Numerical studies of a Matter-Wave Open Quantum System

In a recent experiment \footnote{L. Krinner, arxiv 1712.07791}, we implement a model for an open quantum system consisting of an array of Weisskopf-Wigner type emitters (``artificial atoms'') realized with ultracold atoms in an optical lattice geometry \footnote{I. de Vega et. al, Phys. Rev. Lett. \textbf{101}, 260404, 2008}. Each emitter can spontaneously emit matter waves, with fully tunable decay strength and excited state energy. In a recent theoretical analysis \footnote{M. Stewart et. al, Phys. Rev. A \textbf{95}, 013626, 2017}, we studied a single site coupled to a one-dimensional waveguide and analyzed the transition from Markovian to non-Markovian dynamics including the formation of a bound state. In the experiment, we found strong qualitative deviations of the data compared to the single site analytical treatment. We present numerical studies on the effect of neighboring ground-state emitters, which suggest that the observed differences can be explained in terms of resonant re-absorption of emitted matter waves, such as tunneling and diffusion. We also propose schemes for direct characterization of transport properties in the lattice.