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Quantum-enhanced metrology with single-mode coherent states

Lewis A. Clark, Adam Stokes, Almut Beige

Published Dec 4, 2015• 0 citations
OpenAlex

Abstract

In this paper, we use the temporal quantum correlations in the photon statistics of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with an accuracy above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the phase space volume occupied by the resonator field, thereby increasing the dependence of its final state on the measured phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly-efficient single photon detectors, it should be of practical interest until technologies for the generation of highly-entangled many-photon states become more readily available.

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In this paper, we use the temporal quantum correlations in the photon statistics of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with an accuracy above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the phase space volume occupied by the resonator field, thereby increasing the dependence of its final state on the measured phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly-efficient single photon detectors, it should be of practical interest until technologies for the generation of highly-entangled many-photon states become more readily available.
In this paper, we use the nonlinear generator of dynamics of the individual quantum trajectories of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with a precision above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the dependence of the state of the resonator on the unknown phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly efficient single photon detectors, it should be of practical interest until highly entangled many-photon states become more readily available.
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.
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.
The quantum Fisher information and quantum correlation parameters are employed to study the application of nonclassical light to the problem of parameter estimation. It is shown that the optimal measurement sensitivity of a quantum state is determined by its intermode correlations (which depends on path entanglement) and intramode correlations (which depends on the photon statistics). In light of these results, we consider the performance of quantum-enhanced optical interferometers. Furthermore, we propose a Heisenberg-limited metrology protocol involving standard elements from passive and active linear optics, for which the quantum Cram\'er-Rao bound is saturated with an intensity measurement. Interestingly, the quantum advantage for this scheme is derived solely from the nonclassical photon statistics of the probe state and does not depend on entanglement. We study the performance of this scheme in the presence of realistic losses and consequently predict a substantial enhancement over the shot-noise limit with current technological capabilities.
Path-entangled multi-photon states allow optical phase-sensing beyond the shot-noise limit, provided that an efficient parity measurement can be implemented. Realizing this experimentally is technologically demanding, as it requires coincident single-photon detection proportional to the number of photons involved, which represents a severe challenge for achieving a practical quantum advantage over classical methods. Here, we exploit advanced quantum state engineering based on superposing two photon-pair creation events to realize a new approach that bypasses this issue. In particular, optical phase shifts are probed with a two-photon quantum state whose information is subsequently effectively transferred to a single-photon state. Notably, without any multiphoton detection, we infer phase shifts by measuring the average intensity of the single-photon beam on a photodiode, in analogy to standard classical measurements. Importantly, our approach maintains the quantum advantage: twice as many interference fringes are observed for the same phase shift, corresponding to N = 2 path-entangled photons. Our results demonstrate that the advantages of quantum-enhanced phase sensing can be fully exploited in standard intensity measurements, paving the way toward resource-efficient and practical quantum optical metrology.
Quantum dense metrology (QDM) performs high-precision measurements by a two-mode entangled state created by an optical parametric amplifier (PA), where one mode is a meter beam and the other is a reference beam. In practical applications, the photon losses of meter beam are unavoidable, resulting in a degradation of the sensitivity. Here, we employ coherent feedback that feeds the reference beam back into the PA by a beam splitter to enhance the sensitivity in a lossy environment. The results show that the sensitivity is enhanced significantly by adjusting the splitting ratio of the beam splitter. This method may find its potential applications in QDM. Furthermore, such a strategy that two non-commuting observables are simultaneous measurements could provide a new way to individually control the noise-induced random drift in phase or amplitude of the light field, which would be significant for stabilizing the system and long-term precision measurement.