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arXiv:2007.06210 · Physical Review A

Quantum metrology via chaos in a driven Bose-Josephson system

Wenjie Liu, Min Zhuang, Bo Zhu, Jiahao Huang, Chaohong Lee

Published Feb 8, 2021• 18 citations
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Abstract

Entanglement preparation and signal accumulation are essential for quantum parameter estimations, which pose significant challenges to both theories and experiments. Here, we propose how to utilize chaotic dynamics in a periodically driven Bose-Josephson system for achieving high-precision measurements beyond the standard quantum limit (SQL). Starting from an initial nonentangled state, the chaotic dynamics generates many-body quantum entanglement and simultaneously encodes the parameter to be estimated. By using suitable chaotic dynamics, the ultimate measurement precision of the estimated parameter can beat the SQL. The sub-SQL measurement precision scaling can also be reached via specific observables, such as collective spin measurement, which can be realized with state-of-art techniques. Our study not only provides insights for understanding quantum chaos and quantum-classical correspondence, but also of promising applications in entanglement-enhanced quantum metrology.

DOI
10.1103/physreva.103.023309

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Entanglement preparation and signal accumulation are essential for quantum parameter estimations, which pose significant challenges to both theories and experiments. Here, we propose how to utilize chaotic dynamics in a periodically driven Bose-Josephson system for achieving high-precision measurements beyond the standard quantum limit (SQL). Starting from an initial nonentangled state, the chaotic dynamics generates many-body quantum entanglement and simultaneously encodes the parameter to be estimated. By using suitable chaotic dynamics, the ultimate measurement precision of the estimated parameter can beat the SQL. The sub-SQL measurement precision scaling can also be reached via specific observables, such as collective spin measurement, which can be realized with state-of-art techniques. Our study not only provides insights for understanding quantum chaos and quantum-classical correspondence, but also of promising applications in entanglement-enhanced quantum metrology.
Quantum effects in metrology can in principle enhance measurement precision from the so-called standard quantum limit to the Heisenberg limit. Further advancements in quantum metrology largely rely on innovative metrology protocols that can avoid a number of known obstacles, including the challenge of preparing entangled states with sufficient fidelity, the readout noise in measuring highly entangled states, and no-go theorems for quantum metrology under noisy environments. In this Letter, exploiting some peculiar but experimentally feasible dynamical features of a collection of spins with all-to-all time-periodic interactions, we propose a metrology protocol that can circumvent all three mentioned obstacles and yet still make good use of time as a resource for metrology. Specifically, by mapping the dynamics of such a periodically driven spin system to that of a paradigm of quantum chaos but tuned to some high-order quantum resonance, it is shown that a simple SU(2) coherent state can, after evolving to highly entangled states in the ensuing dynamics, be dynamically brought back to the same initial coherent state. The associated quantum Fisher information is found to exhibit quadratic scaling with both the number of spins and the duration of the metrology protocol. The achieved Heisenberg scaling can also largely survive in the presence of Markovian noise. Representing a previously unknown strategy for quantum metrology, the protocol proposed here can be tested on available experimental platforms.
Quantum metrology promises high-precision measurements of classical parameters with far reaching implications for science and technology. So far, research has concentrated almost exclusively on quantum-enhancements in integrable systems, such as precessing spins or harmonic oscillators prepared in non-classical states. Here we show that large benefits can be drawn from rendering integrable quantum sensors chaotic, both in terms of achievable sensitivity as well as robustness to noise, while avoiding the challenge of preparing and protecting large-scale entanglement. We apply the method to spin-precession magnetometry and show in particular that the sensitivity of state-of-the-art magnetometers can be further enhanced by subjecting the spin-precession to non-linear kicks that renders the dynamics chaotic.
Most quantum metrology protocols harness highly entangled probe states and globally accessible measurements to surpass the standard quantum limit. However, it is challenging to satisfy these requirements in realistic many-body sensors. We demonstrate that both of these constraints can be overcome in quantum chaotic sensors. Crucially, we establish that even in the presence of partial measurement accessibility, chaotic dynamics enables initial unentangled states to exhibit Heisenberg scaling of the quantum Fisher information, IαI_αIα​ with time. In the weakly chaotic regime, we identify spin-coherent states placed at the edge of the regular islands in the mixed classical phase space as optimal initial states for enhanced sensitivity. On the other hand, in the strongly chaotic regime, IαI_αIα​ is insensitive to the choice of the initial state. Notably, quantum-enhanced sensitivity is achieved even when a very low fraction (∼5%\sim 5\%∼5%) of the qubits are accessible. These results establish quantum chaos as a robust resource for quantum-enhanced sensing under realistic accessibility constraints on accessibility.
Entanglement-enhanced quantum metrology explores the utilization of quantum entanglement to enhance measurement precision. When particles in a probe are prepared into a suitable quantum entangled state, they may collectively accumulate information about the physical quantity to be measured, leading to an improvement in measurement precision beyond the standard quantum limit and approaching the Heisenberg limit. The rapid advancement of techniques for quantum manipulation and detection has enabled the generation, manipulation, and detection of multi-particle entangled states in synthetic quantum systems such as cold atoms and trapped ions. This article aims to review and illustrate the fundamental principles and experimental progresses that demonstrate multi-particle entanglement for quantum metrology, as well as discuss the potential applications of entanglement-enhanced quantum sensors.
Quantum information scrambling, the dispersal of local information into many-body degrees of freedom, provides a powerful mechanism for generating large-scale correlations and entanglement essential for quantum-enhanced metrology. However, experimentally verifying such quantum-enhanced metrology remains a demanding task. Here, we correlate thousands of spins by engineering chaotic scrambling dynamics in a solid-state nuclear spin system. By leveraging the newly developed scramblon theory, we reveal exponential scaling in both the quantum Fisher information and the signal response to a phase shift. The signal response achieves a correlation-enabled enhancement of 33(2)33(2)33(2) dB over uncorrelated spins. After accounting for signal loss due to imperfect time reversal in the readout stage, we obtain a total metrological gain of 18(1) dB with a phase sensitivity of 40(3) μrad{\mathrm{μrad}}μrad. Our results bridge quantum chaos with practical quantum metrology, establishing reversible scrambling dynamics as a powerful resource for precision measurements.
Many-body quantum chaos has immense potential as a tool to accelerate the preparation of entangled states and overcome challenges due to decoherence and technical noise. Here, we study how chaos in the paradigmatic Dicke model, which describes the uniform coupling of an ensemble of qubits to a common bosonic mode, can enable the rapid generation of non-Gaussian entangled spin-boson states without fine-tuning of system parameters or initial conditions. However, the complexity of these states means that unlocking their utility for quantum-enhanced sensing with standard protocols would require the measurement of complex or typically inaccessible observables. To address this challenge, we develop a sensing scheme based on interaction-based readout that enables us to implement near-optimal quantum-enhanced metrology of global spin rotations or bosonic displacements using only spin measurements. We show that our approach is robust to technical noise and imperfections and thus opens new opportunities to exploit complex entangled states generated by chaotic dynamics in current quantum science platforms such as trapped-ion and cavity-QED experiments.