Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Scientific Reports

Quantum-enhanced precision measurement of nonlinear absorption

Sungsik Yu, Seunghyun Noh, Taeyeon Kim, Seongjin Hong

Published Sep 21, 2026• 0 citations
Publisher

Abstract

Abstract Nonlinear optics plays a crucial role in science and technology, with applications ranging from spectroscopy to quantum information processing. Therefore, precise estimation of their nonlinear optical parameters is of fundamental importance. Here, we investigate quantum-enhanced sensitivity in the estimation of nonlinear absorption parameters, including saturable absorption (SA) and reverse saturable absorption (RSA). By employing the quantum Fisher information, we quantify the enhancement in sensitivity for estimating transmission ( T ), linear absorption coefficient ( $$\alpha _0$$ ), saturable intensity ( $$I_s$$ ), and two-photon absorption coefficient ( $$\beta $$ ) using bright two-mode squeezed states (bTMSS) and applied it to analyze the nonlinear parameters of Pt nanoparticle samples as an example. In addition, we propose an experimental scheme based on an open-aperture Z-scan with bTMSS to realize quantum-enhanced sensitivity. Our findings establish a pathway toward quantum-enhanced estimation of nonlinear optical parameters.

DOI
10.1038/s41598-026-70715-y

Related papers

Quantum metrology of absorption and gain parameters using two-mode bright squeezed light

Mrunal Kamble, Jiaxuan Wang, G. S. Agarwal

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 $G=1.05$ and around 6.35 times for $G=1.01$. 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.

arXiv:2404.00871•Physical Review A•May 16, 2024•14 citations

Nonlinear Interferometry for Quantum-Enhanced Measurements of Multiphoton Absorption

S. Panahiyan, Carlos Sánchez Muñoz, Maria V. Chekhova +1 more

Multiphoton absorption is of vital importance in many spectroscopic, microscopic, or lithographic applications. However, given that it is an inherently weak process, the detection of multiphoton absorption signals typically requires large field intensities, hindering its applicability in many practical situations. In this Letter, we show that placing a multiphoton absorbent inside an imbalanced nonlinear interferometer can enhance the precision of multiphoton cross section estimation with respect to strategies based on photon-number measurements using coherent or even squeezed light directly transmitted through the medium. In particular, the power scaling of the sensitivity with photon flux can be increased by 1 order compared with transmission measurements of the sample with coherent light, such that the measurement precision at any given intensity can be greatly enhanced. Furthermore, we show that this enhanced measurement precision is robust against experimental imperfections leading to photon losses, which usually tend to degrade the detection sensitivity. We trace the origin of this enhancement to an optimal degree of squeezing which has to be generated in a nonlinear SU(1,1) interferometer.

arXiv:2209.02697•Physical Review Letters•May 19, 2023•22 citations

Enhancing measurement precision of non-degenerate two-photon absorption

Gaurav Shukla, S. Panahiyan, Devendra Kumar Mishra +1 more

Abstract Recent theoretical and experimental advances have shown that squeezed states of light can be engineered to enhance the resolution of optical measurements. Extending such quantum-enhanced techniques to nonlinear optical processes has therefore attracted considerable interest. In particular, two-photon absorption (TPA), which has wide-ranging applications in physics, chemistry, and biology, has emerged as a promising platform for exploiting these quantum advantages. In this work, we investigate whether and how correlations between light modes can be used to improve optical resolution in TPA. We analyze non-degenerate TPA transmission measurements using two-mode squeezed light and compare different measurement strategies. We find that intensity correlation measurements offer better performance in terms of the achievable estimation error compared to normalized intensity correlations or measurements of the noise reduction factor (NRF). The achievable enhancement from intensity and NRF measurements are degraded by competing photon losses. In contrast, the normalized intensity correlation approach remains robust to loss, albeit at the cost of forfeiting the scaling enhancement at large photon numbers achievable with nonclassical light fields. Thus, we establish a trade-off between robustness to loss and the achievable quantum advantage. We further compute the corresponding Cramér–Rao bound, which sets the ultimate lower limit on the achievable estimation error for the photon-counting-based measurement strategies investigated in this work.

arXiv:2506.07384•Quantum Science and Technology•Sep 8, 2026•0 citations

Quantum enhanced multiple transmission estimation with a bright squeezed light field

Seongjin Hong

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.

Journal of the Optical Society of America B•Sep 24, 2024•0 citations

Optimal quantum metrology of two-photon absorption

Athena Karsa, Ranjith Nair, A. Chia +2 more

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.

