T 2 can be greater than 2 T 1

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 theo...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of chemical physics 1989-08, Vol.91 (3), p.1775-1782
Main Authors: Sevian, H. M., Skinner, J. L.
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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. 49, 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.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.457648