Entanglement and quantal coherence: a study of two limiting cases of rapid system--bath interactions

Abstract

We consider the dynamics of a system coupled to a thermal bath, going beyond the standard two-level system through the addition of an energy excitation degree of freedom. Further extensions are to systems containing many fermions, with the master equations modified to take Fermi-Dirac statistics into account, and to potentials with a time-dependent bias that induce resonant avoided crossing transitions. The limit $Q\to \infty$, where the interaction rate with the bath is much greater than all free oscillation rates for the system, is interrogated. Two behaviors are possible: freezing (quantum Zeno effect) or synchronization (motional narrowing). We clarify the conditions that give rise to each possibility, making an explicit connection with quantum measurement theory. We compare the evolution of quantal coherence for the two cases as a function of $Q$, noting that full coherence is restored as $Q\to \infty$. Using an extended master equation, the effect of system-bath interactions on entanglement in bipartite system states is computed. In particular, we show that the sychronization case sees bipartite system entanglement fully preserved in the large $Q$ limit.

Comments: 31 pages, 8 figures. This paper subsumes the material in quant-ph/0008133. The connection between synchronization and motional narrowing is explained. Extensive new material on entanglement, Fermi statistics, and adiabatic inversion has been added. Erroneous statement in section III corrected. Conclusions unchanged. This version accepted by Physical Review A