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

TL;DR

This paper develops enhanced shortcuts to adiabaticity (eSTA) methods for coherent atom transport in various two-dimensional optical lattices, improving speed and robustness over traditional STA techniques.

Contribution

It introduces an improved eSTA control scheme tailored for complex 2D optical lattices, enabling faster and more robust atom transport compared to standard STA methods.

Findings

eSTA outperforms STA in transport speed and robustness

Transport fidelity is higher with eSTA across various lattice parameters

eSTA effectively handles anharmonic trapping potentials

Abstract

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 Schr\"{o}dinger 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.