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arXiv:0903.5016 · Physical Review Letters

Pulsating and Persistent Vector Solitons in a Bose-Einstein Condensate in a Lattice upon Phase Separation Instability

Uttam Shrestha, Juha Javanainen, Janne Ruostekoski

Published Nov 6, 2009• 24 citations
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Abstract

We study numerically the outcome of the phase separation instability of a dual-species Bose-Einstein condensate in an optical lattice. When only one excitation mode is unstable a bound pair of bright and dark solitonlike structures periodically appears and disappears, whereas for more than one unstable mode a persistent soliton-antisoliton pair develops. The oscillating soliton represents a regime where the two-species condensate neither remains phase-separated nor is dynamically stable.

DOI
10.1103/physrevlett.103.190401

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We study numerically the outcome of the phase separation instability of a dual-species Bose-Einstein condensate in an optical lattice. When only one excitation mode is unstable a bound pair of bright and dark solitonlike structures periodically appears and disappears, whereas for more than one unstable mode a persistent soliton-antisoliton pair develops. The oscillating soliton represents a regime where the two-species condensate neither remains phase-separated nor is dynamically stable.
Bose-Einstein condensates (BECs) in an optical lattice driven out of equilibrium and the subsequent dynamics are investigated in the limit of weak atom-atom interactions both within the classical mean-field approximation and by incorporating an approximate model for quantum fluctuations. A prediction of pulsating dynamical instability in which atoms periodically collect together and subsequently disperse back into the initial homogeneous state is made. This instability is a unique feature of this Hamiltonian system characterized by a single unstable mode and can be considered as a remnant of the integrability of the non-integrable system. A phase-space model has been employed to incorporate the quantum fluctuations within the truncated Wigner approximation. It is observed that the quasiperiodic behavior of the pulsating dynamics persists in the individual stochastic realizations that represent the typical experimental outcomes, but the effect of quantum fluctuations is manifested in the ensemble averages of various properties of the system. Quantum effects are increasingly prominent and the revivals of the ensemble averages of the wave function become progressively weaker when the effective interaction strength is increased. Motivated by these predictions, we apply similar methods to two-component BECs. Within the mean-field model we demonstrate a spontaneous emergence of a vector soliton like structure, a bound pair of a soliton and an anti-soliton, from the homogeneous imbalanced mixture of two BEC species. This is a feature that uniquely combines phase separation, pulsating instability, and formation of a dark-bright soliton pair when the parameters involved are tuned properly. ^
The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.
We show that the presence of a soliton in a single-species condensate, at zero temperature, enhances the quantum depletion sufficiently enough to induce dynamical instability of the system. We also predict that for two-species condensates, two Goldstone modes emerge in the excitation spectrum at phase separation. Of these, one is due to the presence of the soliton. We use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution, and demonstrate that when the anomalous mode collides with a higher energy mode it renders the solitonic state oscillatory unstable. We also report a soliton-induced change in the topology of the density profiles of the two-species condensates at phase separation.
The dynamics of a bright—bright vector soliton in cigar-shaped Bose—Einstein condensate trapping in a harmonic potential is studied. The interaction between bright solitons in different species with small separation is derived. Unlike the interaction between solitons of the same species, it is independent of the phase difference between the solitons, and may be of attraction or repulsion. In the former case, each soliton will oscillate about and pass through each other around the mass center of the system, which will also oscillate harmonically due to harmonic trapping potential.