Quantum metrology of two-photon absorption

TL;DR

This paper investigates how nonclassical squeezed light sources can enhance the precision of two-photon absorption measurements, revealing quantum advantages and unusual scaling behaviors in measurement strategies.

Contribution

It establishes the metrological limits of squeezed light for TPA measurement and compares quantum and classical strategies, highlighting the advantages of quadrature measurements with squeezed states.

Findings

No fundamental limit for precision with squeezed states at small cross sections.

Squeezed states outperform coherent states in quadrature measurements with a scaling of ~n^4.

Coherent states can also achieve a ~n^3 scaling due to TPA nonlinearity.

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 there is no 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 $\sim n^4$. 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 a $\sim n^3$ scaling in both quadrature and photon-counting measurements.