Shortcuts to adiabaticity for coherent atom transport in an adjustable family of two-dimensional optical lattices

Abstract: Motivated by the compelling need for coherent atom transport in a variety of emerging quantum technologies, we investigate such transport on the example of an adjustable family of two-dimensional optical lattices [L. Tarruell {\em et al.}, Nature (London) 483, 302 (2012)] that includes square, triangular, honeycomb, dimerized, and checkerboard lattices as its special cases; dynamical optical lattices of this type have already been utilized for the demonstration of topological pumping and the realiza- tion of two-qubit quantum gates with neutral atoms. At the outset, we propose the appropriate arrangements of acousto-optic modulators that give rise to a frequency imbalance between coun- terpropagating laser beams, thus leading to the dynamical-lattice effect in an arbitrary direction in the lattice plane. We subsequently obtain the dynamical-lattice trajectories that enable atom transport using shortcuts to adiabaticity (STA) in the form of inverse engineering based on a dy- namical invariant of Lewis-Riesenfeld type. We then quantify the resulting atom dynamics using the transport fidelity computed from the numerical solutions of the relevant time-dependent Schroedinger equation. We do so for various choices of the system parameters and transport directions, finding favorable results for the achievable transport times and robustness of the resulting transport to various experimental imperfections.