Nonexponential Quantum Decay under Environmental Decoherence

A system prepared in an unstable quantum state generally decays following an exponential law, as environmental decoherence is expected to prevent the decay products from recombining to reconstruct the initial state. Here we show the existence of deviations from exponential decay in open quantum systems under very general conditions. Our results are illustrated with the exact dynamics under quantum Brownian motion and suggest an explanation of recent experimental observations.

Figure 1

Decay of the survival probability under quantum Brownian motion. The change in the power law governing the survival probability of a pure initial Gaussian state (solid line) is shown in a log-log scale as a function of time in units of the decoherence time. The long-time asymptotic expressions for $t\gg {\tau }_D$ in the two distinct regimes $\gamma t\ll 1$ (dotted-dashed line) and $\gamma t\gg 1$ (dashed line) are also shown, with $\gamma ={10}^{-3}$ and $D{\sigma }^2=100$, with $\hslash /m{\sigma }^2$ as a unit of frequency.