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

TL;DR

This study theoretically compares coherent RET and non-Markovian bath effects, revealing deviations from traditional FRET distance dependence and highlighting the significance of quantum coherence and bath dynamics at short distances.

Contribution

It introduces a theoretical comparison of CRET and non-Markovian FRET, demonstrating their impact on distance dependence beyond the classical inverse sixth power law.

Findings

RET rate deviates from inverse sixth power law due to quantum coherence.

Non-Markovian bath effects moderate the distance dependence.

Quantum effects are prominent at sub-picosecond timescales.

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 F\"{o}rster'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.