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arXiv:2310.06142 · Physical Review Research

Quantum advantage of time-reversed ancilla-based metrology of absorption parameters

Jiaxuan Wang, R. L. de Matos Filho, G. S. Agarwal, L. Davidovich

Published Jan 10, 2024• 12 citations
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Abstract

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

DOI
10.1103/physrevresearch.6.013034

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•Jan 22, 2026•0 citations
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
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.
Phase-insensitive optical amplifiers uniformly amplify each quadrature of an input field and are of both fundamental and technological importance. We find the quantum limit on the precision of estimating the gain of a quantum-limited phase-insensitive amplifier using a multimode probe that may also be entangled with an ancilla system. In stark contrast to the sensing of loss parameters, the average photon number N and number of input modes M of the probe are found to be equivalent and interchangeable resources for optimal gain sensing. All pure-state probes whose reduced state on the input modes to the amplifier is diagonal in the multimode number basis are proven to be quantum optimal under the same gain-independent measurement. We compare the best precision achievable using classical probes to the performance of an explicit photon-counting-based estimator on quantum probes and show that an advantage exists even for single-photon probes and inefficient photodetection. A closed-form expression for the energy-constrained Bures distance between two product amplifier channels is also derived.
Abstract Two-photon absorption (TPA) is a nonlinear optical process with wide-ranging applications from spectroscopy to super-resolution imaging. Despite this, the precise measurement and characterisation of TPA parameters are challenging due to their inherently weak nature. We study the potential of single-mode quantum light to enhance TPA parameter estimation through the quantum Fisher information (QFI). Discrete variable quantum states (defined to be a finite superposition of Fock states) are optimised to maximise the QFI for given absorption, revealing a quantum advantage compared to both the coherent state (classical) benchmark and the single-mode squeezed vacuum state. For fixed average energy n ¯ ∈ 2 N , the Fock state is shown to be optimal for large TPA parameters, while a superposition of vacuum and a particular Fock state is optimal for small absorption for all n ¯ . This differs from single-photon absorption where the Fock state is always optimal. Notably, photon counting is demonstrated to offer optimal or nearly optimal performance compared to the QFI bound for all levels of TPA parameters for the optimised quantum probes, and their quantum advantage is shown to be robust to single-photon loss. Our findings provide insight into known limiting behaviours of Gaussian probes and their different FI scalings under photon counting ( ∝ n ¯ 2 for squeezed vacuum states versus n ¯ 3 for coherent states). The squeezed state outperforms coherent states for small TPA parameters but underperforms in the intermediate regime, becoming comparable in the large absorption limit. This can be explained through fundamental differences between behaviours of even and odd number Fock states: the former’s QFI diverges in both large and small absorption limits, while the latter diverges only in the small absorption limit, dominating at intermediate scales.
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).
Optical quantum metrology uses specially-prepared states of light to probe sensitive samples. Choosing a suitable probe state allows one to extract more information per probe photon about an unknown parameter than is possible using any classical technique. In effect, these techniques improve the sensitivity of the measurement whenever the number of probe photons is constrained in some way. This thesis presents experimental and theoretical results on the use of pairs of time-frequency entangled photons in precision measurements. It begins with an overview of necessary background knowledge about quantum optics and quantum information. This is followed by a theoretical discussion on the estimation of a single delay using two-photon interference. We show that constraints on the probe photon's bandwidth complicate the measurement problem, requiring suitable optimization of the two-photon quantum state to avoid losing precision. We then consider the use of two-photon interference for linear spectroscopic measurements. Linear spectroscopy relates the absorption and phase spectrum of a sample to unknown electronic parameters. We describe a proof-of-principle experiment demonstrating that two-photon interferometric spectroscopy can be used for simultaneously measurement of both absorption and phase. This is followed by an information-theoretic discussion of the precision of this technique. For low losses, we show that the method provides phase sensitivity similar to classical interferometry while approaching the optimal absorption precision of any possible measurement. If the absorption and phase values are both related to a single unknown parameter, then our technique provides improved sensitivity to this parameter compared to both classical measurements and other quantum techniques in the presence of realistic levels of loss. We conclude with a discussion of quantum-optical coherence tomography, which is a two-photon interferometric method for determining the material structure of a sample. We present an ongoing experiment which aims to apply the method to tissue-like samples, where the quantum measurement is limited by a poor signal-to-noise ratio. Preliminary results demonstrate that this noise can be largely reduced by suitable frequency-domain filtering. This allows us to precisely determine the position of a scattering center using a few hundred detected photon pairs despite the presence of large amounts of noise. We follow this with a theoretical discussion of signal artifacts which are known to complicate the measured interferogram. We show these artifacts are due to a distinct interferometric effect, which can be distinguished from the signal of interest using the relative time delay between detected photons. We conclude with a brief discussion on possible techniques for artifact removal.