A Gross-Pitaevskii-equation description of the momentum-state lattice: roles of the trap and many-body interactions

TL;DR

This paper presents a comprehensive 3D Gross-Pitaevskii equation model for synthetic momentum-state lattices, capturing trap effects and many-body interactions, providing insights into decoherence, self-trapping, and topological phase transitions.

Contribution

It introduces an exact GPE-based theoretical framework that surpasses tight-binding models in describing experimental momentum-state lattices, including inhomogeneous interactions and trap effects.

Findings

Trap modifies dispersion and density distribution, causing decoherence.

Shallow traps are preferable for long-term dynamics in weakly interacting regimes.

Mean-field interactions influence transport and topological phases.

Abstract

We report a theoretical description of the synthetic momentum-state lattices with a 3D Gross-Pitaevskii equation (GPE), where both the external trap potential and the mean-field spatial-density-dependent many-body interactions are naturally included and exactly treated. The GPE models exhibit better performance than the tight-binding model to depict the experimental observations. Since the trap modifies the dispersion relation for free particles and shapes the spatial density distribution that leads to inhomogeneous interactions, decoherences (damping oscillation) appear even for a short-time evolution. Our parametric calculations for the two-state oscillation suggest that we should work with a relatively shallow trap in the weakly interacting regime, especially when the long-term dynamics are concerned. The impact of the mean-field interaction, i.e., the self-trapping behavior, on the transport dynamics and the topological phase transition in a finite multiple-state lattice chain is also specifically investigated. Such an accurate treatment of the inhomogeneous interactions allows for further investigations on the interplay with disorder, the pair correlation dynamics, and the thermalization process in momentum space.