Two - Level Atom - Field Interaction: Exact Master Equations for Non-Markovian Dynamics, Decoherence and Relaxation

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  • 30 January 1999
Abstract
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 backreaction 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, a cavity field, and for the field being in vacuum, coherent and thermal states. In response to the search for mechanisms to preserve maximal coherence in quantum computations in ion trap prototypes, we applied these equations to analyse the decoherence of a 2LA in an EMF. We found that decoherence time is equal to relaxation time and is independent of temperature. This is at variance to 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 it does while it serves as a bath on a quantum Brownian particle.

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