Exact Decoherence to Pointer States in Free Open Quantum Systems is Universal

In this Letter it is shown that exact decoherence to minimal uncertainty Gaussian pointer states is generic for free quantum particles coupled to a heat bath. More specifically, the Letter is concerned with damped free particles linearly coupled under product initial conditions to a heat bath at arbitrary temperature, with arbitrary coupling strength and spectral densities covering the Ohmic, sub-Ohmic, and supra-Ohmic regime. Then it is true that there exists a time $t_c$ such that for times $t>t_c$ the state can always be exactly represented as a mixture (convex combination) of particular minimal uncertainty Gaussian states, regardless of and independent from the initial state. This exact “localization” is hence not a feature specific to high temperature and weak damping limit, but is a generic property of damped free particles.

Figure 1

This figure shows $\log T_c=\underset{T\to \infty }{lim}\log t_c$, where for a given temperature the number, $t_c>0$ is the smallest number such that (9) is satisfied for all $t>t_c$ for the case of strictly Ohmic damping, as a function of $\log \zeta$. The stronger the damping, the faster is the localization process.