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Journal of the Optical Society of America B

Quantum enhanced multiple transmission estimation with a bright squeezed light field

Seongjin Hong

Published Sep 24, 2024• 0 citations
Publisher

Abstract

Recently, there has been significant interest in multiple-parameter quantum estimation techniques that exploit quantum resources. In particular, the estimation of optical transmission is a crucial parameter in various scientific fields and industries. In optical-based sensing, precision can be enhanced through two approaches: increasing the number of photons that interact with the samples and utilizing quantum states of light. In this paper, we investigate multiple transmission estimation using bright two-mode squeezed states (bTMSSs), which combine the advantages of both bright light and quantum states. We calculate the precision bound for multiple transmission estimation by employing multiple copies of bTMSSs with experimentally feasible optimal measurement, determining both the quantum Cramer-Rao bound and the Cramer-Rao bound. Our results demonstrate that multiple copies of bTMSSs can achieve quantum-enhanced sensitivity for multiple transmissions compared to coherent states, and the ultimate limit of precision can be attained in regions with high nonlinear gain. Furthermore, as an application, we show the quantum-enhanced sensing in circular dichroism sensing using a pair of bTMSSs. Our strategy for multiple transmission estimation offers a practical platform for exploring real-world quantum sensing applications.

DOI
10.1364/josab.534086

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Recently, there has been significant interest in multiple-parameter quantum estimation techniques that exploit quantum resources. In particular, the estimation of optical transmission is a crucial parameter in various scientific fields and industries. In optical-based sensing, precision can be enhanced through two approaches: increasing the number of photons that interact with the samples and utilizing quantum states of light. In this paper, we investigate multiple transmission estimation using bright two-mode squeezed states (bTMSSs), which combine the advantages of both bright light and quantum states. We calculate the precision bound for multiple transmission estimation by employing multiple copies of bTMSSs with experimentally feasible optimal measurement, determining both the quantum Cramer-Rao bound and the Cramer-Rao bound. Our results demonstrate that multiple copies of bTMSSs can achieve quantum-enhanced sensitivity for multiple transmissions compared to coherent states, and the ultimate limit of precision can be attained in regions with high nonlinear gain. Furthermore, as an application, we show the quantum-enhanced sensing in circular dichroism sensing using a pair of bTMSSs. Our strategy for multiple transmission estimation offers a practical platform for exploring real-world quantum sensing applications.
The minimum possible uncertainty when estimating a parameter, in this case transmission, is bounded by the quantum Cramér-Rao bound (QCRB). This bound is independent of the measurement technique and as result can be used to quantify how close a measurement is to the optimal one for a given system and probing state, as an optimal measurement saturates the QCRB. The ability to perform transmission measurements through an optical system at the QCRB can lead to enhancements in the calibration of optimal states for interferometers, the characterization of high efficiency photodetectors, or the sensitivity of sensing devices based on transmission, such as plasmonic sensors or spectroscopy. We show theoretically that the ultimate sensitivity limit per photon in the estimation of transmission, achievable with Fock states or vacuum two-mode squeezed states (vTMSS), can be approached through the use of bright quantum states of light, such as bright single-mode squeezed states (bSMSS) or bright two-mode squeezed states (bTMSS). The use of bright quantum states has the advantage that they can be generated with a significantly larger number of photons, which leads to an absolute sensitivity that can be many orders of magnitude larger than the one achieved with Fock states or vTMSS. We identify a measurement strategy that saturates the QCRB for these bright quantum states and shown experimentally that transmission estimation at the QCRB can be achieved with bTMSS through optimized intensity difference measurements.
The field of quantum metrology seeks to apply quantum techniques and/or resources to classical sensing approaches with the goal of enhancing the precision in the estimation of a parameter beyond what can be achieved with classical resources. Theoretically, the fundamental minimum uncertainty in the estimation of a parameter for a given probing state is bounded by the quantum Cramér-Rao bound. From a practical perspective, it is necessary to find physical measurements that can saturate this fundamental limit and to show experimentally that it is possible to perform measurements with the required precision to do so. Here we perform experiments that saturate the quantum Cramér-Rao bound for transmission estimation over a wide range of transmissions when probing the system under study with a continuous wave bright two-mode squeezed state. To properly take into account the imperfections in the generation of the quantum state, we extend our previous theoretical results to incorporate the measured properties of the generated quantum state. For our largest transmission level of 84%, we show a 62% reduction over the optimal classical protocol in the variance in transmission estimation when probing with a bright two-mode squeezed state with -8 dB of intensity-difference squeezing. Given that transmission estimation is an integral part of many sensing protocols, such as plasmonic sensing, spectroscopy, calibration of the quantum efficiency of detectors, etc., the results presented promise to have a significant impact on a number of applications in various fields of research.
