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arXiv:cond-mat/0409475 · Physical Review A

Nonadiabatic dynamics of a Bose-Einstein condensate in an optical lattice

Lorenzo Isella, Janne Ruostekoski

Published Jul 12, 2005• 60 citations
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Abstract

We study the nonequilibrium dynamics of a Bose-Einstein condensate that is split in a harmonic trap by turning up a periodic optical lattice potential. We evaluate the dynamical evolution of the phase coherence along the lattice and the number fluctuations in individual lattice sites within the stochastic truncated Wigner approximation when several atoms occupy each site. We show that the saturation of the number squeezing at high lattice strengths, which was observed in recent experiments by Orzel et al. [Science 291, 2386 (2001)] can be explained by the nonadiabaticity of the splitting.

DOI
10.1103/physreva.72.011601

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We study the nonequilibrium dynamics of a Bose-Einstein condensate that is split in a harmonic trap by turning up a periodic optical lattice potential. We evaluate the dynamical evolution of the phase coherence along the lattice and the number fluctuations in individual lattice sites within the stochastic truncated Wigner approximation when several atoms occupy each site. We show that the saturation of the number squeezing at high lattice strengths, which was observed in recent experiments by Orzel et al. [Science 291, 2386 (2001)] can be explained by the nonadiabaticity of the splitting.
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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 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.
The dynamics of a Bose-Einstein condensate nonadiabatically loaded into a one-dimensional optical lattice is studied by analyzing the phase coherence between sites along the lattice as well as the radial profile of the condensate after a time-of flight. A simple model is proposed that predicts the short-time dephasing as a function of the condensate parameters. In the radial direction, heavily damped oscillations are observed, as well as an increase in the condensate temperature. These findings are interpreted as a rethermalization due to dissipation of the initial condensate excitations into high-lying modes.