Entanglement and quantal coherence: Study of two limiting cases of rapid system-bath interactions
Nicole F. Bell, R. F. Sawyer, Raymond R. Volkas · Physical Review A · 2002
In this paper, 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 $\stackrel{\ensuremath{\rightarrow}}{Q}\ensuremath{\infty},$ where the interaction rate with the bath is much greater than all free oscillation rates for the system, is investigated. 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 $\stackrel{\ensuremath{\rightarrow}}{Q}\ensuremath{\infty}.$ 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.