Finite-rate quenches of site bias in the Bose-Hubbard dimer

TL;DR

This paper investigates how finite-rate changes in site bias affect the energy and quantum self-trapping in a Bose-Hubbard dimer, bridging the gap between sudden and adiabatic quenches.

Contribution

It provides a detailed analysis of the excess energy and self-trapping behavior during finite-time quenches in the Bose-Hubbard dimer, extending understanding of non-equilibrium dynamics.

Findings

Excess energy depends on quench rate, interpolating between sudden and adiabatic limits.

Finite-rate quenches influence the persistence of quantum self-trapping.

Results relate to the Kibble-Zurek mechanism in a minimal model.

Abstract

For a Bose-Hubbard dimer, we study quenches of the site energy imbalance, taking a highly asymmetric Hamiltonian to a fully symmetric one. The ramp is carried out over a finite time that interpolates between the instantaneous and adiabatic limits. We provide results for the excess energy of the final state compared to the ground state energy of the final Hamiltonian, as a function of the quench rate. This excess energy serves as the analog of the defect density that is considered in the Kibble-Zurek picture of ramps across phase transitions. We also examine the fate of quantum `self-trapping' when the ramp is not instantaneous.