Dynamical localization of interacting bosons in the few-body limit

TL;DR

This paper demonstrates that in a few-body quantum kicked Lieb-Liniger model, two interacting bosons always exhibit dynamical localization with energy saturation, but their momentum distribution decays algebraically rather than exponentially, influenced by Tan's contact.

Contribution

It provides the first analysis of dynamical localization in a few-body interacting bosonic system beyond mean-field, showing persistent energy saturation and algebraic momentum decay.

Findings

Energy saturates at long times for any interaction strength.

Momentum distribution decays as 1/k^4, not exponentially.

Tan's contact remains finite at long times.

Abstract

The quantum kicked rotor is well-known to display dynamical localization in the non-interacting limit. In the interacting case, while the mean-field (Gross-Pitaevskii) approximation displays a destruction of dynamical localization, its fate remains debated beyond mean-field. Here we study the kicked Lieb-Liniger model in the few-body limit. We show that for any interaction strength, two kicked interacting bosons always dynamically localize, in the sense that the energy of the system saturates at long time. However, contrary to the non-interacting limit, the momentum distribution $\Pi(k)$ of the bosons is not exponentially localized, but decays as $\mathcal C/k^4$, as expected for interacting quantum particles, with Tan's contact $\mathcal C$ which remains finite at long time. We discuss how our results will impact the experimental study of kicked interacting bosons.