Universality of Fragmentation in the Schr\"odinger Dynamics of Bosonic Josephson Junctions

TL;DR

This paper demonstrates that in a one-dimensional bosonic Josephson junction, the many-body fragmentation dynamics are universal across different particle numbers, and cannot be fully captured by mean-field approximations even at weak interactions.

Contribution

It reveals a universal fragmentation phenomenon in bosonic Josephson junctions and provides an analytical explanation based on the Bose-Hubbard model, challenging the validity of mean-field theory at long times.

Findings

Fragmentation reaches the same value for different particle numbers at constant interaction.

Universal behavior is observable in correlation functions.

Many-body effects dominate dynamics regardless of particle number or interaction strength.

Abstract

The many-body Schr\"odinger dynamics of a one-dimensional bosonic Josephson junction is investigated for up to ten thousand bosons and long times. The initial states are fully condensed and the interaction strength is weak. We report on a universal fragmentation dynamics on the many-body level: systems consisting of different numbers of particles fragment to the same value at constant mean-field interaction strength. The phenomenon manifests itself in observables such as the correlation functions of the system. We explain this universal fragmentation dynamics analytically based on the Bose-Hubbard model. We thereby show that the extent to which many-body effects become important at later times depends crucially on the initial state. Even for arbitrarily large particle numbers and arbitrarily weak interaction strength the dynamics is many-body in nature and the fragmentation universal. There is no weakly interacting limit where the Gross-Piatevskii mean-field is valid for long times.