Non-Markovian dynamics and entanglement of two-level atoms in a common field

Abstract

We derive the stochastic equations and consider the non-Markovian dynamics of\na system of multiple two-level atoms in a common quantum field. We make only\nthe dipole approximation for the atoms and assume weak atom-field interactions.\nFrom these assumptions we use a combination of non-secular open- and\nclosed-system perturbation theory, and we abstain from any additional\napproximation schemes. These more accurate solutions are necessary to explore\nseveral regimes: in particular, near-resonance dynamics and low-temperature\nbehavior. In detuned atomic systems, small variations in the system energy\nlevels engender timescales which, in general, cannot be safely ignored, as\nwould be the case in the rotating-wave approximation (RWA). More problematic\nare the second-order solutions, which, as has been recently pointed out, cannot\nbe accurately calculated using any second-order perturbative master equation,\nwhether RWA, Born-Markov, Redfield, etc.. This latter problem, which applies to\nall perturbative open-system master equations, has a profound effect upon\ncalculation of entanglement at low temperatures. We find that even at zero\ntemperature all initial states will undergo finite-time disentanglement\n(sometimes termed "sudden death"), in contrast to previous work. We also use\nour solution, without invoking RWA, to characterize the necessary conditions\nfor Dickie subradiance at finite temperature. We find that the subradiant\nstates fall into two categories at finite temperature: one that is temperature\nindependent and one that acquires temperature dependence. With the RWA there is\nno temperature dependence in any case.\n