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Optical and Quantum Sensing and Precision Metrology II

Time-reversed quantum metrology using squeezed states of light and matter

G. S. Agarwal

Published Mar 8, 2023• 0 citations
Publisher

Abstract

It is now well appreciated that quantum physics can be used to build better sensors. Such sensors can be based on unitary systems [1,2] like interferometers or open systems based on scattering and lossy transmission channels [3-5]. The framework of the quantum Fisher information enables one to obtain best estimates of the parameters and then one can design possible experiments that can reach Cramer- Rao bounds. I would bring out not only the importance of the quantum states used as probes, but also the importance of the ‘quantum’ measurement schemes especially the ones that depend on time reversed arrangements. I would illustrate the great usefulness of squeezed states of matter and light for metrology. [1] S. C. Burd et al., Quantum amplification of mechanical oscillator motion, Science 364, 1163 (2019). [2] G. S. Agarwal, and L. Davidovich, Quantifying quantum-amplified metrology via Fisher information, Phys. Rev. Res. 4, L 012014 (2022). [3] J. Wang, L. Davidovich, and G. S. Agarwal, Quantum sensing of open systems: Estimation of damping constants and temperature, Phys. Rev. Res. 2, 033389 (2020). [4] F. Li, T. Li, M. O. Scully, and G. S. Agarwal, Quantum advantage with seeded squeezed light for absorption measurement, Phys. Rev. Applied 15, 044030 (2021). [5] T.Li, F. Li, X. Liu, V. Yakovlev and G. S. Agarwal, Quantum-enhanced stimulated Brillouin scattering spectroscopy and imaging, OPTICA 9, 959 (2022).

