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Register a new userEntangled Two-Photon Absorption by Atoms and Molecules: A Quantum Optics Tutorial
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Two-photon absorption (TPA) and other nonlinear interactions of molecules with time-frequency-entangled photon pairs (EPP) has been predicted to display a variety of fascinating effects. Therefore, their potential use in practical quantum-enhanced molecular spectroscopy requires close examination. This paper presents in tutorial style a detailed theoretical study of one- and two-photon absorption by molecules, focusing on how to treat the quantum nature of light. We review some basic quantum optics theory, then we review the density-matrix (Liouville) derivation of molecular optical response, emphasizing how to incorporate quantum states of light into the treatment. For illustration we treat in detail the TPA of photon pairs created by spontaneous parametric down conversion, with an emphasis on how quantum light TPA differs from that with classical light. In particular, we treat the question of how much enhancement of the TPA rate can be achieved using entangled states. The paper includes review of known theoretical methods and results, as well as some extensions, especially the comparison of TPA processes that occur via far-off-resonant intermediate states only and those that involve off-resonant intermediate state by virtue of dephasing processes. A brief discussion of the main challenges facing experimental studies of entangled TPA is also given.
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While two-photon absorption (TPA) and other forms of nonlinear interactions of molecules with isolated time-frequency-entangled photon pairs (EPP) have been predicted to display a variety of fascinating effects, their potential use in practical quantum-enhanced molecular spectroscopy requires close examination. This paper presents a detailed theoretical study of quantum-enhanced TPA by both photon-number correlations and spectral correlations, including an account of the deleterious effects of dispersion. While such correlations in EPP created by spontaneous parametric down conversion can increase the TPA rate significantly in the regime of extremely low optical flux, we find that for typical molecules in solution this regime corresponds to such low TPA event rates as to be unobservable in practice. Our results support the usefulness of EPP spectroscopy in atomic or other narrow-linewidth systems, while questioning the efficacy of such approaches for broadband systems including molecules in solution.
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.
Entangled two-photon absorption spectroscopy (TPA) has been widely recognized as a powerful tool for revealing relevant information about the structure of complex molecular systems. However, to date, the experimental implementation of this technique has remained elusive, mainly because of two major difficulties. First, the need to perform multiple experiments with two-photon states bearing different temporal correlations, which translates in the necessity to have at the experimenters disposal tens, if not hundreds, of sources of entangled photons. Second, the need to have emph{a priori} knowledge of the absorbing mediums lowest-lying intermediate energy level. In this work, we put forward a simple experimental scheme that successfully overcomes these two limitations. By making use of a temperature-controlled entangled-photon source, which allows the tuning of the central frequencies of the absorbed photons, we show that the TPA signal, measured as a function of the temperature of the nonlinear crystal that generates the paired photons, and a controllable delay between them, carries all information about the electronic level structure of the absorbing medium, which can be revealed by a simple Fourier transformation.
Path-entangled N-photon states can be obtained through the coalescence of indistinguishable photons inside linear networks. They are key resources for quantum enhanced metrology, quantum imaging, as well as quantum computation based on quantum walks. However, the quantum tomography of path-entangled indistinguishable photons is still in its infancy as it requires multiple phase estimations increasing rapidly with N. Here, we propose and implement a method to measure the quantum tomography of path-entangled two-photon states. A two-photon state is generated through the Hong-Ou-Mandel interference of highly indistinguishable single photons emitted by a semiconductor quantum dot-cavity device. To access both the populations and the coherences of the path-encoded density matrix, we introduce an ancilla spatial mode and perform photon correlations as a function of a single phase in a split Mach-Zehnder interferometer. We discuss the accuracy of standard quantum tomography techniques and show that an overcomplete data set can reveal spatial coherences that could be otherwise hidden due to limited or noisy statistics. Finally, we extend our analysis to extract the truly indistinguishable part of the density matrix, which allows us to identify the main origin for the imperfect fidelity to the maximally entangled state.
Entangled photon pairs have been promised to deliver a substantial quantum advantage for two-photon absorption spectroscopy. However, recent work has challenged the previously reported magnitude of quantum enhancement in two-photon absorption. Here, we present an experimental comparison of sum-frequency generation and molecular absorption, each driven by isolated photon pairs. We establish an upper bound on the enhancement for entangled-two-photon absorption in Rhodamine-6G, which lies well below previously reported values.
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