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arXiv:2103.10530 · Optics Express

Quantifying the enhancement of two-photon absorption due to spectral-temporal entanglement

Tiemo Landes, Michael G. Raymer, Markus Allgaier, Sofiane Merkouche, Brian J. Smith, Andrew H. Marcus

Published May 13, 2021• 76 citations
arXivHTMLPDF

Abstract

When a low flux of time-frequency-entangled photon pairs (EPP) illuminates a two-photon transition, the rate of two-photon absorption (TPA) can be enhanced considerably by the quantum nature of photon number correlations and frequency correlations. We use a quantum-theoretic derivation of entangled TPA (ETPA) and calculate an upper bound on the amount of quantum enhancement that is possible in such systems. The derived bounds indicate that in order to observe ETPA the experiments would need to operate at a combination of significantly higher rates of EPP illumination, molecular concentrations, and conventional TPA cross sections than are achieved in typical experiments.

DOI
10.1364/oe.422544

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When a low flux of time-frequency-entangled photon pairs (EPP) illuminates a two-photon transition, the rate of two-photon absorption (TPA) can be enhanced considerably by the quantum nature of photon number correlations and frequency correlations. We use a quantum-theoretic derivation of entangled TPA (ETPA) and calculate an upper bound on the amount of quantum enhancement that is possible in such systems. The derived bounds indicate that in order to observe ETPA the experiments would need to operate at a combination of significantly higher rates of EPP illumination, molecular concentrations, and conventional TPA cross sections than are achieved in typical experiments.
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.
We present an ongoing experiment to investigate the potential enhancement of the two-photon absorption (TPA) rate of an atom using time–frequency-entangled photon pairs, a process known as entangled two-photon absorption (ETPA). There has been significant debate in the literature regarding the existence and magnitude of such enhancement. Previous studies have primarily focused on ETPA in molecular fluorophores, which are relevant for biological imaging applications but typically exhibit relatively low two-photon cross sections, often not exceeding 10⁻⁵⁰ cm⁴s/photon. In this work, we sacrifice broad applicability for experimental practicality, and instead probe ETPA in rubidium vapor, which has a comparatively large two-photon cross section (∼10⁻¹⁸ cm⁴s/photon) relative to most molecular fluorophores used in prior studies. We have developed and characterized an entangled photon-pair source, and have observed two-photon absorption in rubidium vapor. We have also reproduced previous theoretical models of ETPA. Preliminary results are presented, along with a discussion of the future direction of the experiment.
Entangled two-photon absorption (ETPA) could form the basis of nonlinear quantum spectroscopy at very low photon fluxes, since, at sufficiently low photon fluxes, ETPA scales linearly with the photon flux. When different pairs start to overlap temporally, accidental coincidences are thought to give rise to a "classical" quadratic scaling that dominates the signal at large photon fluxes and, thus, recovers a supposedly classical regime, where any quantum advantage is thought to be lost. Here, we scrutinize this assumption and demonstrate that quantum-enhanced absorption cross sections can persist even for very large photon numbers. To this end, we use a minimal model for quantum light, which can interpolate continuously between the entangled pair and a high-photon-flux limit, to analytically derive ETPA cross sections and the intensity crossover regime. We investigate the interplay between spectral and spatial degrees of freedom and how linewidth broadening of the sample impacts the experimentally achievable enhancement.
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.
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.