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arXiv:1904.03806 · The Journal of Physical Chemistry Letters

Entangled Photon Resonance Energy Transfer in Arbitrary Media

Kobra Nasiri Avanaki, George Chappell Schatz

Published May 22, 2019• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1021/acs.jpclett.9b00902

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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.
This paper presents a comprehensive study of the theory of entangled two-photon emission/absorption (E2P-EA) between a many-level cascade donor and a many-level acceptor (which could be quantum dots or molecules) using second-order perturbation theory and where the donor-acceptor pair is in a homogeneous but dispersive medium. To understand the mechanism of E2P-EA, we analyze how dipole orientation, radiative lifetime, energy detuning between intermediate states, separation distance, and entanglement time impact the E2P-EA rate. Our study shows that there are quantum interference effects in the E2P-EA rate expression that lead to oscillations in the rate as a function of entanglement time. Furthermore, we find that the E2P-EA rate for a representative system consisting of two quantum dots can be comparable to one-photon emission/absorption (OP-EA) when donor and acceptor are within a few nm. However, the E2P-EA rate falls off much more quickly with separation distance than does OP-EA.
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.
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.
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.
Two uncoupled two-level atoms cannot be jointly excited by classical light under general circumstances, due to destructive interference of excitation pathways in two-photon absorption. However, with temporally entangled light, two-atom excitation is shown possible. Photons arising from three-level cascade decay are intrinsically ordered in time of emission. This field correlation induces a joint resonance in the two-atom excitation probability via suppression of one of the time-ordered excitation pathways. The relative gain in two-photon absorption increases with the time-frequency entanglement.
We study 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 unentangled, separable, correlated states, produced either by an atomic cascade or parametric down-conversion, or even appropriate combinations of coherent states, have comparable efficiencies. We show that the key ingredient for the increase of simultaneous excitation probability is the presence of strong frequency anticorrelation and neither time correlation nor time-frequency entanglement.