Analysis of non-Markovian coupling of a lattice-trapped atom to free space

TL;DR

This paper investigates the non-Markovian dynamics of an atom in an optical lattice coupled to free space, analyzing emission properties and evanescent states using a one-dimensional model.

Contribution

It provides a detailed analysis of non-Markovian effects in a lattice-trapped atom system, extending previous three-dimensional studies.

Findings

Identification of non-Markovian behavior in atom emission

Characterization of evanescent matter-wave states

Comparison of 1D and 3D emission dynamics

Abstract

Behavior analogous to that of spontaneous emission in photonic band gap materials has been predicted for an atom-optical system consisting of an atom confined in a well of a state-dependent optical lattice that is coupled to free space through an internal-state transition [de Vega et al., Phys. Rev. Lett. 101, 260404 (2008)]. Using the Weisskopf-Wigner approach and considering a one-dimensional geometry, we analyze the properties of this system in detail, including the evolution of the lattice-trapped population, the momentum distribution of emitted matter waves, and the detailed structure of an evanescent matter-wave state below the continuum boundary. We compare and contrast our findings for the transition from Markovian to non-Markovian behaviors to those previously obtained for three dimensions.