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Journal of Physics B Atomic Molecular and Optical Physics

Probing the dynamics of Bose–Einstein condensates via boundary dissipation

Roberto Franzosi, Roberto Livi, Gian‐Luca Oppo

Published Mar 5, 2007• 25 citations
Publisher

Abstract

A model of a Bose-Einstein condensate in an optical lattice provided with dissipative boundary conditions is studied. We show how measurements on the emitted atoms can be exploited for determining the presence, nature and interaction of localized states inside the lattice. A travelling breather can, for example, determine presence and position of self-trapped stationary states through periodic bounces at the lossy boundaries. By measuring densities and phases of the emitted atoms, multi-breather states and breather interactions are characterized. © 2007 IOP Publishing Ltd.

DOI
10.1088/0953-4075/40/6/010

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A model of a Bose-Einstein condensate in an optical lattice provided with dissipative boundary conditions is studied. We show how measurements on the emitted atoms can be exploited for determining the presence, nature and interaction of localized states inside the lattice. A travelling breather can, for example, determine presence and position of self-trapped stationary states through periodic bounces at the lossy boundaries. By measuring densities and phases of the emitted atoms, multi-breather states and breather interactions are characterized. © 2007 IOP Publishing Ltd.
Discrete breathers, originally introduced in the context of biopolymers and coupled nonlinear oscillators, are also localized modes of excitation of Bose–Einstein condensates (BEC) in periodic potentials such as those generated by counter-propagating laser beams in an optical lattice. Static and dynamical properties of breather states are analysed in the discrete nonlinear Schrödinger equation that is derived in the limit of deep potential wells, tight-binding and the superfluid regime of the condensate. Static and mobile breathers can be formed by progressive re-shaping of initial Gaussian wave-packets or by transporting atomic density towards dissipative boundaries of the lattice. Static breathers generated via boundary dissipations are determined via a transfer-matrix approach and discussed in the two analytic limits of highly localized and very broad profiles. Mobile breathers that move across the lattice are well approximated by modified analytical expressions derived from integrable models with two independent parameters: the core-phase gradient and the peak amplitude. Finally, possible experimental realizations of discrete breathers in BEC in optical lattices are discussed in the presence of residual harmonic trapping and in interferometry configurations suitable to investigate discrete breathers' interactions.
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.
The properties of Bose-Einstein condensates (BEC) can be studied and controlled effectively when trapped in optical lattices. In the limit of tight binding, BEC in optical lattices are well described by the discrete nonlinear Schrödinger equation (DNLSE). Spatially localised modes of excitations, known as discrete breathers or lattice solitons, can occur in the DNLSE. These have been shown to evolve from initial conditions of Gaussian wave-packets. Using this method with the addition of an initial momentum, mobile breathers that travel across the lattice with a constant velocity can also be formed.
Bose-Einstein condensates of alkali atoms inside an optical lattice provide a unique opportunity to investigate such issues as coherent transport of matter, Josephson-type phenomena, and dissipation of superfluidity under highly controllable experimental conditions. We give a short review of theoretical progress in evaluating the collective excitations of a periodic condensate and the coherent transport of matter in different configurations, which has been based on an adaptation of the Wannier function representation of quasi-particle states in periodic potentials and on the use of advanced numerical methods for the solution of the Gross-Pitaevskii equation. We present various methods by which the band structure of the elementary excitations may be probed and show that in the superfluid regime the combination of a constant force and a harmonic force in the presence of the optical lattice drives Josephson-type oscillations of the condensate, leading to observable resonances and multimode behaviour. Finally, we discuss decoherence of the condensate and dissipation via sound wave emission above a local velocity threshold.