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The Bose–Hubbard model with squeezed dissipation

Fernando Quijandira (16224236), Uta Naether, Diego Porras, Juan José García‐Ripoll, David Zueco

Published Jan 30, 2015• 3 citations
OpenAlex

Abstract

The stationary properties of the Bose–Hubbard model under squeezed dissipation are investigated. The dissipative model does not possess aU (1) symmetry but conserves parity. We find that 〈a j 〉 = 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. As we increase the latter, 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 ansatz and the Gaussian Hartree–Fock–Bogoliubov approximation.

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The stationary properties of the Bose–Hubbard model under squeezed dissipation are investigated. The dissipative model does not possess aU (1) symmetry but conserves parity. We find that 〈a j 〉 = 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. As we increase the latter, 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 ansatz and the Gaussian Hartree–Fock–Bogoliubov approximation.
Abstract The stationary properties of the Bose–Hubbard model under squeezed dissipation are investigated. The dissipative model does not possess a symmetry but conserves parity. We find that 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. As we increase the latter, 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 ansatz and the Gaussian Hartree–Fock–Bogoliubov approximation.
We examine theoretically the driven-dissipative Bose-Hubbard dimer in the optical bistable regime. Various approximation schemes based on a Gutzwiller mean-field decoupling are applied and compared. Depending on the system parameters, we show that a decoupling with respect to the real space or to the reciprocal space can be more accurate. The Gutzwiller decoupling is applied both at the level of the density matrix and for the wave function during a quantum trajectory simulation. The latter is shown to be a more accurate approximation. A Gaussian approximation for the nonhomogeneous antibonding mode is also explored. We also show that entanglement in this system is witnessed by squeezing in reciprocal space.
In this paper, we study the decoherence and entanglement properties for the two-site Bose–Hubbard model in the presence of a non-linear damping. We apply the techniques of thermo field dynamics and then use Hartree-Fock approximation to solve the corresponding master equation. The expectation values of the approximated field operators appearing in the solution of master equation are computed self-consistently. We solve this master equation for a small time t so that we get the analytical solution, thereby we compute the decoherence and entanglement properties of the solution of the two-mode bosonic system. We have found that for a small initial time t, the entanglement of the system increases but at the same time the system decoheres exponentially.
We theoretically explore the quantum correlation properties of a dissipative Bose-Hubbard dimer in the presence of a coherent drive. In particular, we focus on the regime where the semiclassical theory predicts a bifurcation with a spontaneous spatial symmetry breaking. The critical behavior in a well-defined thermodynamical limit of large excitation numbers is considered and analyzed within a Gaussian approach. The case of a finite boson density is also examined by numerically integrating the Lindblad master equation for the density matrix. We predict the critical behavior around the bifurcation points accompanied by large quantum correlations of the mixed steady state, in particular, exhibiting a peak in the logarithmic entanglement negativity.
Motivated by recent experiments, we study the properties of large Bose-Hubbard chains with single-particle losses at one site using classical field methods. We construct and validate a compact effective model that reduces computations to only a few sites. We show that in the mean-field approach the description captures the stationary states of the dissipative mode very well. Not only is there good quantitative agreement in the hysteresis loop, but the dark soliton state can be reproduced as well due to the preservation of the U(1)\text{U}(1)U(1) symmetry. Bimodality of the steady states, observed on longer timescales, is studied using the truncated Wigner method. We compare the switching statistics and derive the effective Liouvillian gap as a function of the tunneling, showing that the effective description underestimates fluctuations.
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.