We analyze an efficient frequency estimation scheme that is applied to measure the unknown frequency of an atomic state in Ramsey spectroscopy. The scheme is employing appropriate combinations of uncorrelated probe atoms and Greenberger–Horne–Zeilinger (GHZ) type correlated probe atoms to estimate its frequency. The estimation value of frequency is obtained through the Bayesian analysis of the final measurement outcomes. The proposed scheme allows us to obtain better precision than the scheme without quantum correlation and it also prevents us from ambiguity in the frequency estimation procedure with GHZ correlations only. We show that the scheme can beat the shot-noise limit and, in addition, it is found that there is a trade-off relation between the precision of the frequency estimation and the decoherence rate in the atomic states.
We analyze an efficient frequency estimation scheme that is applied to measure the unknown frequency of an atomic state in Ramsey spectroscopy. The scheme is employing appropriate combinations of uncorrelated probe atoms and Greenberger–Horne–Zeilinger (GHZ) type correlated probe atoms to estimate its frequency. The estimation value of frequency is obtained through the Bayesian analysis of the final measurement outcomes. The proposed scheme allows us to obtain better precision than the scheme without quantum correlation and it also prevents us from ambiguity in the frequency estimation procedure with GHZ correlations only. We show that the scheme can beat the shot-noise limit and, in addition, it is found that there is a trade-off relation between the precision of the frequency estimation and the decoherence rate in the atomic states.
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.
For single-parameter sensing, Greenberger-Horne-Zeilinger (GHZ) probes achieve optimal quantum-enhanced precision across the unknown parameter range, solely relying on parameter-independent separable measurement strategies for all values of the unknown parameter. However, in the multiparameter setting, a single GHZ probe not only fails to achieve quantum advantage but also the corresponding optimal measurement becomes complex and dependent on the unknown parameters. Here, we provide a recipe for multiparameter sensing with GHZ probes using quantum error correction techniques by treating all but one unknown parameters as noise, whose effects can be corrected. This strategy restores the core advantage of single parameter GHZ-based quantum sensing, namely reaching optimally quantum-enhanced precision for all unknown parameter values while keeping the measurements separable and fixed. Specifically, given one shielded ancilla qubit per GHZ probe, our protocol extracts optimal possible precision for any probe size. While this optimal precision is shot-noise limited for a single GHZ probe, we recover the Heisenberg scaling through use of multiple complementary GHZ probes. We demonstrate the effectiveness of the protocol with Bayesian estimation.
The use of correlated states and measurements promises improvements in the accuracy of frequency metrology and the stability of atomic clocks. However, developing strategies robust against dominant noise processes remains challenging. We address the issue of decoherence due to spontaneous decay and show that Greenberger-Horne-Zeilinger (GHZ) states, in conjunction with a correlated measurement and nonlinear estimation strategy, achieve gains of up to 2.25 dB, comparable to fundamental bounds for up to about 80 atoms in the presence of decoherence. This result is surprising since GHZ states do not provide any enhancement under dephasing due to white frequency noise compared to the standard quantum limit of uncorrelated states. The gain arises from a veto signal, which allows for the detection and mitigation of errors caused by spontaneous emission events. Through comprehensive Monte-Carlo simulations of atomic clocks, we demonstrate the robustness of the GHZ protocol.
The use of correlated states and measurements promises improvements in the accuracy of frequency metrology and the stability of atomic clocks. However, developing strategies robust against dominant noise processes remains challenging. We address the issue of decoherence due to spontaneous decay and show that Greenberger-Horne-Zeilinger (GHZ) states, in conjunction with a correlated measurement and nonlinear estimation strategy, achieve gains of up to 2.25 decibel, comparable to fundamental bounds for up to about 80 atoms in the presence of decoherence. This result is unexpected because GHZ states do not provide any enhancement under dephasing due to white frequency noise compared to the standard quantum limit of uncorrelated states. The gain arises from a veto signal, which allows for the detection and mitigation of errors caused by spontaneous emission events. Through comprehensive Monte Carlo simulations of atomic clocks, we demonstrate the robustness of the GHZ protocol.
Dephasing noise is a ubiquitous source of decoherence in current atomic sensors. We address the problem of entanglement-assisted frequency estimation subject to classical dephasing noise with full spatial correlations (collective) and arbitrary temporal correlations. Our contributions are threefold. (i) We derive rigorous, state-independent bounds on the achievable estimation precision, showing how they are entirely determined by the short-time behavior of the decoherence function. For temporally uncorrelated (Markovian) dephasing, precision is limited by a probe-independent constant. For temporally correlated stationary noise, the bound approaches the noiseless limit for classical states, precluding any asymptotic quantum advantage. (ii) We show that these scaling bounds are tight, by constructing generalized Ramsey protocols that saturate them. These optimal protocols use squeezing at the input and before readout, both of which are available in state-of-the-art atomic interferometers. Implementing a perfect-echo protocol, which reaches Heisenberg scaling in the absence of noise, remains optimal in this noisy setting, irrespective of the noise temporal correlations. (iii) We prove that arbitrary collective open-loop control cannot lift the no-go for super-classical precision scaling under either Markovian or colored stationary noise, highlighting the detrimental nature of full spatial correlations. In the latter case, temporal correlations may nonetheless enable constant-factor improvements over the standard quantum limit, which may still be important in practical metrological scenarios.
The use of correlated states and measurements promises improvements in the accuracy of frequency metrology and the stability of atomic clocks. However, developing strategies robust against dominant noise processes remains challenging. We address the issue of decoherence due to spontaneous decay and show that Greenberger-Horne-Zeilinger (GHZ) states, in conjunction with a correlated measurement and nonlinear estimation strategy, achieve gains of up to 2.25 decibel, comparable to fundamental bounds for up to about 80 atoms in the presence of decoherence. This result is unexpected because GHZ states do not provide any enhancement under dephasing due to white frequency noise compared to the standard quantum limit of uncorrelated states. The gain arises from a veto signal, which allows for the detection and mitigation of errors caused by spontaneous emission events. Through comprehensive Monte Carlo simulations of atomic clocks, we demonstrate the robustness of the GHZ protocol.