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

摘要

We perform a first- principles derivation of the general master equation tostudy the non-Markovian dynamics of a two-level atom (2LA) interacting with anelectromagnetic field (EMF). We use the influence functional method which canincorporate the full backreaction of the field on the atom, while adoptingGrassmannian variables for the 2LA and the coherent state representation forthe EMF. We find exact master equations for the cases of a free quantum fieldand a cavity field in the vacuum. In response to the search for mechanisms topreserve maximal coherence in quantum computations in ion trap prototypes, weapply these equations to analyse the decoherence of a 2LA in an EMF, and finethat decoherence time is close to relaxation time. This is at variance to theclaims by authors who studied the same system but used a different couplingmodel. We explain the source of difference and argue that, contrary to commonbelief, the EMF when resonantly coupled to an atom does not decohere it asefficiently as a bath does on a quantum Brownian particle. The master-equationsfor non-Markovian dynamics derived here is expected to be useful for exploringnew regimes of 2LA-EMF interaction, which is becoming physically importantexperimentally.