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arXiv:2105.04121 · Physical Review A

Energy-time entanglement and intermediate-state dynamics in two-photon absorption

Baihong Li, Holger Friedrich Hofmann

Published Aug 27, 2021• 10 citations
arXivHTMLPDF

Abstract

It is well known that energy-time entanglement can enhance two-photon absorption (TPA) by simultaneously optimizing the two-photon resonance and the coincidence rate of photons at the absorber. However, the precise relation between entanglement and the TPA rate depends on the coherences of intermediate states involved in the transition, making it a rather challenging task to identify universal features of TPA processes. In the present paper, we show that the theory can be simplified greatly by separating the two-photon resonance from the temporal dynamics of the intermediate levels. The result is a description of the role of entanglement in the TPA process by a one-dimensional coherence in the Hilbert space defined by the arrival-time difference of the two photons. Transformation into the frequency-difference basis results in Kramers-Kronig relations for the TPA process, separating off-resonant contributions of virtual levels from resonant contributions. In particular, it can be shown that off-resonant contributions are insensitive to the frequencies of the associated virtual states, indicating that virtual-state spectroscopy of levels above the final two-photon excited state is not possible.

DOI
10.1103/physreva.104.022434

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It is well known that energy-time entanglement can enhance two-photon absorption (TPA) by simultaneously optimizing the two-photon resonance and the coincidence rate of photons at the absorber. However, the precise relation between entanglement and the TPA rate depends on the coherences of intermediate states involved in the transition, making it a rather challenging task to identify universal features of TPA processes. In the present paper, we show that the theory can be simplified greatly by separating the two-photon resonance from the temporal dynamics of the intermediate levels. The result is a description of the role of entanglement in the TPA process by a one-dimensional coherence in the Hilbert space defined by the arrival-time difference of the two photons. Transformation into the frequency-difference basis results in Kramers-Kronig relations for the TPA process, separating off-resonant contributions of virtual levels from resonant contributions. In particular, it can be shown that off-resonant contributions are insensitive to the frequencies of the associated virtual states, indicating that virtual-state spectroscopy of levels above the final two-photon excited state is not possible.
Energy-time entanglement can enhance two photon absorption by combining a precise two photon resonance with temporal correlations between the arrival times of the two photons. In general, the optimal timing of photon arrival is determined by the dynamics of the system between the initial and the final excitations. In this presentation, we show that the optimal timing of photon arrival corresponds to a specific phase dispersion in the frequency difference of the two photons. The absorption cross-section of energy-time entangled photons can be enhanced beyond the rate observed for optimal photon coincidence by adjusting the phase dispersion of one of the photons to match the optimal characteristics. We determine the maximal enhancement factor as a function of the bandwidth of the intermediate states and their detuning relative to the average photon frequency. Significant additional enhancements can be achieved when the bandwidth of the intermediate states is very narrow.
Broadband energy-time entanglement can be used to enhance the rate of two-photon absorption (TPA) by combining a precise two-photon resonance with a very short coincidence time. Because of this short coincidence time, broadband TPA is not sensitive to the spectrum of intermediate levels, making it the optimal choice when the intermediate transitions are entirely virtual. In the case of distinct intermediate resonances, it is possible to enhance TPA by introducing a phase dispersion that matches the intermediate resonances. Here, we consider the effects of a phase flip in the single photon spectrum, where the phases of all frequencies above a certain frequency are shifted by half a wavelength relative to the frequencies below this frequency. The frequency at which the phase is flipped can then be scanned to reveal the position of intermediate resonances. We find that a resonant phase flip maximizes the contributions of the asymmetric imaginary part of the dispersion that characterizes a typical resonance, resulting in a considerable enhancement of the TPA rate. Due to the bosonic symmetry of TPA, the enhancement is strongest when the resonance occurs when the frequency difference of the two photons is much higher than the linewidth of the resonance. Our results indicate that broadband entangled TPA with spectral phase flips may be suitable for phase-sensitive spectroscopy at the lower end of the spectrum where direct photon detection is difficult.
