Numerical model for atomtronic circuit analysis

TL;DR

This paper introduces a numerical model for analyzing atomtronic circuits using finite temperature Bose-condensed gases, enabling studies of dynamics and steady states in complex configurations.

Contribution

It presents a novel computational approach combining Bose-Hubbard Hamiltonian and cluster expansion for atomtronic device simulation.

Findings

Demonstrated phase-locking in a double-well potential

Enabled analysis of both rapid and long-term dynamics

Validated the model with atom injection and extraction scenarios

Abstract

A model for studying atomtronic devices and circuits based on finite temperature Bose-condensed gases is presented. The approach involves numerically solving equations of motion for atomic populations and coherences, derived using the Bose-Hubbard Hamiltonian and the Heisenberg picture. The resulting cluster expansion is truncated at a level giving balance between physics rigor and numerical demand mitigation. This approach allows parametric studies involving time scales that cover both the rapid population dynamics relevant to non-equilibrium state evolution, as well as the much longer time durations typical for reaching steady-state device operation. The model is demonstrated by studying the evolution of a Bose-condensed gas in the presence of atom injection and extraction in a double-well potential. In this configuration phase-locking between condensates in each well of the potential is readily observed, and its influence on the evolution of the system is studied.