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.
Highlights
Two-photon absorption (TPA), the simultaneous absorption of two quanta of light by a quantum system, was first described theoretically by Göppert-Mayer in 1931 [1] and was first observed experimentally only one year after Maiman’s development of the laser [2]
We have examined precision bounds on the measurement of two-photon absorption cross sections
We found that there is no fundamental lower bound on the achievable precision of TPA measurements using squeezed light, as the quantum Fisher information (QFI) for squeezed states diverges in the limit of small absorbances
Summary
Two-photon absorption (TPA), the simultaneous absorption of two quanta of light by a quantum system, was first described theoretically by Göppert-Mayer in 1931 [1] and was first observed experimentally only one year after Maiman’s development of the laser [2]. Quantum-enhanced absorption measurements have received renewed attention recently [16,17,18,19,20,21,22,23,24] with the development of new quantum light sources and an increased interest in sensing technologies [25], as well as the demonstration of “sensing with undetected photons” [26,27,28,29,30] Interest in this problem dates back to 2007, where the optimal estimation of single-photon losses was first considered [31,32]. [35,36], which noted that interactions can enable socalled “super-Heisenberg scaling” with the photon number n in the sense that the optimal scaling of linear phase estimation precision (∼n−1) can be surpassed These studies concern linear spectroscopy, i.e., the absorption of single photons, or the combination of classical lasers with quantum light sources in two-photon Raman transitions [37,38]. We show this scaling can be improved even further using squeezed states, where the QFI diverges in the limit of very weak TPA losses and homodyne measurements of the squeezed quadrature provide a ∝ n4 scaling of the corresponding Fisher information
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