Two-photon absorption (TPA) and other nonlinear interactions of molecules with time-frequency-entangled photon pairs have been predicted to display a variety of fascinating effects. Therefore, their potential use in practical quantum-enhanced molecular spectroscopy requires close examination. This Tutorial presents 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 and 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. This Tutorial includes a 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 states by virtue of dephasing processes. A brief discussion of the main challenges facing experimental studies of entangled two-photon absorption is also given.
Abstract We theoretically analyze the transient dynamics in two-photon absorption (TPA) driven by a rectangular pulse consisting of entangled photons with time delay in terms of verifying the quantum virtual-state spectroscopy (VSS) method. We consider two types of three-level atomic systems: one is the atomic system having an intermediate state between ground and excited states, considered in common TPA, and another is the atomic system having an intermediate state above the excited state, assumed in the original VSS theory. We show that for common TPA configuration VSS does not occur at all, whereas for the original VSS configuration VSS-like signals can be obtained regardless of whether the incident photons are entangled or not, where photon entanglement simply contributes to the enhancement of the signal. In addition, by introducing frequency cutoff to the spectrum of incident photons, we also show that the VSS-like signal disappears even for the original VSS configuration when the intermediate state is completely virtually excited. Thus, the obtained results suggest that both the broad spectrum of incident photons causing the real excitation of intermediate state and energy configuration of intermediate state above the excited state are essential for VSS-like signals and that VSS in itself does not occur in a strict sense at least. The effect of unphysical parameters appearing in the original VSS scheme, recently theoretically predicted, is also discussed.
The true role of entanglement in two-photon virtual-state spectroscopy (Saleh et al 1998 Phys. Rev. Lett. 80 3483), a two-photon absorption spectroscopic technique that can retrieve information about the energy level structure of an atom or a molecule, is controversial. The consideration of closely related techniques, such as multidimensional pump–probe spectroscopy (Roslyak et al 2009 Phys. Rev. A 79 , 063409), suggests that spectroscopic information might also be retrieved by using uncorrelated pairs of photons. Here we show that this is not the case. In the two-photon absorption process, the ability to obtain information about the energy level structure of a medium depends on the spectral shape of existing temporal (frequency) correlations between the absorbed photons. In fact, it is a combination of both the presence of frequency correlations (entanglement) and their specific spectral shape that makes the realization of two-photon virtual-state spectroscopy possible. This result helps in selecting the type of two-photon source that needs to be used in order to experimentally perform the two-photon virtual-state spectroscopy technique.
The Two-photon absorption processes (TPA) is of great interest due to its variety of technical applications. Two-photon transitions can be excited using light with different statistical properties, such as laser light (coherent light), pseudo-thermal light and entangled photons-pairs (ETPA). For a TPA process driven with entangled photons (ETPA), a linear dependence of the signal with the photon flux has been theoretically predicted and experimentally demonstrated by various groups. The main motivation for studying ETPA relies on the capability of inducing TPA with a low photon flux. This is advantageous to analyze, among other things, biological samples with a reduced probability of destroying them in the process. However, ETPA experiments developed to date raise many questions regarding the difficulty of isolating a signal in organic molecules. One of the main problems in these experiments is the difficulty to study independently all the systematic effects due to the complex structure of organic molecules. An alternative to clarify the origin of the signal is to study the ETPA process in atomic systems. In this case, the possibility to excite narrow band transitions with tunable single frequency lasers can provide a clear signature of the ETPA process. To achieve this objective, the first step consists of understanding TPA with coherent light, or classical TPA, and measuring the corresponding cross-section in atomic systems. Once the classical regime is characterized, the ETPA process can be studied considering decoherence effects and coherence between intermediate states. For this, the ETPA cross section must be calculated and measured. In this work we present a theoretical calculation of the ETPA transition probability and cross-section with the density operator formalism for the transition 62S1/2 →82S1/2. The theoretical results will be complemented with an experiment with atomic Cesium based in a coincidence detection scheme.