Symmetry between repulsive and attractive interactions in driven-dissipative Bose-Hubbard systems

Adil A Gangat,Ying-Jer Kao,Ian P Mcculloch

doi:10.1038/s41598-018-21845-5

Abstract

The driven-dissipative Bose-Hubbard model can be experimentally realized with either negative or positive onsite detunings, inter-site hopping energies, and onsite interaction energies. Here we use one-dimensional matrix product density operators to perform a fully quantum investigation of the dependence of the non-equilibrium steady states of this model on the signs of these parameters. Due to a symmetry in the Lindblad master equation, we find that simultaneously changing the sign of the interaction energies, hopping energies, and chemical potentials leaves the local boson number distribution and inter-site number correlations invariant, and the steady-state complex conjugated. This shows that all driven-dissipative phenomena of interacting bosons described by the Lindblad master equation, such as “fermionization” and “superbunching”, can equivalently occur with attractive or repulsive interactions.

Highlights

The non-equilibrium behaviour of Bose-Hubbard systems has received considerable theoretical attention recently[1,2,3,4,5,6,7,8]
In this work we point out a symmetry in the Lindbladian equation of motion for the driven-dissipative BHM (DDBHM) that implies that the driven-dissipative physics of repulsive interactions can be replicated with attractive interactions, irrespective of the magnitude of the interaction strength
We look at two cases: Case 1 examines the change in the non-equilibrium steady state (NESS) under the number-conserving transformation argued above; Case 2 examines the change in the NESS under a transformation that is different from the number-conserving transformation discussed in the previous section: the sign of J is kept fixed while the sign of U and Δ are changed

Summary

Introduction

The non-equilibrium behaviour of Bose-Hubbard systems has received considerable theoretical attention recently[1,2,3,4,5,6,7,8]. In superconducting circuits, which are a natural setting for studying the non-equilibrium physics of driven-dissipative many-body systems[9,10,11], strong interactions are more accessible with attractive interaction energies than with repulsive interaction energies[12,13]. We demonstrate that this observable symmetry persists even in the presence of strong disorder in all of the sign-flipped parameters This symmetry can be experimentally tested with existing superconducting circuit technology, which has the potential to realize the BHM such that the chemical potential, on-site interaction energy, and inter-site hopping energy are all tunable in situ (within a limited range) in both magnitude and sign[13,14,15]. Ωd, which plays the role of a chemical potential, is the site-dependent drive detuning when ωl is the bare frequency of the lth site and ωd is the drive frequency

Methods

Results

Conclusion