Non-Markovian population and phase relaxation and absorption lineshape for a two-level system strongly coupled to a harmonic quantum bath

Abstract

The study of the relaxation of open quantum systems is fundamental to both nonequilibrium statistical mechanics and spectroscopy. In this paper we study theoretically a model of two nondegenerate quantum levels coupled linearly and off-diagonally to a harmonic quantum-mechanical bath. In the weak-coupling limit it is well known for this model that after the system is perturbed from equilibrium the reduced density matrix elements relax exponentially to their equilibrium values, and that T2 = 2T1, where T1 and T2 are the population and phase relaxation times, respectively. In addition, the absorption lineshape is Lorentzian, with a FWHM in Hz of Δν = 12πT1. In this paper we go beyond lowest order in the system-bath interaction by using a time-convolutionless projection operator approach that allows us to avoid the usual “factorization assumption” for the initial density matrix and to include explicitly the effect of the initially prepared state, which we calculate by subjecting the system to a short intense pulse of radiation. We find that although when one is outside the weak-coupling regime the relaxation becomes non-Markovian, the relaxation times T1 and T2 are still well defined in an asymptotic sense. In some cases we find that T2>2T1. The absorption lineshape function becomes non-Lorentzian, and in some instances we find that Δν<12πT1. We find that the equilibrium population of the upper quantum level is nonzero at T = 0. We also investigate the infinite-temperature limit, making the connection to stochastic models of relaxation. Finally, we propose some possible experiments to verify some of our predictions.