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arXiv:2601.00708

Effects of Donor-Acceptor Quantum Coherence and Non-Markovian Bath on the Distance Dependence of Resonance Energy Transfer

Seogjoo J. Jang

quant-phphysics.bio-phphysics.chem-phphysics.opticsSubmitted Jan 2, 2026• Announced Jan 5, 2026

Abstract

Accurate information on the distance dependence of resonance energy transfer (RET) is crucial for its utilization as a spectroscopic ruler \re{of} nanometer scale distances. In this regard, understanding the effects of donor-acceptor quantum coherence and non-Markovian bath, which become significant at short distances, has significant implications. The present work investigates this issue theoretically by comparing results from a theory of coherent RET (CRET) with a nonequilibrium version of Förster's RET (FRET) theory, both accounting for non-Markovian bath effects. Even for a model where the donor-acceptor electronic coupling is of transition dipole interaction form, it is shown that the RET rate in general deviates from the inverse sixth power distance dependence as opposed to the prediction of the original FRET. It is shown that the donor-acceptor quantum coherence makes the \re{distance} dependence steeper than the sixth power although detailed manner of enhancement is sensitive to specific values of parameters. On the other hand, the non-Markovian bath effects make the \re{distance} dependence more moderate than the sixth power for both CRET and nonueqilibrium FRET because finite time scale of the bath causes the rate to be smaller than the prediction of original FRET. While these effects are \re{demonstrated clearly} in the population dynamics at sub-picosecond time scales, their contributions to the conventional RET efficiency are relatively minor. This indicates that the actual detection of such effects through conventional RET efficiency measurement requires either high precision or utilization of a donor with fast spontaneous decay rate of excitation.

Journal reference: ournal of Physical Chemistry C 123, 5767-5775 (2019)
DOI: 10.1021/acs.jpcc.8b12481
Comments: 11 pages, 5 figures

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Accurate information on the distance dependence of resonance energy transfer (RET) is crucial for its utilization as a spectroscopic ruler \re{of} nanometer scale distances. In this regard, understanding the effects of donor-acceptor quantum coherence and non-Markovian bath, which become significant at short distances, has significant implications. The present work investigates this issue theoretically by comparing results from a theory of coherent RET (CRET) with a nonequilibrium version of Förster's RET (FRET) theory, both accounting for non-Markovian bath effects. Even for a model where the donor-acceptor electronic coupling is of transition dipole interaction form, it is shown that the RET rate in general deviates from the inverse sixth power distance dependence as opposed to the prediction of the original FRET. It is shown that the donor-acceptor quantum coherence makes the \re{distance} dependence steeper than the sixth power although detailed manner of enhancement is sensitive to specific values of parameters. On the other hand, the non-Markovian bath effects make the \re{distance} dependence more moderate than the sixth power for both CRET and nonueqilibrium FRET because finite time scale of the bath causes the rate to be smaller than the prediction of original FRET. While these effects are \re{demonstrated clearly} in the population dynamics at sub-picosecond time scales, their contributions to the conventional RET efficiency are relatively minor. This indicates that the actual detection of such effects through conventional RET efficiency measurement requires either high precision or utilization of a donor with fast spontaneous decay rate of excitation.

The rates of exciton transfer within dyads of perylene diimide and terrylene diimide connected by oligophenylene bridge units have been shown to deviate significantly from those of Förster's resonance energy transfer theory, according to single molecule spectroscopy experiments. The present work provides a detailed computational and theoretical study investigating the source of such discrepancy. Electronic spectroscopy data are calculated by time-dependent density function theory and then compared with experimental results. Electronic couplings between exciton donor and acceptor are estimated based on both transition density cube method and transition dipole approximation. These results confirm that the delocalization of exciton to the bridge parts contribute to significant enhancement of donor-acceptor electronic coupling. Mechanistic details of exciton transfer are examined by estimating the contributions of the bridge electronic states, vibrational modes of the dyads commonly coupled to both donor and acceptor, inelastic resonance energy transfer mechanism, and dark exciton states. These analyses suggest that the contribution of common vibrational modes serves as the main source of deviation from Förster's spectral overlap expression.

