Dark-state mechanism for the long-time transfer of excitations in a donor-acceptor system

The excitation energy transfer between a donor-acceptor pair with fixed distance apart through energy exchanging with environment is investigated. The total system is modeled as two two-level systems (TLSs) interacting with many harmonic oscillators. The pair behaves coherently or incoherently, depending on whether the dipolar coupling is stronger or weaker than the TLS-environment coupling. The environmental linear dispersion relation gives an analytical solution to the pairʼs probability involving all the retardation times. We found that the long-time trapping of energy within the pair is caused by the inhibiting dark-state radiative decay when two TLSs are at half a resonant wavelength.