The master equation for short- and long-time interaction intervals of single two-level atom with electromagnetic field vacuum for studying non-exponential emission is proposed. The exact non-stationary solution for the density matrix is obtained.
We perform a first-principles derivation of the general master equation to study the non-Markovian dynamics of a two-level atom (2LA) interacting with an electromagnetic field (EMF). We use the influence functional method, which can incorporate the full back reaction of the field on the atom, while adopting Grassmannian variables for the 2LA and the coherent-state representation for the EMF. We find exact master equations for the cases of a free quantum field and a cavity field in the vacuum. In response to the search for mechanisms to preserve maximal coherence in quantum computations in ion trap prototypes, we apply these equations to analyze the decoherence of a 2LA in an EMF, and find that decoherence time is close to relaxation time. This is at variance with the claims by authors who studied the same system but used a different coupling model. We explain the source of difference and argue that, contrary to common belief, the EMF, when resonantly coupled to an atom, does not decohere it as efficiently as a bath does on a quantum Brownian particle. The master equations for non-Markovian dynamics derived here are expected to be useful for exploring new regimes of 2LAEMF interaction, which is becoming physically important experimentally.
Exact solutions of the master equations which describe single-mode m-photon absorption and m-photon emission processes in a two-level atomic system are obtained using a density-matrix approach. Some aspects of the photon statistics, e.g., antibunching, are discussed.
The dissipative and decoherence properties of a two-level atom interacting with a squeezed vacuum field reservoir are investigated based on the nonautonomous master equation of the atomic density matrix in the framework of algebraic dynamics. The nonautonomous master equation is converted into a Schrödinger-like equation and its dynamical symmetry is found based on the left and right representations of the relevant algebra. The time-dependent solutions and the steady solutions are obtained analytically. The asymptotic behaviour of the solutions is examined and the approach to the equilibrium state is proved. Based on the analytic solution the response of the system to the squeezed vacuum field reservoir is studied numerically.
N two-level "atoms" are considered in interaction with a single-mode resonant electromagnetic field. The exact solution is given nonrelativistically for all times for the case of spontaneous emission, when only one atom is initially excited. The solution is given for the general case of the N atoms in inequivalent mode positions.