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Physical Review A

Phase amplification via synthetic two-axis-twisting echo from interaction-fixed one-axis twisting

Jihao Ma, Jungeng Zhou, Jiahao Huang, Chaohong Lee

Published Aug 5, 2024• 4 citations
Publisher

Abstract

One-axis twisting (OAT) and two-axis twisting (TAT) are well-known methods for achieving entanglement-enhanced quantum metrology, and their time-reversal echo offers a potent tool for approaching the Heisenberg limit even with detection noise. However, flipping the sign of interaction to implement the time-reversal echo is generally challenging. Here, we propose an echo protocol based on synthetic TAT from interaction-fixed OAT in a pseudospin-1/2 ensemble to achieve time-reversal quantum metrology. By applying modulation pulses around two different orthogonal directions, the effective TAT and its echo can be realized without changing the interaction. We demonstrate that this protocol not only outperforms the OAT echo scheme in both metrological gain and evolution time but is also robust against detection noise. Our protocol presents a TAT echo scheme that effectively avoids flipping the sign of interaction, providing a viable method for improving precision and robustness of quantum metrology.

DOI
10.1103/physreva.110.022407

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•Jan 1, 2023•0 citations
One-axis twisting (OAT) and two-axis twisting (TAT) are well-known methods for achieving entanglement-enhanced quantum metrology, and their time-reversal echo offers a potent tool for approaching the Heisenberg limit even with detection noise. However, flipping the sign of interaction to implement the time-reversal echo is generally challenging. Here, we propose an echo protocol based on synthetic TAT from interaction-fixed OAT in a pseudospin-1/2 ensemble to achieve time-reversal quantum metrology. By applying modulation pulses around two different orthogonal directions, the effective TAT and its echo can be realized without changing the interaction. We demonstrate that this protocol not only outperforms the OAT echo scheme in both metrological gain and evolution time but is also robust against detection noise. Our protocol presents a TAT echo scheme that effectively avoids flipping the sign of interaction, providing a viable method for improving precision and robustness of quantum metrology.
Entanglement-enhanced atom interferometry has the potential of surpassing the standard quantum limit and eventually reaching the ultimate Heisenberg bound. The experimental progress is, however, hindered by various technical noise sources, including the noise in the detection of the output quantum state. The influence of detection noise can be largely overcome by exploiting echo schemes, where the entanglement-generating interaction is repeated after the interferometer sequence. Here, we propose an echo protocol that uses two-axis countertwisting as the main nonlinear interaction. We demonstrate that the scheme is robust to detection noise and its performance is superior compared to the already demonstrated one-axis twisting echo scheme. In particular, the sensitivity maintains the Heisenberg scaling in the limit of a large particle number. Finally, we show that the protocol can be implemented with spinor Bose-Einstein condensates. Our results thus outline a realistic approach to mitigate the detection noise in quantum-enhanced interferometry.
One core of quantum metrology is the utilization of entanglement to enhance measurement precision beyond the standard quantum limit. Here, we utilize the Floquet-engineered two-axis twisting (TAT) and turn dynamics to generate GHZ-like states for quantum metrology. Using both analytical semi-classical and quantum approaches, we find that the desired NNN-particle GHZ-like state can be produced in a remarkably short time topt∝ln⁡N/Nt_\mathrm{opt}\propto \ln{N}/{N}topt​∝lnN/N, and its quantum Fisher information FQopt∝N2F^\mathrm{opt}_\mathrm{Q}\propto N^2FQopt​∝N2 approaches the Heisenberg limit. Owing to the rapid state preparation, it shows outstanding robustness against decoherence. Moreover, using the Floquet-engineered anti-TAT-and-turn, one may implement an efficient interaction-based readout protocol to extract the signal encoded in this GHZ-like state. This Floquet-engineered anti-TAT-and-turn approach offers a viable method to achieve effective time-reversal dynamics to improve measurement precision and resilience against detection noise, all without the need to invert the sign of the nonlinear interaction. This study paves a way for achieving entanglement-enhanced quantum metrology via rapid generation of GHZ-like states at high particle numbers through continuous Floquet engineering.
Spin cat states are promising candidates for quantum-enhanced measurement. Here, we analytically show that the ultimate measurement precision of spin cat states approaches the Heisenberg limit, where the uncertainty is inversely proportional to the total particle number. In order to fully exploit their metrological ability, we propose to use the interaction-based readout for implementing phase estimation. It is demonstrated that the interaction-based readout enables spin cat states to saturate their ultimate precision bounds. The interaction-based readout comprises a one-axis twisting, two $\frac{\ensuremath{\pi}}{2}$ pulses, and a population measurement, which can be realized via current experimental techniques. Compared with the twisting echo scheme on spin squeezed states, our scheme with spin cat states is more robust against detection noise. Our scheme may pave an experimentally feasible way to achieve Heisenberg-limited metrology with non-Gaussian entangled states.
We study a variational class of generalized Ramsey protocols that include two one-axis twisting (OAT) operations, one performed before the phase imprint and the other after. In this framework, we optimize the axes of the signal imprint, the OAT interactions, and the direction of the final projective measurement. We distinguish between protocols that exhibit symmetric or antisymmetric dependencies of the spin projection signal on the measured phase. Our results show that the quantum Fisher information, which sets the limits on the sensitivity achievable with a given one-axis twisted input state, can be saturated within our class of variational protocols for almost all initial twisting strengths. By incorporating numerous protocols previously documented in the literature, our approach creates a unified framework for Ramsey echo protocols with OAT states and measurements.
Quantum-enhanced sensing with atomic ensembles has predominantly focused on qubit-based protocols, despite the growing ability of many experimental platforms to coherently control and entangle multi-level systems. Here, we investigate quantum-enhanced sensing with qutrit ensembles by introducing three experimentally feasible qutrit generalisations of the one-axis twisting (OAT) model that involve entangling operations only between two levels, while the third level primarily acts as a spectator. We characterize the metrological utility of the dynamically generated states using the quantum Fisher information toolbox. We find numerically that all three models offer considerable freedom in encoding direction for quantum-enhanced sensing, with up to 6 out of 8 possible directions exhibit near-Heisenberg scaling after a short evolution time. We discuss experimental access to this enhanced metrological precision via effective time-reversal protocols. Furthermore, we examine the practical issues of estimation ambiguity and local dissipation, and show that they can be largely overcome by optimizing the sensor operating point. Finally, we show that the measurement incompatibility in estimating multiple parameters simultaneously encoded in different directions with near-Heisenberg scaling of precision is suppressed at the zero operating point as the system size increases. In the process, we find that one of the models enables near-Heisenberg scaling metrology with a pair of commuting generators, a possibility that arises from the su(3)su(3)su(3) algebra and is thus absent in qubit-ensemble based sensors of collective SU(2)SU(2)SU(2) rotations.
We study a variational class of generalized Ramsey protocols that include two one-axis twisting (OAT) operations, one performed before the phase imprint and the other after. In this framework, we optimize the axes of the signal imprint, the OAT interactions, and the direction of the final projective measurement. We distinguish between protocols that exhibit symmetric or antisymmetric dependencies of the spin projection signal on the measured phase. Our results show that the quantum Fisher information, which sets the limits on the sensitivity achievable with a given one-axis twisted input state, can be saturated within our class of variational protocols for almost all initial twisting strengths. By incorporating numerous protocols previously documented in the literature, our approach creates a unified framework for Ramsey echo protocols with OAT states and measurements.