Control of tunneling processes with an external field in a four-level system: An analytic approach

We investigate the control of population transfer by the application of an external field to a four-level system that is coupled to dissipative baths. The system consists of two tunnel doublets separated by a large energy gap. The external field couples to the system's dipole moment operator and induces transitions between left and right and lower and upper states. Vibrational relaxation couples the lower and upper doublers, and the left-right transitions are modulated by strong coupling to solvent modes. We show that our previously obtained relaxation equations are amenable to analytic approximations. Expressions for the steady lower-upper state populations and the left-right transfer rate, when there is efficient vibrational relaxation, are developed. For no vibrational relaxation, the time evolution of these quantities is obtained, When the external field is resonant with the large energy gap, we find that population initially localized in the left lower state can be rapidly and irreversibly transferred to the right lower and upper states, even when vibrational relaxation is absent, by a mechanism that relies on there being a left-to-right dissipative rate process. An expression for the overall left-to-right transfer rate is obtained as a Boltzmann weighted sum of the lower and upper doubler left-to-right rate constants, with an effective temperature that includes the effect of the external field.