CONTROL OF TUNNELING REACTIONS WITH AN EXTERNAL HELD IN A 4-LEVEL SYSTEM - A GENERAL REDFIELD APPROACH

We investigate the possibility of controlling tunneling in a four-leve l system by the application of an external field. The four level syste m is defined by a symmetric double well potential energy surface that supports two sets of tunnel doubler states, as is characteristic of so me proton transfer potential energy surfaces. The time-dependent exter nal field couples to the dipole moment operator of the tunneling syste m. In a four-level system, there is the possibility of intrawell trans itions via vibrational relaxation and external field induced transitio ns, in addition to the interwell tunneling transitions. We obtain a ge neralization of Redfield theory that describes the time evolution of t he elements of the reduced density matrix for the system in the presen ce of the external field. The elements of the resulting Redfield tenso r are constructed with the use of symbolic algebra. The theory is illu strated with a simple example that shows how the external field can co ntrol the rate of population transfer (tunneling) in the presence of t he vibrational transitions.