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arXiv:1811.01004 · Physical Review A

Quantum jump metrology

Lewis A. Clark, Adam Stokes, Almut Beige

Published Feb 4, 2019• 16 citations
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Abstract

Quantum metrology exploits quantum correlations in specially prepared entangled or other nonclassical states to perform measurements that exceed the standard quantum limit. Typically, though, such states are hard to engineer, particularly when larger numbers of resources are desired. As an alternative, this paper aims to establish quantum jump metrology, which is based on generalized sequential measurements as a general design principle for quantum metrology and discusses how to exploit open quantum systems to obtain a quantum enhancement. By analyzing a simple toy model, we illustrate that parameter-dependent quantum feedback can indeed be used to exceed the standard quantum limit without the need for complex state preparation.

DOI
10.1103/physreva.99.022102

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Quantum metrology exploits quantum correlations in specially prepared entangled or other nonclassical states to perform measurements that exceed the standard quantum limit. Typically, though, such states are hard to engineer, particularly when larger numbers of resources are desired. As an alternative, this paper aims to establish quantum jump metrology, which is based on generalized sequential measurements as a general design principle for quantum metrology and discusses how to exploit open quantum systems to obtain a quantum enhancement. By analyzing a simple toy model, we illustrate that parameter-dependent quantum feedback can indeed be used to exceed the standard quantum limit without the need for complex state preparation.
© 2019 American Physical Society. Quantum metrology exploits quantum correlations in specially prepared entangled or other nonclassical states to perform measurements that exceed the standard quantum limit. Typically, though, such states are hard to engineer, particularly when larger numbers of resources are desired. As an alternative, this paper aims to establish quantum jump metrology, which is based on generalized sequential measurements as a general design principle for quantum metrology and discusses how to exploit open quantum systems to obtain a quantum enhancement. By analyzing a simple toy model, we illustrate that parameter-dependent quantum feedback can indeed be used to exceed the standard quantum limit without the need for complex state preparation.
Quantum metrology enhances measurement precision by utilizing the properties of quantum physics. In interferometry, this is typically achieved by evolving highly entangled quantum states before performing single-shot measurements to reveal information about an unknown parameter. While this is often the optimum approach, implementation with all but the smallest states is still extremely challenging. An alternative approach is quantum jump metrology [L. A. Clark et al., Phys. Rev. A 99, 022102 (2019)], which deduces information by continuously monitoring an open quantum system while inducing phase-dependent temporal correlations with the help of quantum feedback. Taking this approach here, we analyze measurements of a relative phase in an optical network of two cavities with quantum feedback in the form of laser pulses. It is shown that the proposed approach can exceed the standard quantum limit without the need for complex quantum states while being scalable and more practical than previous related schemes.
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 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 is studied in the presence of quantum correlation. The quantum correlation measure based on quantum Fisher information enables us to gain a deeper insight on how quantum correlations are instrumental in setting metrological precision. Our analysis shows that not only the entanglement but also the quantum correlation plays important roles to enhance precision in quantum metrology. Even in the absence of entanglement, quantum correlation can be exploited as the resource to beat standard quantum limit and reach Heisenberg limit in metrology. Clearly unraveling the role of quantum correlations, the tighter bounds on the metrological precision are derived.
There are a number of different strategies to measure the phase shift between two pathways of light more efficiently than suggested by the standard quantum limit. One way is to use highly entangled photons. Another way is to expose photons to a non-linear or interacting Hamiltonian. This paper emphasises that the conditional dynamics of open quantum systems provides an interesting additional tool for quantum-enhanced metrology. As a concrete example, we review a recent scheme which exploits the conditional dynamics of a laser-driven optical cavity with spontaneous photon emission inside a quantum feedback loop. Deducing information from second-order photon correlation measurements requires neither optical non-linearities nor entangled photons and should therefore be of immediate practical interest.