The Bose Hubbard model with squeezed dissipation

TL;DR

This paper studies the stationary behavior of the Bose-Hubbard model under squeezed dissipation, revealing how interactions destroy critical entanglement and lead to a thermal state characterized by an effective temperature.

Contribution

It introduces a detailed analysis of the Bose-Hubbard model with squeezed dissipation, showing the transition from critical entanglement to thermalization due to interactions.

Findings

No symmetry breaking occurs with squeezed dissipation.

Interactions destroy critical entanglement at the phase transition.

System approaches a thermal state with an effective temperature.

Abstract

The stationary properties of the Bose-Hubbard model under squeezed dissipation are investigated. The dissipative model does not possess a $U(1)$ symmetry, but parity is conserved: $\langle a_j \rangle \to -\langle a_j \rangle$. We find that $\langle a_j \rangle = 0$ always holds, so no symmetry breaking occurs. Without the onsite repulsion, the linear case is known to be critical. At the critical point the system freezes to an EPR state with infinite two mode entanglement. We show here that the correlations are rapidly destroyed whenever the repulsion is switched on. Then, the system approaches a thermal state with an effective temperature defined in terms of the squeezing parameter in the dissipators. We characterize this transition by means of a Gutzwiller {\it ansatz} and the Gaussian Hartree-Fock-Bogoliubov approximation.