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Journal of Physics B Atomic Molecular and Optical Physics

Two-photon absorption dynamics by a rectangular entangled-photon pulse with time delay

Hisaki Oka

Published Feb 9, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1361-6455/acbad1

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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.
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.
We theoretically investigate two-photon excitation by spectrally shaped entangled photons with energy anticorrelation in terms of how the real excitation of an intermediate state affects two-photon absorption by entangled photons. Spectral holes are introduced in the entangled photons around the energy levels of an intermediate state so that two-step excitation via the real excitation of the intermediated state can be suppressed. Using a three-level atomic system as an example, we show that the spectral holes well suppress the real excitation of the intermediate state and recover two-photon absorption via a virtual state. Furthermore, for a short pulse close to a monocycle, we show that the excitation efficiency by the spectrally shaped entangled photons can be enhanced a thousand times as large as that by uncorrelated photons.
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.
Multiphoton absorption of entangled photons offers ways for obtaining unique information about chemical and biological processes. Measurements with entangled photons may enable sensing biological signatures with high selectivity and at very low light levels to protect against photodamage. In this paper, we present a theoretical and experimental study of the excitation wavelength dependence of the entangled two-photon absorption (ETPA) process in a molecular system, which provides insights into how entanglement affects molecular spectra. We demonstrate that the ETPA excitation spectrum can be different from that of classical TPA as well as that for one-photon resonant absorption (OPA) with photons of doubled frequency. These results are modeled by assuming the ETPA cross-section is governed by a two-photon excited state radiative linewidth rather than by electron-phonon interactions, and this leads to excitation spectra that match the observed results. Further, we find that the two-photon-allowed states with highest TPA and ETPA intensities have high electronic entanglements, with ETPA especially favoring states with the longest radiative lifetimes. These results provide concepts for the development of quantum light-based spectroscopy and microscopy that will lead to much higher efficiency of ETPA sensors and low-intensity detection schemes.
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.
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.