Enhancing the precision of a measurement requires maximizing the information that can be gained about the quantity of interest from probing a system. For optical-based measurements, such an enhancement can be achieved through two approaches, increasing the number of photons used to interrogate the system and using quantum states of light to increase the amount of quantum Fisher information gained per photon. Here we consider the use of quantum states of light with a large number of photons, namely the bright single-mode squeezed state and the bright two-mode squeezed state, which take advantage of both of these approaches for the problem of transmission estimation. We show that, in the limit of large squeezing, these states approach the maximum possible quantum Fisher information per photon for transmission estimation that is achieved with the Fock state and the vacuum two-mode squeezed state. Since the bright states we consider can be generated at powers much higher than those of the quantum states that achieve the maximum quantum Fisher information per photon, they can achieve a much higher absolute precision as quantified by the quantum Cram\'er-Rao bound. We discuss the effects of losses external to the system on the precision of transmission estimation and identify simple measurement techniques that can saturate the quantum Cram\'er-Rao bound for the bright squeezed states even in the presence of such external losses.
Recent developments in quantum technologies have enabled significant improvements in the precision of optical sensing systems. This work explores the integration of distributed quantum sensing with optical gyroscopes to improve the estimation accuracy of angular velocity. Utilizing bright two-mode squeezed states (bTMSS), which offer high photon numbers and strong bipartite quantum correlations, we propose a configuration that leverages continuous-variable entanglement across multiple spatially separated optical gyroscopes. Unlike traditional quantum sensing that enhances a single sensor, our approach focuses on estimating a global phase shift—corresponding to the average angular rotation—across distributed optical gyroscopes with quantum-enhanced sensitivity. We analyze the phase sensitivities of different bTMSS configurations, including mode entangled bTMSS and separable M -bTMSS, and evaluate their performance through the quantum Cramér-Rao bound. The analysis shows that, with 5 % photon loss in every channel in the system, the proposed scheme shows a sensitivity enhancement of ∼ 9.3 dB beyond the shot-noise limit, with an initial squeezing of ∼ 9.8 dB . The present scheme has potential applications in quantum-enhanced inertial navigation and precision metrology within emerging quantum networks.
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.
Abstract Quantum states of light can enable sensing configurations with sensitivities beyond the shot-noise limit. In order to better take advantage of available quantum resources and obtain the maximum possible sensitivity, it is necessary to determine fundamental sensitivity limits for different possible configurations for a given sensing system. Here, due to their wide applicability, we focus on optical resonance sensors, which detect a change in a parameter of interest through a resonance shift. We compare their fundamental sensitivity limits set by the quantum Cramér–Rao bound (QCRB) based on the estimation of changes in transmission or phase of a probing bright two-mode squeezed state (bTMSS) of light. We show that the fundamental sensitivity results from an interplay between the QCRB and the transfer function of the system. As a result, for a resonance sensor with a Lorentzian lineshape a phase-based scheme outperforms a transmission-based one for most of the parameter space; however, this is not the case for lineshapes with steeper slopes, such as higher order Butterworth lineshapes. Furthermore, such an interplay results in conditions under which the phase-based scheme provides a higher sensitivity but a smaller degree of quantum enhancement than the transmission-based scheme. We also study the effect of losses external to the sensor on the degree of quantum enhancement and show that for certain conditions, probing with a classical state can provide a higher sensitivity than probing with a bTMSS. Finally, we discuss detection schemes, namely optimized intensity-difference and optimized homodyne detection, that can achieve the fundamental sensitivity limits even in the presence of external losses.