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

TL;DR

This work demonstrates that invariant-based shortcuts to adiabaticity (STA), grounded in Lewis-Riesenfeld invariants and Lewis-Leach Hamiltonians, can generate robust, time-efficient trajectories for coherent single-atom transport in an adjustable family of two-dimensional optical lattices. By designing dynamical-lattice paths via ninth-degree polynomial controls in the x and y directions and evaluating the resulting dynamics with Fourier-split-operator method in the comoving frame, the authors quantify transport fidelity and robustness across square, triangular, honeycomb, dimerized, and checkerboard lattices. The study identifies the fundamental trade-off between transport speed and confinement in deep lattices, showing a breakdown at short times when accelerations exceed a lattice-dependent maximum, and demonstrates high fidelity in the adiabatic limit. The results have direct relevance for scalable neutral-atom quantum computing, including the implementation of fast, high-fidelity two-qubit gates, and provide a pathway toward experimental realization of STA-based transport in complex lattice geometries.

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.

Figures (8)

• Figure 1: Schematic of a setup that enables the adjustable optical-lattice formed from three folded retro-reflected beams. The direct digital synthesizer (DDS) is used to control the frequency change induced by the acousto-optic modulator (AOM), giving rise to the phase $\theta$. The half-wave plates (HWP) can be adjusted in their angular orientation to set the specific intensities wanted for the three laser beams. The red dot indicates the center of the optical-lattice potential.
• Figure 2: Density plots of the optical potential for the (a) square, (b) dimerized, (c) honeycomb, and (d) 1D-chains, optical lattices, obtainable by adjusting the different lattice depths present in the expression for $U_\mathrm{L}(x,y)$ [cf. Eq. \ref{['eqOptPot']}]. For each lattice structure, the corresponding unit cell is indicated by the dashed white line. The point $(x_0, y_0)=(0,0)$, around which the harmonic approximation of the full potential is developed, lies in the center od the unit cell.
• Figure 3: Adapted schematic of a setup that enables atom transport for the adjustable optical-lattice. The direct digital synthesizer (DDS) is used to control the frequency change induced by the acousto-optic modulator (AOM), giving rise to the dynamical-lattice velocity $v$. The red dot indicates the center of the optical-lattice potential.
• Figure 4: Path of a potential minimum as a function of time, obtained using the STA approach, for transport times $t_f$ comparable to (a), and an order of magnitude longer than (b) the internal timescale $T_\mathrm{x}$.
• Figure 5: Dependence of the atom-transport fidelity on the transport time $t_\mathrm{f}$ for different transport distances $d_x$ and potential depths using the STA scheme. The ratio of the lattice depths corresponds to that of a honeycomb lattice. Panels (a)-(c) show results for potential depths of $(U_X, U_{\overline{X}}, U_Y) = (200, 600, 200) E_R$, $(400, 1200, 400) E_R$, and $(800, 2400, 800) E_R$, respectively.