Fast collisional $\sqrt{\mathrm{SWAP}}$ gate for fermionic atoms in an optical superlattice

TL;DR

This paper proposes a fast, high-fidelity $\,\sqrt{\mathrm{SWAP}}$ gate for fermionic atoms in optical superlattices, utilizing optimized control of lattice depths and transient collisions, significantly outperforming tunneling-based methods.

Contribution

It introduces a novel, optimized control protocol for a fast entangling gate in superlattices, surpassing previous tunneling-based approaches in speed and fidelity.

Findings

Gate operates in ~21 microseconds, over ten times faster than tunneling methods.

Achieves fidelities greater than 99%.

Simulation matches experimental dynamics and demonstrates robustness.

Abstract

Collisional gates in optical superlattices have recently achieved record fidelities, but their operation times are typically limited by tunneling. Here we propose and analyze an alternative route to a fast $\sqrt{\mathrm{SWAP}}$ gate for two fermionic atoms in an optical superlattice based on optimized, time-dependent control of the short and long lattice depths. The gate is implemented by transiently releasing the atoms into a quasi-harmonic confinement centered between the two sites. With an appropriately chosen contact interaction strength, a controlled collision accumulates the exchange phase required for $\sqrt{\mathrm{SWAP}}$ and generates entanglement. We employ a continuum, time-dependent Schr\"odinger-equation simulation that goes beyond a two-site Fermi--Hubbard description and benchmark it against experimentally implemented tunneling-based protocols, reproducing the observed single-particle tunneling and spin-exchange dynamics. For experimentally accessible lattice depths, we find that the proposed gate operates in $\sim 21\,\mu\mathrm{s}$, more than an order of magnitude faster than tunneling-based implementations, while achieving fidelities $\gtrsim 99\%$. We further analyze sensitivity to lattice-depth variations and show that a composite sequence improves robustness. Our results establish fast, collision-mediated entangling gates in superlattices as a promising building block for scalable neutral-atom quantum computation.