Dynamics of the dissipative two-state system under ac modulation of bias and coupling energy

Driven electron transfer in an environment with slow and fast degrees of freedom

Driven electron transfer in a polar medium with slow and fast degrees of freedom is studied in the framework of a spin-boson Hamiltonian. Evolution dynamics is rigorously found when omega(s)(c)/(Gamma(a))sqrt[E(rs)/kT]<<1, where omega(s)(c) is the Debye cutoff frequency in the spectral function for the slow modes, E(rs) is the reorganization energy of slow degrees of freedom, and Gamma(-1)(a) is the reaction time dependent on the laser intensity parameter a=muE(0)/Planck's over 2piomega. Here omega and E0 are the frequency and the amplitude of a cw electric field, and mu is the electron dipole moment difference between the initial and final states. The master equation is derived for an arbitrary driving force affecting both the transition matrix element and the potential energy. For a cw electric field, the time dependent probability of staying at the product state, P1(t), is shown to be strongly dependent on the field intensity parameter a: P1(a,t) approximately (Gamma(m(1),m(2))t)(-E(rf)/E(rs)) or P1(a,t) approximately (Gamma(m(0))t)(-E(rf)/E(rs)), double or single resonances, respectively. Here E(rf) is the reorganization energy of fast degrees of freedom, Gamma(m(1),m(2)) approximately J(2)(m(1))(a)+J(2)(m(2))(a), and Gamma(m(0)) approximately J(2)(m(0))(a), where J(a) is a Bessel function. By changing the parameter a, one is able to manipulate the rate and direction of the reaction. When J(2)(m(0))(a) is close to zero the reaction is slow. Hence, slow modes turn out to be fast. This changes the character of the evolution dynamics from non- to mono- exponential decay, respectively. For the double resonance, the equilibrium constant is studied with the field intensity. It is shown that the reaction is almost insensitive to temperature. However, it strongly depends on the reaction heat, which provides a condition for the resonance.

Phase diffusion as a model for coherent suppression of tunneling in the presence of noise

We study the stabilization of coherent suppression of tunneling in a driven double-well system subject to random periodic delta-function "kicks." We model dissipation due to this stochastic process as a phase diffusion process for an effective two-level system, and derive a corresponding set of Bloch equations with phase damping terms that agree with the periodically kicked system at discrete times. We demonstrate that the ability of noise to localize the system on either side of the double-well potential arises from overdamping of the phase of oscillation, and not from any cooperative effect between the noise and the driving field. The model is investigated with a square wave drive, which has qualitatively similar features to the widely studied cosinusoidal drive, but has the additional advantage of allowing one to derive exact analytic expressions.

Tunneling through a fluctuating barrier: two-level model

We investigate the problem of tunneling across a randomly fluctuating barrier in the presence of dissipation in the two-level approximation. The barrier fluctuations are induced by a random telegraph noise whose switching rate nu is taken as a control parameter. For infinitely fast fluctuations the dynamics of the system is similar to the static case, while, for very small nu, the barrier evolution is a superposition of static solutions for both configurations. This leads to a resonant beating or long-time periodic localization. For an intermediate value of nu we have found a resonancelike suppression of coherent tunneling. When the system levels are detuned, a resonant enhancement of decay in the incoherent regime also occurs.