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arXiv:2105.01561 · Physical Review Research

Quantum metrology of two-photon absorption

Carlos Sánchez Muñoz, Gaetano Frascella, Frank Schlawin

Published Sep 15, 2021• 42 citations
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Abstract

Two-photon absorption (TPA) is of fundamental importance in super-resolution imaging and spectroscopy. Its nonlinear character allows for the prospect of using quantum resources, such as entanglement, to improve measurement precision or to gain new information on, e.g., ultrafast molecular dynamics. Here, we establish the metrological properties of nonclassical squeezed light sources for precision measurements of TPA cross sections. We find that the Cram\'er-Rao bound does not provide a fundamental limit for the precision achievable with squeezed states in the limit of very small cross sections. Considering the most relevant measurement strategies---namely, photon-counting and quadrature measurements---we determine the quantum advantage provided by squeezed states as compared to coherent states. We find that squeezed states outperform the precision achievable by coherent states when performing quadrature measurements, which provide improved scaling of the Fisher information with respect to the mean photon number $\ensuremath{\sim}{n}^{4}$. Due to the interplay of the incoherent nature and the nonlinearity of the TPA process, unusual scaling can also be obtained with coherent states, which feature an $\ensuremath{\sim}{n}^{3}$ scaling in both quadrature and photon-counting measurements.

DOI
10.1103/physrevresearch.3.033250

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Two-photon absorption (TPA) is of fundamental importance in super-resolution imaging and spectroscopy. Its nonlinear character allows for the prospect of using quantum resources, such as entanglement, to improve measurement precision or to gain new information on, e.g., ultrafast molecular dynamics. Here, we establish the metrological properties of nonclassical squeezed light sources for precision measurements of TPA cross sections. We find that the Cram'er-Rao bound does not provide a fundamental limit for the precision achievable with squeezed states in the limit of very small cross sections. Considering the most relevant measurement strategies---namely, photon-counting and quadrature measurements---we determine the quantum advantage provided by squeezed states as compared to coherent states. We find that squeezed states outperform the precision achievable by coherent states when performing quadrature measurements, which provide improved scaling of the Fisher information with respect to the mean photon number \ensuremath∼n4\ensuremath{\sim}{n}^{4}\ensuremath∼n4. Due to the interplay of the incoherent nature and the nonlinearity of the TPA process, unusual scaling can also be obtained with coherent states, which feature an \ensuremath∼n3\ensuremath{\sim}{n}^{3}\ensuremath∼n3 scaling in both quadrature and photon-counting measurements.
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 (DV) 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 nˉ∈2N\bar{n} \in 2\mathbb{N}nˉ∈2N, 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 nˉ\bar{n}nˉ. 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. Our findings provide insight into known limiting behaviours of Gaussian probes and their different Fisher information (FI) scalings under photon counting (∝nˉ2\propto \bar{n}^2∝nˉ2 for squeezed vacuum states versus nˉ3\bar{n}^3nˉ3 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.
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.
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.
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 discuss how two-photon absorption (TPA) of squeezed and coherent states of light can be detected in measurements of the transmitted light fields. Such measurements typically suffer from competing loss mechanisms such as experimental imperfections (i.e., imperfect photodetectors) and other linear scattering losses inside the sample itself, which can lead to incorrect assessments of the two-photon-absorption cross section. We evaluate the sensitivity with which TPA can be detected and find that at sufficiently large photon numbers TPA sensitivity of squeezed vacua or squeezed coherent states can become independent of linear losses that occur after the TPA event has taken place. In particular, this happens for measurements of the photon number or of the antisqueezed field quadrature, where large fluctuations counteract and exactly cancel the degradation caused by single-photon losses.