The rate of energy transfer in donor-acceptor systems can be manipulated via the common interaction with the confined electromagnetic modes of a micro-cavity. We analyze the competition between the near-field short range dipole-dipole energy exchange processes and the cavity mediated long-range interactions in a simplified model consisting of effective two-level quantum emitters that could be relevant for molecules in experiments under cryogenic conditions. We find that free-space collective incoherent interactions, typically associated with sub-and superradiance, can modify the traditional resonant energy transfer scaling with distance. The same holds true for cavity-mediated collective incoherent interactions in a weak-coupling but strong-cooperativity regime. In the strong coupling regime, we elucidate the effect of pumping into cavity polaritons and analytically identify an optimal energy flow regime characterized by equal donor/acceptor Hopfield coefficients in the middle polariton. Finally we quantify the build-up of quantum correlations in the donor-acceptor system via the two-qubit concurrence as a measure of entanglement.

The rate of energy transfer in donor-acceptor systems can be manipulated via the common interaction with the confined electromagnetic modes of a micro-cavity. We analyze the competition between the near-field short range dipole-dipole energy exchange processes and the cavity mediated long-range interactions in a simplified model consisting of effective two-level quantum emitters that could be relevant for molecules in experiments under cryogenic conditions. We find that free-space collective incoherent interactions, typically associated with sub- and superradiance, can modify the traditional resonant energy transfer scaling with distance. The same holds true for cavity-mediated collective incoherent interactions in a weak-coupling but strong-cooperativity regime. In the strong coupling regime, we elucidate the effect of pumping into cavity polaritons and analytically identify an optimal energy flow regime characterized by equal donor/acceptor Hopfield coefficients in the middle polariton. Finally we quantify the build-up of quantum correlations in the donor-acceptor system via the two-qubit concurrence as a measure of entanglement.

We derive a unified quantum theory of coherent and incoherent energy transfer between two atoms (donor and acceptor) valid in arbitrary Markovian nanophotonic environments. Our theory predicts a fundamental bound η m a x = γ a γ d + γ a for energy transfer efficiency arising from the spontaneous emission rates γ d and γ a of the donor and acceptor. We propose the control of the acceptor spontaneous emission rate as a new design principle for enhancing energy transfer efficiency. We predict an experiment using mirrors to enhance the efficiency bound by exploiting the dipole orientations of the donor and acceptor. Of fundamental interest, we show that while quantum coherence implies the ultimate efficiency bound has been reached, reaching the ultimate efficiency does not require quantum coherence. Our work paves the way towards nanophotonic analogues of efficiency-enhancing environments known in quantum biological systems.

We derive a unified quantum theory of coherent and incoherent energy transfer between two atoms (donor and acceptor) valid in arbitrary Markovian nanophotonic environments. Our theory predicts a fundamental bound

η_{max} = \frac{γ_a}{γ_d + γ_a}

for energy transfer efficiency arising from the spontaneous emission rates

γ_{d}

and

γ_a

of the donor and acceptor. We propose the control of the acceptor spontaneous emission rate as a new design principle for enhancing energy transfer efficiency. We predict an experiment using mirrors to enhance the efficiency bound by exploiting the dipole orientations of the donor and acceptor. Of fundamental interest, we show that while quantum coherence implies the ultimate efficiency bound has been reached, reaching the ultimate efficiency does not require quantum coherence. Our work paves the way towards nanophotonic analogues of efficiency enhancing environments known in quantum biological systems.

The quantum electrodynamical theory of coherent fluorescence resonance energy transfer (FRET) between two dipoles (free atoms, molecules or dopant centres in crystalline matrices at low temperature conditions) in an arbitrary non-dissipative environment is elaborated using a canonical quantization scheme. It is shown that population dynamics of both atoms can be expressed in terms of a classical Green function. This general theory corresponds well to the problem of description of controllable quantum manipulations under the donor-acceptor system (e.g. its application for FRET scanning near-field optical microscopy-based quantum computing). In addition, its usefulness is illustrated for the case of coherent FRET in free space and for the case when atoms are placed near an ideally conducting plane. The possibility of creating an entangled state of three atoms is demonstrated.