Thermalisation in a Bose-Hubbard dimer with modulated tunneling

TL;DR

This paper investigates how a modulated Bose-Hubbard dimer exhibits quantum thermalisation and chaos, linking out-of-time-order correlators, Lyapunov exponents, and mode delocalisation measures.

Contribution

It establishes a connection between quantum thermalisation, chaos indicators, and classical dynamics in a Floquet Bose-Hubbard dimer.

Findings

FOTOCs grow exponentially indicating chaos

Quantum Lyapunov exponent correlates with mode delocalisation

System thermalises to a periodic Gibbs ensemble

Abstract

The periodically modulated Bose-Hubbard dimer model offers an experimentally realizable and highly tunable platform for observing the scrambling of quantum information and the apparent thermalisation of isolated, interacting quantum many-body systems. In this work we apply fidelity out-of-time-order correlators to establish connections between thermalisation in Floquet system, the exponential growth of FOTOCs as quantified by a non-zero quantum Lyapunov exponent, and the underlying classical transition from regular to chaotic dynamics in the dimer. Moreover, we demonstrate that a non-zero quantum Lyapunov exponent can also be inferred from measures quantifying the delocalisation of the Floquet modes of the system such as the Shannon entropy, which approaches unity if the system thermalises to the periodic Gibbs ensemble prediction.