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arXiv:0810.4199

Classical and quantum dynamics of pulsating instability in a Bose-Einstein condensate in an optical lattice

Uttam Shrestha

Published Oct 23, 2008• 0 citations
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Abstract

We study the dynamics of a Bose-Einstein condensate (BEC) in a one dimensional optical lattice in the limit of weak atom-atom interactions. Numerically we find that a BEC may develop a pulsating instability in which atoms nearly periodically collect themselves into a pulse and subsequently disperse back into the initial homogeneous state. A qualitative explanation of the quasi-periodic behavior is given by drawing an analogy with a double-well system. In an extension we introduce quantum effects approximately within Truncated Wigner Approximation (TWA). In pure classical mean field theory the condensate shows an undamped pulsating instability, whereas we have observed a damping in the oscillation when we average over many stochastic realizations.

DOI
10.48550/arxiv.0810.4199

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We study the dynamics of a Bose-Einstein condensate (BEC) in a one dimensional optical lattice in the limit of weak atom-atom interactions. Numerically we find that a BEC may develop a pulsating instability in which atoms nearly periodically collect themselves into a pulse and subsequently disperse back into the initial homogeneous state. A qualitative explanation of the quasi-periodic behavior is given by drawing an analogy with a double-well system. In an extension we introduce quantum effects approximately within Truncated Wigner Approximation (TWA). In pure classical mean field theory the condensate shows an undamped pulsating instability, whereas we have observed a damping in the oscillation when we average over many stochastic realizations.
We study quantum dynamics of a Bose-Einstein condensate in a one-dimensional optical lattice in the limit of weak atom-atom interactions within the truncated Wigner approximation for a system with one dynamically unstable mode. This extends previous classical studies of a pulsating dynamical instability in which atoms periodically collect together and subsequently disperse back into the initial homogeneous state. We observe that the quasiperiodic behavior still persists in the presence of quantum fluctuations for a single realization that represents a typical experimental outcome, but ensemble averages show various manifestations of quantum statistics. Quantum effects become more prominent when the effective interaction strength is increased.
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. ^
We study the Bloch dynamics of a quasi-one-dimensional Bose-Einstein condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian of Bose-Hubbard type. The corresponding mean-field system described by a discrete nonlinear Schr\"odinger equation can exhibit dynamical (or modulation) instability due to chaotic dynamics and equipartition over the quasimomentum modes. It is shown that these phenomena are related to Bogoliubov's depletion of the Bose-Einstein condensate and a decoherence of the condensate in the many-particle description. Three types of dynamics are distinguished: (i) decaying oscillations in the region of dynamical instability and (ii) persisting Bloch oscillations or (iii) periodic decay and revivals in the region of stability.
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We study systematically the period-doubled Bloch states for a weakly interacting Bose–Einstein condensate in a one-dimensional optical lattice. This kind of state is of form ψ k = e ikx ϕ k ( x ) , where ϕ k ( x ) is of a period twice the optical lattice constant. Our numerical results show how these nonlinear period-doubled states grow out of linear period-doubled states at a quarter away from the Brillouin zone center as the repulsive interatomic interaction increases. This is corroborated by our analytical results. We find that all nonlinear period-doubled Bloch states have both Landau instability and dynamical instability .