. The tiny mode volume and high quality factor of the microsphere ensure the strong atom-microcavity coupling in the bad-cavity regime. As a result, both saturation photon and critical atom numbers, which characterize the laser performance, are substantially reduced below unity. We explore the lasing action of the coupled system by using the Monte Carlo approach. Our scheme may be potentially generalized to the microlasers based on the forbidden clock transitions, holding the prospect for microscale active optical clocks in precision measurement and frequency metrology.
We demonstrate the state-of-the-art technique of an active clock to provide a continuous superradiant lasing signal using an ensemble of trapped Cs atoms in an optical lattice. A magic wavelength of the proposed $|7{S}_{1/2};F=4,{M}_{F}=0\ensuremath{\rangle}\ensuremath{\rightarrow}|6{P}_{3/2};F=3,{M}_{F}=0\ensuremath{\rangle}$ clock transition in Cs atoms is identified at 1181 nm for constructing the optical lattice. Pertinent optical lines are also found for pumping and repumping atoms from their ground states. A fractional uncertainty about ${10}^{\ensuremath{-}15}$ in the clock frequency has been predicted by carrying out rigorous calculations of several atomic properties. The bad-cavity operational mode of the active clock is anticipated to improve remarkably its short-term stability by suppressing intrinsic thermal fluctuations. Thus, a composite clock system with better short-term and long-term stabilities can be built by combining the proposed active clock with another high-accuracy passive optical clock.
Active optical clocks, a new class of optical atomic clocks, work through stimulated emission lasing, a unique mechanism that is distinct from laser absorption spectroscopy of conventional optical clocks. With coherent weak optical feedback from a Fabry-Perot resonator operating in the bad-cavity regime, active optical clocks sustain a lasing oscillation at an atomic transition frequency. They are used directly as quantum optical frequency standards with expected stability better by about two orders of magnitude than that of the best clocks. This review starts with a simplified account of historical developments and the limitations of critical techniques in optical atomic clocks. After an introduction of the basic mechanism underlying active optical clocks, we discuss the most recent experimental results for several configurations and experimental set-ups of active optical clocks. These include those based on a 2-level atomic beam and 3-level laser-cooled trapped-atom system, those based on a 4-level atom scheme, and the Faraday active optical clock. Moreover, following the successful lasing and preliminary results on a Faraday active optical frequency standard with Faraday atomic filter using thermal Cs cell, we describe an experimental scheme of a Faraday active optical clock with a Faraday atomic filter using magic-lattice-trapped Sr atoms at the 689-nm transition, and Faraday optical clocks operating in the good-cavity regime. We conclude with a comprehensive comparison of the different active optical clocks, prospects for active Faraday optical clocks, and potential applications of active optical clocks.
Abstract Active optical clocks take advantage of the substantial suppression of cavity pulling in the bad‐cavity lasing regime and feature the simple structure and excellent portability. In the extreme case, where the cavity mirror reflection approaches zero and cannot support any quasi‐bound modes for light waves, conventional bad‐cavity lasers become the cavityless lasing and the cavity pulling vanishes. Consequently, the laser frequency is determined entirely by the atomic transition. This work is dedicated to theoretically explore the potential application of the cavityless lasing in active optical clocks. Without loss of generality, Cs atoms with well‐established quantum control techniques are employed as the gain medium that is pumped by a 459‐nm laser. The clock laser wavelength is 1470 nm. The simulation shows that the frequency stability of the clock laser with feasible physical quantities reaches at 1 s of averaging time, one order of magnitude better than the recently demonstrated compact passive optical clocks that are built upon a two‐photon transition in a hot Rb vapor and upon the modulation transfer spectroscopy of thermal Cs atoms. Such compact cavityless lasing‐based active optical clocks have the broad application prospect in satellite navigation and communications and promise an architecture for the integrated photonic metrology.
We consider various approaches to the creation of a high-stability active optical frequency standard, where the atomic ensemble itself produces a highly stable and accurate frequency signal. The short-time frequency stability of such standards may overcome the stability of lasers stabilized to macroscopic cavities which are used as local oscillators in the modern optical frequency standard systems. The main idea is to create a “superradiant” laser operating deep in the bad cavity regime, where the decay rate of the cavity field significantly exceeds the decoherence rate of the lasing transition. Two main approaches towards the realization of an active optical frequency standard have been proposed already: the optical lattice laser, and the atomic beam laser. We consider these and some alternative approaches, and discuss the parameters for atomic ensembles necessary to attain the metrology relevant level of short-time frequency stability, and various effects and main challenges critical for practical implementations.