Apker Award (2021): Coherent Dynamics and Quantum States of Ultracold Atoms in Lattices with Ring Topology*

We consider ultracold atoms trapped in a toroidal trap with an azimuthal lattice for utility as a macroscopic simulator of quantum optics phenomena [1]. We examine the dynamics induced by the adiabatic introduction of the lattice that serves to couple the normal modes, as an analog of a laser field coupling electronic states. The system is found to display two distinct behaviors, manifest in the angular momentum - coherent oscillation and self-trapping - reminiscent of non-linear dynamics, yet not requiring interatomic interactions. The choice is set by the interplay of discrete parameters, the specific initial mode and the periodicity of the lattice. However, rotation can cause continuous transition between the two regimes, causing periodic quenches and revivals in the oscillations as a function of the angular velocity. Curiously, the impact of rotation is determined entirely by the energy spectrum in the absence of the lattice, a feature that can be attributed to adiabaticity. We assess the effects of varying the lattice parameters, and consider applications in rotation sensing.

A stack of rings can be used to consturct a two-dimensional lattice with a cylindrical configuration.  In such a system, we include the presence of a gauge field and examine the impact of the ring topology on the spectrum and the quantum states, both of which are found to become gauge sensitive [2].

We will also briefly touch on a biophysics project associated with this award, where we develop a statistical model that explains the fractal-like structure in phenotypic patterns observed in the growth of bacterial biofilms [3].