T 2 can be greater than 2T 1 even at finite temperature

Abstract

The relaxation of a nondegenerate two‐level quantum system linearly and off‐diagonally coupled to a thermal bath of quantum‐mechanical harmonic oscillators is studied. The population and phase relaxation times,T 1 and T 2, are calculated to fourth order in the system/bath interaction. Focus is on a specific model of the bath spectral density that is both Ohmic (proportional to frequency at low frequency) and Lorentzian, and which has the property that, in the semiclassical or high‐temperature limit, it reproduces the stochastic model studied previously by Budimir and Skinner [J. Stat. Phys. 4 9, 1029 (1987)]. For this fully quantum‐mechanical model, it is found that under certain conditions the standard inequality,T 2≤2T 1, is violated, demonstrating that this unusual result, which was originally derived from the (infinite‐temperature) stochastic model, is valid at finite temperature as well.