DOI
10.1117/12.2657367

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It is now well appreciated that quantum physics can be used to build better sensors. Such sensors can be based on unitary systems [1,2] like interferometers or open systems based on scattering and lossy transmission channels [3-5]. The framework of the quantum Fisher information enables one to obtain best estimates of the parameters and then one can design possible experiments that can reach Cramer- Rao bounds. I would bring out not only the importance of the quantum states used as probes, but also the importance of the ‘quantum’ measurement schemes especially the ones that depend on time reversed arrangements. I would illustrate the great usefulness of squeezed states of matter and light for metrology. [1] S. C. Burd et al., Quantum amplification of mechanical oscillator motion, Science 364, 1163 (2019). [2] G. S. Agarwal, and L. Davidovich, Quantifying quantum-amplified metrology via Fisher information, Phys. Rev. Res. 4, L 012014 (2022). [3] J. Wang, L. Davidovich, and G. S. Agarwal, Quantum sensing of open systems: Estimation of damping constants and temperature, Phys. Rev. Res. 2, 033389 (2020). [4] F. Li, T. Li, M. O. Scully, and G. S. Agarwal, Quantum advantage with seeded squeezed light for absorption measurement, Phys. Rev. Applied 15, 044030 (2021). [5] T.Li, F. Li, X. Liu, V. Yakovlev and G. S. Agarwal, Quantum-enhanced stimulated Brillouin scattering spectroscopy and imaging, OPTICA 9, 959 (2022).
It is now well appreciated that quantum physics can be used to build better sensors. Such sensors can be based on unitary systems like various types of interferometers or open systems based on scattering and lossy transmission channels. I would highlight not only the importance of the quantum states used as probes, but also the importance of the quantum-ness of the measurement schemes. I would bring out the especial importance of the squeezed states of matter and light for sensing studies. I would illustrate the results with experiments.
Quantum estimation of parameters defining open-system dynamics may be enhanced by using ancillas that are entangled with the probe but are not submitted to the dynamics. Here we consider the important problem of estimation of transmission of light by a sample, with losses due to absorption and scattering. We show, through the determination of the quantum Fisher information, that the ancilla strategy leads to the best possible precision in single-mode estimation—the one obtained for a Fock-state input—through joint photon counting of probe and ancilla, which are modes of a bimodal squeezed state produced by an optical parametric amplifier. This proposal overcomes the challenge of producing and detecting high-photon-number Fock states, and it is quite robust in the presence of additional noise: We show that it is immune to phase noise and the precision does not change if the incoming state gets disentangled. Furthermore, the quantum gain is still present under moderate photon losses of the input beams. We also discuss an alternative to joint photon counting, which is readily implementable with present technology and approaches the quantum Fisher information result for weak absorption, even with moderate photon losses of the input beams before the sample is probed: a time-reversal procedure, placing the sample between two optical parametric amplifiers, with the second undoing the squeezing produced by the first one. The precision of estimation of the loss parameter is obtained from the average outgoing total photon number and its variance. In both procedures, the state of the probe and the detection procedure are independent of the value of the parameter. Published by the American Physical Society 2024
Quantum metrology involves the application of quantum resources to enhance measurements. Several communities have developed quantum-metrology strategies that leverage effective time reversals. These strategies, we posit, form four classes. First, echo metrology begins with a preparatory unitary and ends with that unitary's time-reverse. The protocol amplifies the visibility of a small parameter to be sensed. Similarly, weak-value amplification enhances a weak coupling's detectability. The technique exhibits counterintuitive properties captured by a retrocausal model. Using the third strategy, one simulates closed timelike curves, worldlines that loop back on themselves in time. The fourth strategy involves indefinite causal order, which characterises channels applied in a superposition of orderings. We review these four strategies, which we unify under the heading of time-reverse metrology. We also outline opportunities for this toolkit in quantum metrology; quantum information science; quantum foundations; atomic, molecular, and optical physics; and solid-state physics.
Absorption and gain processes are fundamental to any light-matter interaction and a precise measurement of these parameters is important for various scientific and technological applications. Quantum probes, specifically the squeezed states, have proved very successful, particularly in the applications that deal with phase shift and force measurements. In this paper, we focus on improving the sensitivity of the estimation of the photon-loss coefficient of a weakly absorbing medium as well as the estimation of the gain parameter using a two-mode bright squeezed state. The generation of this state combines the advantage of a coherent beam for its large photon number with the quantum properties of the two-mode squeezing operation in an optical parametric amplifier. We present two measurement schemes: balanced photodetection and time-reversed metrology, both utilizing two-mode bright squeezed light. The maximum quantum advantage we can achieve using two-mode bright squeezed light is 3.7 times for the absorption parameter $\ensuremath{\alpha}=0.05$ and 8.4 times for $\ensuremath{\alpha}=0.01$ as compared to using only the coherent state. Similarly, the maximum quantum advantage for the estimation of optical gain is found around 2.95 times for the gain coefficient G=1.05G=1.05G=1.05 and around 6.35 times for G=1.01G=1.01G=1.01. We discuss the significance of using one measurement scheme over the other under different squeezing conditions. We compare our results with the Cram\'er-Rao bound for a two-mode bright squeezed state to assess the quality of the proposed methodologies.
We present a unified framework, based on quantum metrology concepts, for defining and quantifying deterministic noiseless quantum amplification of parameter-dependent processes, which plays an important role in increasing the precision of quantum sensing.Recent experiments [Burd et al., Science 364, 1163 (2019)] can be encompassed by this concept, which also leads to new suggestions of experimental work.The unified view presented here allows the identification of the basic steps for quantum amplification and of the measurements that lead to the best possible precision, beyond the quantum standard limit, in the estimation of parameters involved in the process.This is applied to the estimation of displacements of trapped ions and of the phase in SU(1,1) optical interferometers and atomic interferometry.
For a given quantum state used in sensing, the quantum Cramér-Rao bound (QCRB) sets a fundamental limit on the precision achievable by an unbiased estimator of an unknown parameter, determined by the inverse of the quantum Fisher information (QFI). The QFI serves as an upper bound on the classical Fisher information (CFI), representing the maximum extractable information about the unknown parameter from measurements on a physical system. Thus, a central goal in quantum parameter estimation is to find a measurement, described by a POVM, that saturates the QFI (achieves maximum CFI), and thereby achieves the QCRB. In the idealization that one uses pure states and unitary encodings for sensing, discontinuities can appear in the CFI but not the QFI. In this article, we demonstrate that these discontinuities are important features, quantifying how much Fisher information is lost in the presence of noise. We refer to this as the Fisher information "fragility". We present a simple framework for understanding how discontinuities increase fragility through Jensen's inequality, and demonstrate how one can use this framework to design more robust POVMs for quantum advantage in metrology.