Dissipation-induced Transition Of A Simple Harmonic

We investigate the dissipation-induced transition probabilities between any two eigenstates of a simple harmonic oscillator. Using the method developed by Yu and Sun [Phys. Rev. A 49, 592(1994)], the general analytical expressions for the transition probabilities are obtained. The special cases: transition probabilities from the ground state to the first few excited states are then discussed in detail. Different from the previous studies in the literature where only the effect of damping was considered, it is found that the Brownian motion makes the transitions between states of different parity possible. The limitations of the applicability of our results are also discussed.The content of the paper is organized as follows: We first give a brief review of the work of YS in section II. In section III, the details of the calculation and the exact analytical expression for the dissipation induced transition probability are presented. Then we discuss the special case:transition from the ground to higher states. The limitations of the applicabilities of our results are discussed and concluding remarks are made in section V.