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Advanced Quantum Technologies

Prospects for an Active Optical Clock Based on Cavityless Lasing

Deshui Yu, Jia Zhang, Shougang Zhang, Jingbiao Chen

Published Dec 31, 2023• 8 citations
Publisher

Abstract

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.

DOI
10.1002/qute.202300308

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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.

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Lasing of cesium active optical clock with 459 nm laser pumping

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We realize the lasing of cesium active optical clock with 459 nm laser pumping, which operates deep in the optical bad-cavity regime. The ratio between cavity bandwidth and gain bandwidth is 55.08 theoretically. With 459 nm laser pumping, the population inversion occurs between the cesium 7S1/2state and 6P3/2state, and the stimulated radiation between the two states is realized. The 1469.9 nm output signal of cesium active optical clock can reach a power of 8 μW. The output power also shows a threshold character with pumping laser power and can be influenced by the Cs cell temperature. This active optical clock has an advantage in stability over the conventional optical clocks, due to its suppression of cavity pulling effect, which is also demonstrated experimentally.

Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)•May 1, 2014•18 citations
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.
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 Optical clocks with thermal atoms are characterized by compact size, simple structure, reduced weight, and low power consumption and have the potential for broad out-of-the-lab and commercial applications. Here, we demonstrate a 459 nm optical clock based on the 6S 1/2 –7P 1/2 transition in thermal 133 Cs atoms. Two methods, modulation transfer spectroscopy (MTS) and frequency modulation spectroscopy (FMS), are employed to stabilize the frequency of a 459 nm commercial laser to the atomic transition. The MTS-MTS and MTS-FMS beat-note measurements show short-term frequency stabilities of 3.7 × 10 − 13 / τ and 6.4 × 10 − 13 / τ , respectively, at the averaging time τ . The 459 nm passive optical clock further serves as the pump for an active 1470 nm optical clock based on the cavityless lasing. The resultant 1470 nm output power reaches over 10 μW and the pump-beam-induced light shift is estimated to be 2 π × 11 Hz with a fractional uncertainty of 2.4 × 10 −18 . These results demonstrate the feasibility of hybridizing passive and active optical clocks, providing a promising route toward compact multi-wavelength optical frequency standards.
We experimentally demonstrate the collective emission behavior and suppressed cavity-pulling effect of four-level active optical clock with Cesium atoms. Thermal Cesium atoms in a glass cell velocity selective pumped with a 455.5 nm laser operating at 6S1/2_{1/2}1/2​ to 7P3/2_{3/2}3/2​ transition are used as lasing medium. Population inverted Cesium atoms between 7S1/2_{1/2}1/2​ and 6P3/2_{3/2}3/2​ levels are optical weakly coupled by a pair cavity mirrors working at deep bad-cavity regime with a finesse of 4.3, and the ratio between cavity bandwidth and gain bandwidth is approximately 45. With increased 455.5 nm pumping laser intensity, the output power of cesium active optical clock at 1469.9 nm from 7S1/2_{1/2}1/2​ level to 6P3/2_{3/2}3/2​ level shows a threshold and reach a power of 13 μμμW. Active optical clock would dramatically improve the optical clock stability since the lasing frequency does not follow the cavity length variation exactly, but in a form of suppressed cavity pulling effect. In this letter the cavity pulling effect is measured using a Fabry-Perot interferometer (FPI) to be reduced by a factor of 38.2 and 41.4 as the detuning between the 1469.9 nm cavity length of the Cs active optical clock and the Cs 1469.9 nm transition is set to be 140.8 MHz and 281.6 MHz respectively. The mechanism demonstrated here is of great significance for new generation optical clocks and can be applied to improve the stability of best optical clocks by at least two orders of magnitude.
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.
Atomic clocks can be broadly classified into passive and active types according to their mode of operation. In the microwave domain, active hydrogen masers provide excellent short-term stability and are widely used as flywheel oscillators in timekeeping systems along with the cesium fountain standards. In the optical domain, passive optical clocks have achieved unprecedented accuracy and stability, but at the cost of large and complex infrastructures associated with ultrastable cavities and the preparation of atoms in optical lattices or ion traps. By contrast, active optical clocks generate coherent clock light directly from an atomic transition in the bad-cavity regime, where cavity pulling is strongly suppressed, thereby reducing sensitivity to cavity fluctuations and potentially simplifying optical clock architectures. Over the past decade, active optical clocks have developed from a conceptual proposal into a rapidly advancing field that includes pulsed superradiant systems based on cold atoms and continuous-wave bad-cavity systems based on thermal atomic vapors. This review summarizes recent progress in active optical clocks and discusses future directions of the field.
We realize the lasing of cesium active optical clock with 459 nm laser pumping, which operates deep in the optical bad-cavity regime. The ratio between cavity bandwidth and gain bandwidth is 55.08 theoretically. With 459 nm laser pumping, the population inversion occurs between the cesium 7S1/2state and 6P3/2state, and the stimulated radiation between the two states is realized. The 1469.9 nm output signal of cesium active optical clock can reach a power of 8 μW. The output power also shows a threshold character with pumping laser power and can be influenced by the Cs cell temperature. This active optical clock has an advantage in stability over the conventional optical clocks, due to its suppression of cavity pulling effect, which is also demonstrated experimentally.