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arXiv:2408.03903

Role of time-frequency correlations in two-photon-two-atom resonance energy transfer

Roberto de J. León‐Montiel, Arturo Pedroza-Rojas, Jorge-Alberto Peralta-Ángeles

Published Aug 7, 2024• 0 citations
arXivHTMLPDF

Abstract

Excitation energy transfer is a photophysical process upon which many chemical and biological phenomena are built. From natural small systems to synthetic multichromophoric macromolecules, energy transfer deals with the process of migration of electronic excitation energy from an excited donor to an acceptor. Although this phenomenon has been extensively studied in the past, the rapid evolution of quantum-enabled technologies has motivated the question on whether nonclassical sources of light, such as entangled photon pairs, may provide us with a better control (or enhancement) of energy transfer at the nanoscale. In this work, we provide a comprehensive study of the joint excitation of two non-interacting two-level atoms by time-frequency correlated photon pairs -- whose central frequencies are not resonant with the individual particles -- generated by means of spontaneous parametric down conversion (SPDC). We demonstrate that while strong frequency anti-correlation between photons guarantees a large two-photon excitation (TPE) probability, photons bearing a sine cardinal spectral shape exhibit a $\sim$3.8 times larger TPE signal than photons with a Gaussian spectrum. More importantly, we find that suppression of time-ordered excitation pathways does not substantially modify the TPE probability for two-photon states with a Gaussian spectral shape; whereas photons with a sine cardinal spectrum exhibit the strongest TPE signals when two-photon excitation pathways are not suppressed. Our results not only help elucidating the role of time-frequency correlations in resonance energy transfer with SPDC photons, but also provide valuable information regarding the optimal source to be used in its experimental implementation.

