T 2 can be greater than 2T1

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Abstract
We consider a quantum–mechanical two‐level system under the influence of both diagonal and off‐diagonal stochastic perturbations, and focus on the decay times T1 and T2, which refer to the relaxation to equilibrium of the populations and relative phase of the two levels, respectively. From both theoretical and experimental viewpoints one traditionally expects that T2≤2T1. On the other hand, from a fourth‐order cumulant expansion calculation of the asymptotic time dependence of the density matrix elements, Budimir and Skinner [J. Stat. Phys. 4 9, 1029 (1987)] showed that, in fact, in some instances T2>2T1. In this paper we solve the stochastic model numerically, which leads to the exact time dependence of the density matrix at all times. We find that the analytic prediction that T2>2T1 is not only correct, but also meaningful, in the sense that the density matrix elements decay exponentially after only a short transient time.