Nonlinear quantum model for atomic Josephson junctions with one and two bosonic species

TL;DR

This paper develops an extended Bose-Hubbard model including nonlinear terms to accurately describe the dynamics of atomic Josephson junctions with one or two bosonic species, bridging microscopic quantum models and mean-field dynamics.

Contribution

It introduces a comprehensive EBH model with nonlinear terms for AJJs and demonstrates their importance in matching mean-field and quantum dynamics predictions.

Findings

Nonlinear terms are essential for accurate self-trapping predictions.

The model distinguishes Rabi, Josephson, and Fock regimes.

Good agreement between ODEs and GPEs is achieved with nonlinear terms.

Abstract

We study atomic Josephson junctions (AJJs) with one and two bosonic species confined by a double-well potential. Proceeding from the second quantized Hamiltonian, we show that it is possible to describe the zero-temperature AJJs microscopic dynamics by means of extended Bose-Hubbard (EBH) models, which include usually-neglected nonlinear terms. Within the mean-field approximation, the Heisenberg equations derived from such two-mode models provide a description of AJJs macroscopic dynamics in terms of ordinary differential equations (ODEs). We discuss the possibility to distinguish the Rabi, Josephson, and Fock regimes, in terms of the macroscopic parameters which appear in the EBH Hamiltonians and, then, in the ODEs. We compare the predictions for the relative populations of the Bose gases atoms in the two wells obtained from the numerical solutions of the two-mode ODEs, with those deriving from the direct numerical integration of the Gross-Pitaevskii equations (GPEs). Our investigations shows that the nonlinear terms of the ODEs are crucial to achieve a good agreement between ODEs and GPEs approaches, and in particular to give quantitative predictions of the self-trapping regime.