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arXiv:1803.00441 · Nature Communications

Quantum metrology with quantum-chaotic sensors

Lukas J. Fiderer, Daniel Braun

Published Apr 10, 2018• 85 citations
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Abstract

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.

DOI
10.1038/s41467-018-03623-z

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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.
Quantum-enhanced measurements represent the path towards the best measurement precision allowed by the laws of quantum mechanics. Known protocols usually rely on the preparation of entangled states and promise high or even optimal precision, but fall short in real-word applications because of the difficulty to generate entangled states and to protect them against decoherence. Here, we refrain from the preparation of entangled states but supplement the integrable parameter-encoding dynamics by non-linear kicks driving the system in the dynamical regime of quantum chaos. We show that large improvements in measurement precision are possible by modeling a spin-exchange relaxation-free alkali-vapor magnetometer where the non-linear kicks are realized by exploiting the ac Stark effect.
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 sensors and metrology harness quantum phenomena—such as superposition, entanglement, and squeezing—to achieve precision measurements beyond classical limits. This review presents an overview of the fundamental principles underlying quantum sensing, including quantum coherence, entanglement-assisted measurement, and quantum-enhanced interferometry. Various quantum sensor platforms are discussed, including atomic clocks, nitrogen-vacancy (NV) center magnetometers, superconducting quantum interference devices (SQUIDs), optomechanical sensors, and trapped-ion systems. We explore their operational mechanisms, performance metrics, and technological implementations. Comparative analyses highlight sensitivity, spatial resolution, bandwidth, and environmental robustness. Advances in materials, control techniques, and hybrid architectures are examined, and emerging applications in navigation, geophysics, medical imaging, and fundamental physics are reviewed. Finally, future prospects for scalable and robust quantum metrology are discussed.
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.