Quench from Mott Insulator to Superfluid

TL;DR

This paper investigates the dynamics of the Bose-Hubbard model during a linear quench from a Mott insulator to a superfluid, revealing a universal -1/3 power law scaling of excitation energy across different dimensions and trapping conditions.

Contribution

It introduces a unified analysis of quench dynamics in the Bose-Hubbard model using the truncated Wigner approximation, highlighting a universal scaling law derived from an impulse-adiabatic crossover.

Findings

Excitation energy scales as the inverse third root of quench time.

Universal -1/3 power law applies across 1D, 2D, and 3D systems.

The scaling is explained by a Kibble-Zurek inspired impulse-adiabatic mechanism.

Abstract

We study a linear ramp of the nearest-neighbor tunneling rate in the Bose-Hubbard model driving the system from the Mott insulator state into the superfluid phase. We employ the truncated Wigner approximation to simulate linear quenches of a uniform system in 1,2, and 3 dimensions, and in a harmonic trap in 3 dimensions. In all these setups the excitation energy decays like one over third root of the quench time. The -1/3 scaling arises from an impulse-adiabatic approximation - a variant of the Kibble-Zurek mechanism - describing a crossover from non-adiabatic to adiabatic evolution when the system begins to keep pace with the increasing tunneling rate.