Quantum Science and Technology•May 2, 2024•6 citations

Enhanced Phase Estimation via Photon-Added Two-Mode Squeezed States and Kerr Nonlinearity

Zekun Zhao, Qingqian Kang, Teng Zhao +3 more

Quantum metrology employs quantum resources to achieve measurement precision beyond classical limits. This work investigates a Mach--Zehnder interferometer incorporating a Kerr nonlinear phase shifter, with photon-added two-mode squeezed coherent states generated via four-wave mixing as input. We demonstrate that increasing both the photon-addition order and the input resource strength systematically enhances phase sensitivity, quantum Fisher information, and the corresponding quantum Cramér--Rao bound. The proposed system not only surpasses the standard quantum limit but also approaches or exceeds the Heisenberg limit for linear phase shifts, while Kerr nonlinearity enables surpassing the super-Heisenberg limit. Furthermore, the scheme exhibits enhanced robustness against photon loss, providing a promising pathway toward practical high-precision quantum metrology applications.

quant-pharXiv:2602.00700•Feb 3, 2026•0 citations
Abstract Nonlinear optics plays a crucial role in science and technology, with applications ranging from spectroscopy to quantum information processing. Therefore, precise estimation of their nonlinear optical parameters is of fundamental importance. Here, we investigate quantum-enhanced sensitivity in the estimation of nonlinear absorption parameters, including saturable absorption (SA) and reverse saturable absorption (RSA). By employing the quantum Fisher information, we quantify the enhancement in sensitivity for estimating transmission ( T ), linear absorption coefficient ( α0\alpha _0α0​ ), saturable intensity ( IsI_sIs​ ), and two-photon absorption coefficient ( β\beta β ) using bright two-mode squeezed states (bTMSS) and applied it to analyze the nonlinear parameters of Pt nanoparticle samples as an example. In addition, we propose an experimental scheme based on an open-aperture Z-scan with bTMSS to realize quantum-enhanced sensitivity. Our findings establish a pathway toward quantum-enhanced estimation of nonlinear optical parameters.
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.
Multiphoton absorption is of vital importance in many spectroscopic, microscopic, or lithographic applications. However, given that it is an inherently weak process, the detection of multiphoton absorption signals typically requires large field intensities, hindering its applicability in many practical situations. In this Letter, we show that placing a multiphoton absorbent inside an imbalanced nonlinear interferometer can enhance the precision of multiphoton cross section estimation with respect to strategies based on photon-number measurements using coherent or even squeezed light directly transmitted through the medium. In particular, the power scaling of the sensitivity with photon flux can be increased by 1 order compared with transmission measurements of the sample with coherent light, such that the measurement precision at any given intensity can be greatly enhanced. Furthermore, we show that this enhanced measurement precision is robust against experimental imperfections leading to photon losses, which usually tend to degrade the detection sensitivity. We trace the origin of this enhancement to an optimal degree of squeezing which has to be generated in a nonlinear SU(1,1) interferometer.
Abstract Recent theoretical and experimental advances have shown that squeezed states of light can be engineered to enhance the resolution of optical measurements. Extending such quantum-enhanced techniques to nonlinear optical processes has therefore attracted considerable interest. In particular, two-photon absorption (TPA), which has wide-ranging applications in physics, chemistry, and biology, has emerged as a promising platform for exploiting these quantum advantages. In this work, we investigate whether and how correlations between light modes can be used to improve optical resolution in TPA. We analyze non-degenerate TPA transmission measurements using two-mode squeezed light and compare different measurement strategies. We find that intensity correlation measurements offer better performance in terms of the achievable estimation error compared to normalized intensity correlations or measurements of the noise reduction factor (NRF). The achievable enhancement from intensity and NRF measurements are degraded by competing photon losses. In contrast, the normalized intensity correlation approach remains robust to loss, albeit at the cost of forfeiting the scaling enhancement at large photon numbers achievable with nonclassical light fields. Thus, we establish a trade-off between robustness to loss and the achievable quantum advantage. We further compute the corresponding Cramér–Rao bound, which sets the ultimate lower limit on the achievable estimation error for the photon-counting-based measurement strategies investigated in this work.
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.
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.
Quantum metrology employs quantum resources to achieve measurement precision beyond classical limits. This work investigates a Mach--Zehnder interferometer incorporating a Kerr nonlinear phase shifter, with photon-added two-mode squeezed coherent states generated via four-wave mixing as input. We demonstrate that increasing both the photon-addition order and the input resource strength systematically enhances phase sensitivity, quantum Fisher information, and the corresponding quantum Cramér--Rao bound. The proposed system not only surpasses the standard quantum limit but also approaches or exceeds the Heisenberg limit for linear phase shifts, while Kerr nonlinearity enables surpassing the super-Heisenberg limit. Furthermore, the scheme exhibits enhanced robustness against photon loss, providing a promising pathway toward practical high-precision quantum metrology applications.