Many-body dynamical localization in Fock space

TL;DR

This paper explores many-body dynamical localization in Fock space of a driven interacting bosonic system, revealing quantum suppression of transport akin to Anderson localization and its relation to time crystals.

Contribution

It introduces a mapping to the kicked-top model to analyze MBDL, characterizes localization length scaling, and connects MBDL to spectral statistics and discrete time crystals.

Findings

Quantum dynamics shows strong suppression of transport in Fock space.

Localization length scales with particle number and driving parameters.

Spectral statistics transition from random-matrix to Poisson as localization occurs.

Abstract

We investigate the emergence of many-body dynamical localization (MBDL) in the Fock space of an interacting two-mode bosonic system subject to periodic driving. Using a mapping to the paradigmatic kicked-top model, we analyze the interplay between classical chaotic diffusion and quantum interference effects. While the mean-field (classical) dynamics exhibits bounded ergodic diffusion along the population imbalance axis, the quantum dynamics reveals strong suppression of transport in Fock space, in close analogy with Anderson localization in disordered lattices. We characterize the localization length, its scaling with particle number and driving parameters, and reveal the spectral crossover from random-matrix to Poisson statistics as the many-body ensemble localizes. We highlight the connection between MBDL and discrete time crystals. Our findings offer a promising avenue to study the Anderson transition in Fock space.