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Physical Review Letters

Self-Localization of Bose-Einstein Condensates in Optical Lattices via Boundary Dissipation

Roberto Livi, Roberto Franzosi, Gian‐Luca Oppo

Published Aug 8, 2006• 154 citations
Publisher

Abstract

We introduce a technique to obtain localization of Bose-Einstein condensates in optical lattices via boundary dissipations. Stationary and traveling localized states are generated by removing atoms at the optical lattice ends. Clear regimes of stretched-exponential decay for the number of atoms trapped in the lattice are identified. The phenomenon is universal and can also be observed in arrays of optical waveguides with mirrors at the system boundaries.

DOI
10.1103/physrevlett.97.060401

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We introduce a technique to obtain localization of Bose-Einstein condensates in optical lattices via boundary dissipations. Stationary and traveling localized states are generated by removing atoms at the optical lattice ends. Clear regimes of stretched-exponential decay for the number of atoms trapped in the lattice are identified. The phenomenon is universal and can also be observed in arrays of optical waveguides with mirrors at the system boundaries.
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.
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 self-trapping phenomenon of Bose-Einstein condensates (BECs) in optical lattices is studied by numerically solving the Gross-Pitaevskii equation. Our numerical results reproduce the self-trapping that was observed in a recent experiment [Anker et al., Phys. Rev. Lett. 94, 020403 (2005)]. However, we do not find that the appearance of the steep edges on the boundaries of the wave packet is the critical signal of the self-trapping. More importantly, we discover that the self-trapping breaks down at long evolution times; that is, the self-trapping in optical lattices is only temporary and has a lifetime. This temporariness is caused by the tunneling of atoms at the edge of the BEC wave packet towards outside wells. Our analysis shows that the phenomena observed numerically can all be understood by regarding the optical lattice as a train of double-well potentials.
We analyze the nature of self-localization (SL) of Bose-Einstein condensates in one-dimensional optical lattices in the presence of weak local dissipation. SL has recently been observed in several studies based on the discrete nonlinear Schr\"odinger equation (DNLS); however, its origin is hitherto an open question. We show that SL is based on a self-trapping crossover in the system. Furthermore, we establish that the origin of the crossover is the Peierls-Nabarro barrier, an energy threshold describing the stability of self-trapped states. Beyond the mean-field description the crossover becomes even sharper, which is also reflected by a sudden change of the coherence of the condensate. While we expect that the crossover can be readily studied in current experiments in deep optical lattices, our results allow for the preparation of robust and long-time coherent quantum states.
A model of a Bose-Einstein condensate in a ring optical lattice with atomic dissipations applied at a stationary or at a moving location on the ring is presented. The localized dissipation is shown to generate and stabilize both stationary and traveling lattice solitons. Among many localized solutions, we have generated spatially stationary quasiperiodic lattice solitons and a family of traveling lattice solitons with two intensity peaks per potential well with no counterpart in the discrete case. Collisions between traveling and stationary lattice solitons as well as between two traveling lattice solitons display a critical dependence from the lattice depth. Stable counterpropagating solitons in ring lattices can find applications in gyroscope interferometers with ultracold gases.