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¯∈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 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.

中文翻译：

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双光子吸收的最佳量子计量


双光子吸收（TPA）是一种非线性光学过程，具有从光谱学到超分辨率成像的广泛应用。尽管如此，TPA 参数的精确测量和表征仍然具有挑战性，因为它们本质上很弱。我们研究了单模量子光通过量子费希尔信息 (QFI) 增强 TPA 参数估计的潜力。离散可变量子态（定义为福克态的有限叠加）经过优化，可最大化给定吸收的 QFI，与相干态（经典）基准和单模压缩真空态相比，显示出量子优势。对于固定的平均能量 ńin2N，Fock 状态对于大 TPA 参数来说是最佳的，而真空和特定 Fock 状态的叠加对于所有 n̂ 的小吸收来说是最佳的。这与单光子吸收不同，其中福克状态始终是最佳的。值得注意的是，与优化量子探针的所有 TPA 参数水平的 QFI 相比，光子计数被证明可以提供最佳或接近最佳的性能，并且它们的量子优势对单光子损失具有鲁棒性。我们的研究结果提供了对高斯探针的已知限制行为及其在光子计数下的不同 FI 缩放的深入了解（压缩真空态的 ∝n´2 与相干态的 n´3）。对于小 TPA 参数，压缩态优于相干态，但在中间状态下表现不佳，在大吸收极限下变得相当。 这可以通过偶数和奇数 Fock 态行为之间的根本差异来解释：前者的 QFI 在大吸收极限和小吸收极限上都存在分歧，而后者仅在小吸收极限上存在分歧，在中间尺度上占主导地位。