Phases and dynamics of ultracold bosons in a tilted optical lattice

TL;DR

This paper reviews the phases and dynamics of ultracold bosons in a tilted optical lattice, exploring equilibrium states, non-equilibrium protocols, Floquet theory, and connections to Rydberg atoms and spin models.

Contribution

It provides a comprehensive overview of the low-energy models, non-equilibrium dynamics, and novel phenomena like Hilbert space fragmentation in tilted bosonic systems.

Findings

Floquet Hamiltonian derived for periodic drive

Identification of dynamical freezing in spin models

Relation to Rydberg atom systems

Abstract

We present a brief overview of the phases and dynamics of ultracold bosons in an optical lattice in the presence of a tilt. We begin with a brief summary of the possible experimental setup for generating the tilt. This is followed by a discussion of the effective low-energy model for these systems and its equilibrium phases. We also chart the relation of this model to the recently studied system of ultracold Rydberg atoms. Next, we discuss the non-equilibrium dynamics of this model for quench, ramp and periodic protocols with emphasis on the periodic drive which can be understood in terms of an analytic, albeit perturbative, Floquet Hamiltonian derived using Floquet perturbation theory (FPT). Finally, taking cue from the Floquet Hamiltonian of the periodically driven tilted boson chain, we discuss a spin model which exhibits Hilbert space fragmentation and exact dynamical freezing for wide range of initial states.