Non-Markovian dynamics of the driven spin-boson model

The non-Markovian dynamics of the driven spin-boson model at zero and finite temperature is investigated theoretically. Based on a unitary transformation and convolution theorem, the analytical expression of population difference in Laplace space is obtained. This method provides a tool to help us to understand the interference between driving and dissipation within the non-Markovian frame. We study the transient and the steady-state non-Markovian dynamics of population difference P(t) in the case of different temperature, driving and spin-bath coupling (SBC) strength. It has been shown that it is necessary to use non-Markovian methods when SBC is strong. At zero temperature, the curve of steady-state amplitude P (lt) versus Rabi driving amplitude omega is N-like shaped. While at finite temperature, the curve becomes ?-like shaped. These curves come from the interference between driving and dissipation. Also, from the interference pattern above, we know that large coherent oscillations can be obtained by optimizing the parameters: Rabi driving amplitude, temperature and SBC strength.