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Journal of Modern Optics

Entanglement in two-site Bose–Hubbard model with non-linear dissipation

K. V. S. Shiv Chaitanya, Sibasish Ghosh A, Venkatraman Srinivasan

Published Jul 16, 2014• 5 citations
Publisher

Abstract

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.

DOI
10.1080/09500340.2014.936917

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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.
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 ttt 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 study the effect of decoherence on dynamical phase diffusion in the two-site Bose-Hubbard model. Starting with an odd parity excited coherent state, the initial loss of single-particle coherence varies from small bound oscillations in the Rabi regime, through hyperbolic depletion in the Josephson regime, to a Gaussian decay in the Fock regime. The inclusion of local-site noise, measuring the relative number difference between the modes, is shown to enhance phase diffusion. In comparison, site-indiscriminate noise measuring the population imbalance between the two quasimomentum modes slows down the loss of single-particle coherence. Decoherence thus either enhances or suppresses phase diffusion, depending on the details of system-bath coupling and the overlap of decoherence pointer states with collisional-entanglement pointer states. The deceleration of phase diffusion due to the coupling with the environment may be viewed as a many-body quantum Zeno effect. The extended effective decay times in the presence of projective measurement are further enhanced with increasing number of particles NNN by a bosonic factor of N\sqrt{N}N​ in the Fock regime and N/log NN/\text{log}\text{ }NN/log N in the Josephson regime.
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.
The time-dependent Hamiltonians are a very important portion in the modeling of real systems. In fact, the dynamic description of an entangled quantum systems is reflected in full coherence with the resolution of a wave function, solution of the Schrödinger equation throughout the entire study path. In this regard, we specify in this paper the system of two-site Bose-Hubbard model that obeys tunnel behavior, as two coupled harmonic oscillators, to examine quantum entanglement. The dynamics of such a system is described by the Schrödinger equation have introduced to the solution, the non-linear Ermakov equations as well as through a passage to the Heisenberg picture approach and the general Lewis and Riesenfeld invariant method compute between coupled harmonic oscillators and the coupled Caldirola Kanai oscillators. We prove that a time exponential increase in the mass of the system brings back to an exponential increase of entanglement and the Heisenberg picture approach is the most stable method to quantum entanglement because, this last has reached very large values. Also, we specify a cyclic time evolution, we find analytically the nonadiabatic Berry phases. In a particular case, such an entangled system acquired a nonadiabatic Berry phases that exhibits the same behavior as the Schmidt parameter.
We analyze the self-thermalization dynamics of the MMM-site Bose-Hubbard model in ring geometry using the single-particle density matrix calculated via the pseudoclassical approach. We show that a weak inter-particle interaction, which has a negligible effect on the thermal state given by the Bose-Einstein distribution, suffices to convert the integrable system of non-interacting bosons into a chaotic system. Next we consider two systems of weakly interacting bosons (i.e., two Bose-Hubbard systems) in different thermal states which are coupled by a point contact. We demonstrate that the chaotic nature of the Bose-Hubbard model ensures irreversible relaxation of both systems to global thermal equilibrium. Finally, substituting the point contact with a lattice of length L≪ML\ll ML≪M, we numerically calculate the quasi-stationary current of Bose particles across the lattice and show that its magnitude is consistent with the solution of the master equation for the boundary-driven LLL-site Bose-Hubbard system.