DOI
10.48550/arxiv.2408.03903

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Excitation energy transfer is a photophysical process upon which many chemical and biological phenomena are built. From natural small systems to synthetic multichromophoric macromolecules, energy transfer deals with the process of migration of electronic excitation energy from an excited donor to an acceptor. Although this phenomenon has been extensively studied in the past, the rapid evolution of quantum-enabled technologies has motivated the question on whether nonclassical sources of light, such as entangled photon pairs, may provide us with a better control (or enhancement) of energy transfer at the nanoscale. In this work, we provide a comprehensive study of the joint excitation of two non-interacting two-level atoms by time-frequency correlated photon pairs -- whose central frequencies are not resonant with the individual particles -- generated by means of spontaneous parametric down conversion (SPDC). We demonstrate that while strong frequency anti-correlation between photons guarantees a large two-photon excitation (TPE) probability, photons bearing a sine cardinal spectral shape exhibit a ∼\sim∼3.8 times larger TPE signal than photons with a Gaussian spectrum. More importantly, we find that suppression of time-ordered excitation pathways does not substantially modify the TPE probability for two-photon states with a Gaussian spectral shape; whereas photons with a sine cardinal spectrum exhibit the strongest TPE signals when two-photon excitation pathways are not suppressed. Our results not only help elucidating the role of time-frequency correlations in resonance energy transfer with SPDC photons, but also provide valuable information regarding the optimal source to be used in its experimental implementation.
Excitation energy transfer is a photophysical process upon which many chemical and biological phenomena are built. From natural small systems to synthetic multichromophoric macromolecules, energy transfer deals with the process of migration of electronic excitation energy from an excited donor to an acceptor. Although this phenomenon has been extensively studied in the past, the rapid evolution of quantum-enabled technologies has led to the question of whether nonclassical sources of light, such as entangled photon pairs, may provide us with better control (or enhancement) of energy transfer at the nanoscale. In this work we provide a comprehensive study of the joint excitation of two noninteracting two-level atoms by time-frequency-correlated photon pairs (whose central frequencies are not resonant with the individual particles) generated by means of spontaneous parametric down-conversion (SPDC). We demonstrate that while strong frequency anticorrelation between photons guarantees a large two-photon excitation (TPE) probability, photons bearing a sine cardinal spectral shape exhibit an approximately 3.8 times larger TPE signal than photons with a Gaussian spectrum. More importantly, we find that suppression of time-ordered excitation pathways does not substantially modify the TPE probability for two-photon states with a Gaussian spectral shape, whereas photons with a sine cardinal spectrum exhibit the strongest TPE signals when two-photon excitation pathways are not suppressed. Our results not only help elucidate the role of time-frequency correlations in resonance energy transfer with SPDC photons, but also provide valuable information regarding the optimal source to be used in the experimental implementation of said process.
Inspired by the unique nonclassical character of two-photon interactions induced by entangled photons, we develop a new comprehensive Förster-type formulation for entangled-two-photon resonance energy transfer (E2P-RET) mediated by inhomogeneous, dispersive, and absorptive media with any space-dependent and frequency-dependent dielectric function and with any size of donor/acceptor. In our theoretical framework, two uncoupled particles are jointly excited by the temporally entangled field associated with two virtual photons that are produced by three-level radiative cascade decay in a donor particle. The temporal entanglement leads to frequency anticorrelation in the virtual photon’s field, and vanishing of one of the time-ordered excitation pathways. The underlying mechanism leads to more than 3 orders of magnitude enhancement in the E2P-RET rate compared with the uncorrelated photon case. With the power of our new formulation, we propose a way to characterize E2P-RET through an effective rate coefficient K E2P, introduced here. This coefficient shows how energy transfer can be enhanced or suppressed depending on rate parameters in the radiative cascade, and by varying the donor–acceptor frequency differences.
Nonlinear optics has had extensive application into a vast array of scientific fields. One such nonlinear process, two-photon absorption (TPA), has had a wildly successful \nadoption into the field of biological imaging and microscopy. As far and as fast as this field is progressing, limitations stemming from the use of ultrafast lasers are starting to appear. \nIn this work, an alternative nonclassical light source will be motivated for the application \nof low photon-flux two-photon microscopy. The origin and properties of the chosen \nnonclassical source, spontaneous parametric downconversion (SPDC), will be discussed along with the spatial and spectral properties modelled. Nonlinear processes such as TPA and sum frequency generation (SFG) will be viewed as "ultrafast coincidence measurements" of two photons arriving at a molecule within the time window of excitation. These ultrafast coincidence measurements will be viewed in an alternative manner: in terms of the second-order coherence from a light source. This degree of second-order coherence can be subdivided into two categories arising from different combinations of correlations within and between entangled photon pairs. Of interest, the energy-time correlations within the photon pair allow for enhancements in ultrafast coincidence rates over coherent light sources. The makings of an experimental setup to demonstrate enhanced rates from ultrafast two-photon coincidences taking place in SFG in a nonlinear crystal will be discussed.
We study in this paper the efficiency of different two-photon states of light to induce the simultaneous excitation of two atoms of different kinds when the sum of the energies of the two photons matches the sum of the energies of the two atomic transitions, while no photons are resonant with each individual transition. We find that entangled two-photon states produced by an atomic cascade are indeed capable of enhancing by a large factor the simultaneous excitation probability as compared to uncorrelated photons, as predicted some years ago by Muthukrishnan et al, but that several non-entangled, separable, correlated states, produced either by an atomic cascade or parametric down conversion, or even appropriate combinations of coher- ent states, have comparable efficiencies. We show that the key ingredient for the increase of simultaneous excitation probability is the presence of strong frequency anti-correlation and not time correlation nor time-frequency entanglement.
We study in this paper the efficiency of different two-photon states of light to induce the simultaneous excitation of two atoms of different kinds when the sum of the energies of the two photons matches the sum of the energies of the two atomic transitions, while no photons are resonant with each individual transition. We find that entangled two-photon states produced by an atomic cascade are indeed capable of enhancing by a large factor the simultaneous excitation probability as compared to uncorrelated photons, as predicted some years ago by Muthukrishnan et al, but that several non-entangled, separable, correlated states, produced either by an atomic cascade or parametric down conversion, or even appropriate combinations of coher- ent states, have comparable efficiencies. We show that the key ingredient for the increase of simultaneous excitation probability is the presence of strong frequency anti-correlation and not time correlation nor time-frequency entanglement.