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arXiv:2306.06608 · Physical Review Applied

Atomic clock locking with Bayesian quantum parameter estimation: Scheme and experiment

Chengyin Han, Zhu Ma, Yuxiang Qiu, Ruihuan Fang, Jiatao Wu, Zhan Chang, Maojie Li, Jiahao Huang, Bo Lü, Chaohong Lee

Published Oct 23, 2024• 12 citations
arXivHTMLPDF

Abstract

Atomic clocks are crucial for fundamental science and practical technology, but their sensitivity is often constrained by the standard quantum limit. With a cold-atom coherent-population-trapping clock, the authors design and experimentally demonstrate an adaptive Bayesian quantum frequency estimation protocol that approaches the Heisenberg scaling with respect to total interrogation time. This atomic clock also yields improved fractional frequency stability and enhanced robustness against technical noises. This work provides a high-precision approach to atomic clock locking, and holds promising applications in various interferometry-based quantum sensors.

DOI
10.1103/physrevapplied.22.044058

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Atomic clocks are crucial for fundamental science and practical technology, but their sensitivity is often constrained by the standard quantum limit. With a cold-atom coherent-population-trapping clock, the authors design and experimentally demonstrate an adaptive Bayesian quantum frequency estimation protocol that approaches the Heisenberg scaling with respect to total interrogation time. This atomic clock also yields improved fractional frequency stability and enhanced robustness against technical noises. This work provides a high-precision approach to atomic clock locking, and holds promising applications in various interferometry-based quantum sensors.
Frequency metrology is a cornerstone of modern precision measurements and optical atomic clocks have emerged as one of the most precise measurement devices. In this progress report, we explore various Ramsey interrogation schemes tailored to optical atomic clocks primarily limited by laser noise. To incorporate frequency fluctuations directly into the theoretical model, we consider a Bayesian framework. In this context, we review fundamental bounds arising in Bayesian estimation theory, which serve as a benchmark throughout this work. We investigate the trade-off between entanglement-enhanced sensitivity and robustness against laser noise in order to identify optimal initial states, measurement schemes and estimation strategies. Beside standard protocols based on coherent spin states, spin-squeezed states and Greenberger-Horne-Zeilinger states, we consider variational Ramsey protocols implemented via low-depth quantum circuits based on one-axis twisting operations to approach optimal stability. In particular, we review known and identify new optimal Ramsey interrogation schemes for a variety of scenarios, including different experimental platforms, ensemble sizes and regimes characterized by a wide range of interrogation durations and dead times. Hence, this work establishes a comprehensive theoretical framework for optimizing Ramsey interrogation schemes, providing guidance for the development of next-generation optical atomic clocks.
In atom interferometry the phase evolution of a quantum superposition state is measured with respect to a reference signal. The measurement has a limited unambiguous interval, since not the phase but its projection is measured as a population unbalance on two energetic levels. Resolving phase wrapping brings to a longer interrogation interval and hence instrument sensitivity. We extended the unambiguous probe interval using coherence preserving measurements and phase corrections, and demonstrated the phase lock of the clock oscillator to an atomic superposition state. On this basis we implemented a protocol to improve atomic clocks limited by local oscillator noise, which is the case of optical atomic clocks, nowadays the best frequency standard in terms of both accuracy and precision. The technique could be adopted to enhance the sensitivity of atomic gravimeters.
Atomic gravimeters are the most accurate sensors for measuring gravity, yet a significant challenge lies in achieving high precision while also maintaining high dynamic range and robustness. Here, we develop a protocol for achieving robust high-precision atomic gravimetry based upon adaptive Bayesian quantum estimation. Our protocol incorporates a sequence of interferometry measurements taken with short to long interrogation times and offers several crucial advantages. Firstly, it enables a high dynamic range without the need to scan multiple fringes for pre-estimation, making it more efficient than the conventional frequentist method. Secondly, it improves robustness against noises, allowing for a significant improvement in measurement precision in noisy environments. The enhancement can be more than 5 times for a transportable gravimeter [] and up to an order of magnitude for a state-of-the-art fountain gravimeter []. Notably, by optimizing the interferometry sequence, our approach can improve the scaling of the measurement precision ( Δ g est ) versus the total interrogation time ( T ̃ ) to Δ g est ∝ T ̃ − 2 or even better, in contrast to the conventional one Δ g est ∝ T ̃ − 0.5 . Our approach offers superior precision, increased dynamic range, and enhanced robustness, making it highly promising for a range of practical sensing applications.
A compact cold-atom clock based on coherent population trapping (CPT) has been developed. The clock typically demonstrates a short-term fractional frequency stability of 4×10−11/√τ, limited by frequency noise on the interrogation lasers. The clock interrogates a sample of 2×105atoms under free-fall with typical cycle and Ramsey periods of 50 ms and 16 ms, respectively. The largest two systematic frequency shifts that can limit the clock's long-term stability are the light shift and the Doppler shift.
A review of a cold-atom clock based on coherent population trapping that highlights recent progress will be presented. Improvements in the coherence of the interrogation spectrum have resulted in the generation of dark states in the cold Rb atoms with essentially 100 % transmission – evidence that decoherence in this system is negligible. This improvement in coherence has resulted in improved short-term stability at the level of 1.5E-11 fractional frequency stability for a one second integration period. In combination with improved interrogation schemes, the improved spectrum has also resulted in dramatically smaller light shifts and improved long-term frequency stability – with the clock averaging down to the level of 1E-13 fractional frequency stability on time scales of over 10,000 seconds.
We present a quantum-enhanced atomic clock protocol based on groups of sequentially larger Greenberger-Horne-Zeilinger (GHZ) states that achieves the best clock stability allowed by quantum theory up to a logarithmic correction. Importantly the protocol is designed to work under realistic conditions where the drift of the phase of the laser interrogating the atoms is the main source of decoherence. The simultaneous interrogation of the laser phase with a cascade of GHZ states realizes an incoherent version of the phase estimation algorithm that enables Heisenberg-limited operation while extending the coherent interrogation time beyond the laser noise limit. We compare and merge the new protocol with existing state of the art interrogation schemes, and identify the precise conditions under which entanglement provides an advantage for clock stabilization: it allows a significant gain in the stability for short averaging time.