Sieve of Eratosthenes for Bose-Einstein Condensates in Optical Moir\'e Lattices

TL;DR

This paper introduces a novel method for creating and tuning optical moiré lattices for Bose-Einstein condensates using a geometric sieve approach, enabling control over lattice periodicity and translation without altering laser wavelength.

Contribution

It presents a new geometric analog of the sieve of Eratosthenes for designing optical lattices with tunable periodicity and phase, advancing control of Bose-Einstein condensates in complex lattice structures.

Findings

Cataloged known optical moiré lattices.

Demonstrated tunable lattice periodicity without changing laser wavelength.

Showed ability to spatially translate lattices via structured phase.

Abstract

We catalog known optical moir\'e lattices and uncover exotic lattice configurations following a geometric analog of the ancient sieve of Eratosthenes algorithm for finding prime numbers. Rich dynamics of Bose-Einstein condensates loaded into these optical lattices is revealed from numerical simulations of time-of-flight interference patterns. What sets this method apart is the ability to tune the periodicity of the optical lattices without changing the wavelength of the laser, yet maintaining the local potential at the individual lattices sites. In addition, we discuss the ability to spatially translate the optical lattice through applying a structured phase only.