Emergence of Unique Steady Edge States in Trapped Ultracold Atom Systems

Abstract

We show that, for a one - dimensional open quantum system of ultracold atoms trapped in an array of harmonic potentials that is weakly coupled to a background Bose - Einstein Condensate (BEC), a unique steady state emerges at either of the two edges of the array due to the combined effects of excitation via lasers of these ultracold atoms and decay back to their initial energy levels via emission of excitations into the BEC, acting as an excitation reservoir. We then demonstrate the existence of steady states of the master equation that describes the dynamics of this open quantum system with respect to the expectation value of the position of the harmonic potential containing these states, and show that these steady states occur at the edges of the array of harmonic potentials trapping these atoms. Using the open quantum system's master equation to evolve initial states of the system that are trapped in other harmonic potentials in the array numerically over time, we verify the analytic calculations demonstrating the existence of these steady states at the edge of the system, and further demonstrate that these steady states will emerge regardless of the number of atoms trapped in each of the harmonic potentials in the array. We note that the emergence of these edge states irrespective of the initial state of the system is similar to the non-Hermitian skin effect seen in other open quantum systems, and are of fundamental importance in quantum technological applications such as quantum transport and quantum batteries.