Synthesizing Lattice Structure in Phase Space

TL;DR

This paper explores the creation of lattice structures in phase space using ultracold atoms in driven optical lattices, revealing complex physics due to noncommutative geometry and artificial magnetic fields, and offering new experimental platforms.

Contribution

It introduces a method to synthesize phase space lattice structures in driven ultracold atom systems, highlighting their unique properties and potential for studying non-equilibrium phenomena.

Findings

Phase space lattice exhibits rich and complex band structures.

Artificial magnetic fields influence quasienergy bands significantly.

Thermal properties of phase space lattices are characterized.

Abstract

We consider a realistic model, i.e., ultracold atoms in a driven optical lattice, to realize phase space crystals [Phys. Rev. Lett. 111, 205303 (2013)]. The corresponding lattice structure in phase space is more complex and contains rich physics. A phase space lattice differs fundamentally from a lattice in real space, because its coordinate system, i.e., phase space, has a noncommutative geometry, which naturally provides an artificial gauge (magnetic) field. We study the behavior of the quasienergy band structure as function of the artificial magnetic field and investigate the thermal properties. Synthesizing lattice structures in phase space is not only a new way to create artificial lattice in experiments but also provides a platform to study the intriguing phenomena of driven systems far away from equilibrium.