Dynamics of the superfluid to Mott insulator transition in one dimension

TL;DR

This paper uses advanced numerical simulations to study the dynamics of the superfluid to Mott insulator transition in one-dimensional bosonic systems, comparing results with experiments and exploring the effects of different ramping speeds.

Contribution

It introduces a highly accurate simulation method for the Bose-Hubbard model and applies it to analyze the transition dynamics in large, experimentally relevant systems.

Findings

Superfluid buildup time matches single-atom hopping for slow ramps

Rapid ramps lead to faster superfluid formation than simple hopping models predict

Simulation results agree closely with experimental observations

Abstract

We numerically study the superfluid to Mott insulator transition for bosonic atoms in a one dimensional lattice by exploiting a recently developed simulation method for strongly correlated systems. We demonstrate this methods accuracy and applicability to Bose-Hubbard model calculations by comparison with exact results for small systems. By utilizing the efficient scaling of this algorithm we then concentrate on systems of comparable size to those studied in experiments and in the presence of a magnetic trap. We investigate spatial correlations and fluctuations of the ground state as well as the nature and speed at which the superfluid component is built up when dynamically melting a Mott insulating state by ramping down the lattice potential. This is performed for slow ramping, where we find that the superfluid builds up on a time scale consistent with single-atom hopping and for rapid ramping where the buildup is much faster than can be explained by this simple mechanism. Our calculations are in remarkable agreement with the experimental results obtained by Greiner et al. [Nature (London) 415, 39 (2002)].