Enhanced shortcuts to adiabaticity for coherent atom transport in a family of two-dimensional dynamical optical lattices

In view of the compelling need for coherent atom transport as a prerequisite for a variety of emerging quantum technologies, we investigate such transport on the example of an adjustable family of two-dimensional optical lattices \[L. Tarruell {\em et al.}, Nature (London) {\bf 483}, 302 (2012)\] that includes square, honeycomb, dimerized, and 1D-chains lattices as its special cases; dynamical optical lattices of this type have already been utilized for the demonstration of topological pumping and the realization 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 counterpropagating 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 in the lattices under consideration using two classes of control schemes: (i) shortcuts to adiabaticity (STA) in the form of inverse engineering based on a dynamical invariant of Lewis-Riesenfeld type, and (ii) their modification, known as enhanced STA (eSTA), which is well-suited for the treatment of anharmonic trapping potentials. We then quantify the resulting atom dynamics using transport fidelities computed from the numerical solutions of the relevant time-dependent Schrödinger equations. By doing so for various choices of the system parameters and transport directions, we demonstrate that - except in the special case of the dimerized lattice - the eSTA method consistently outperforms its STA counterpart, both in terms of the achievable transport times and the robustness of the resulting transport against small variations of optical-lattice depths.