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arXiv:1203.3657 · Physical Review A

Beyond mean-field dynamics in open Bose-Hubbard chains

Dirk Witthaut, F. Trimborn, H. Hennig, G. Kordas, Theo Geisel, Sandro Wimberger

Published Jun 7, 2011• 113 citations
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Abstract

We investigate the effects of phase noise and particle loss on the dynamics of a Bose-Einstein condensate in an optical lattice. Starting from the many-body master equation, we discuss the applicability of generalized mean-field approximations in the presence of dissipation as well as methods to simulate quantum effects beyond mean field by including higher-order correlation functions. It is shown that localized particle dissipation leads to surprising dynamics, as it can suppress decay and restorethe coherence of a Bose-Einstein condensate. These effects can be applied to engineer coherent structures such as stable discrete breathers and dark solitons.

DOI
10.1103/physreva.83.063608

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We investigate the effects of phase noise and particle loss on the dynamics of a Bose-Einstein condensate in an optical lattice. Starting from the many-body master equation, we discuss the applicability of generalized mean-field approximations in the presence of dissipation as well as methods to simulate quantum effects beyond mean field by including higher-order correlation functions. It is shown that localized particle dissipation leads to surprising dynamics, as it can suppress decay and restorethe coherence of a Bose-Einstein condensate. These effects can be applied to engineer coherent structures such as stable discrete breathers and dark solitons.
We discuss the dynamics of an open two-mode Bose–Hubbard system subject to phase noise and particle dissipation. Starting from the full many-body dynamics described by a master equation the mean-field limit is derived resulting in an effective non-Hermitian (discrete) Gross–Pitaevskii equation which has been introduced only phenomenologically up to now. The familiar mean-field phase-space structure is substantially altered by the dissipation. In particular, the character of the fixed points shows an abrupt transition from elliptic or hyperbolic to attractive or repulsive, respectively. This reflects the metastable behaviour of the corresponding many-body system which surprisingly also leads to a significant increase of the purity of the condensate. A comparison of the mean-field approximation to simulations of the full master equation using the Monte Carlo wavefunction method shows an excellent agreement for wide parameter ranges.
The present thesis is devoted to the dynamics in open or closed many-body bosonic systems, with the use of beyond mean-field methods. In the first part, inspired by the state-of-the-art experiments, we study the dynamics of a Bose-Einstein condensation which is loaded in an optical lattice with localized loss channels for the atoms. We prove that the particular form of the dissipation can help us to control the many-body dynamics. The loss allows the local manipulation of the system’s coherence properties and creates attractive fixed points in the classical (mean-field) phase space. We predict the dynamical creation of stable nonlinear structures like discrete bright and dark solitons. Furthermore, for specific initial states, the systems produces highly entangled and long-living states, which are of high relevance for practical applications. The first part of this thesis ends with the study of non-equilibrium bosonic transport across optical one-dimensional lattices. In the second part, we present techniques for bosonic many-body systems which are based on path integrals. We analyze the Bose-Einstein condensation phenomenon by using tools from quantum information theory and field theory. Finally, we introduce a coherent state path integral formalism in the continuum, which allows us the systematic development of approximate methods for the study of bosons in optical lattices.
The present thesis is devoted to the dynamics in open or closed manybodybosonic systems, with the use of beyond mean-eld methods.In the rst part, inspired by the state-of-the-art experiments, we study thedynamics of a Bose-Einstein condensation which is loaded in an optical latticewith localized loss channels for the atoms. We prove that the particularform of the dissipation can help us to control the many-body dynamics. Theloss allows the local manipulation of the system's coherence properties andcreates attractive xed points in the classical (mean-eld) phase space. Wepredict the dynamical creation of stable nonlinear structures like discretebright and dark solitons. Furthermore, for specic initial states, the systemsproduces highly entangled and long-living states, which are of high relevancefor practical applications. The rst part of this thesis ends with the study ofnon-equilibrium bosonic transport across optical one-dimensional lattices.In the second part, we present techniques for bosonic many-body systemswhich are based on path integrals. We analyze the Bose-Einstein condensationphenomenon by using tools from quantum information theory and eldtheory. Finally, we introduce a coherent state path integral formalism inthe continuum, which allows us the systematic development of approximatemethods for the study of bosons in optical lattices.
We analyze the decay of ultracold atoms from an optical lattice with loss from a single lattice site. If the initial state is dynamically stable, a suitable amount of dissipation can stabilize a Bose-Einstein condensate, such that it remains coherent even in the presence of strong interactions. A transition between two dynamical phases is observed if the initial state is dynamically unstable. This transition is analyzed here in detail. For strong interactions, the system relaxes to an entangled quantum state with remarkable statistical properties: The atoms bunch in a few ``breathers'' forming at random positions. Breathers at different positions are coherent, such that they can be used in precision quantum interferometry and other applications.
Abstract Mean field and beyond mean field model calculations of Bose–Einstein condensates trapped in optical lattices have shown that initially homogeneous condensates can evolve into self-trapped, strongly localized states in the presence of weak boundary dissipation, a phenomenon called self-localization . A dynamical phase transition from extended to localized states can be observed when the effective nonlinearity exceeds a critical threshold Λ eff c . We investigate this phase transition to self-localization in the mean field approximation of the discrete nonlinear Schrödinger equation. We quantitatively characterize the properties of the discrete breathers , i.e. the nonlinear localized solutions, at the phase transition. This leads us to propose and numerically verify an analytical lower bound Λ eff L for the critical nonlinearity based on the idea of self-induced Anderson localization.
We discuss the dynamics of Bose-Einstein condensates in a double-well potential subject to decoherence (or particle loss). Starting from the full many-body dynamics described by the master equation, an effective Gross-Pitaevskii-like equation is derived in the mean-field approximation. By numerically solving the GP equation, we find that macroscopic quantum self-trapping disappears for strong decoherence, while generalized self-trapping occurs under weak decoherence. The fixed points have been calculated, and we find that an abrupt change from elliptic to an attractor and a repeller occurs, reflecting the metastable behavior of the system around these points.