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Computer Modeling in Engineering & Sciences

Dynamics of Bloch Matter Waves and Its Breakdown : a Bose-Einstein Condensate in a Moving 1D Optical Lattice

C. Fort, Francesco S. Cataliotto, Jacopo Catani, L. De Sarlo, L. Fallani, Jessica Lye, Michele Modugno, Robert Saers, M. Inguscio

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

We present the results of experimental work on the dynamics of a Bose-Einstein condensate (BEC) loaded in a 1D moving optical lattice. The system is studied both in the regime of low atomic density (expanding BEC) and high atomic density (trapped BEC). In the low-density regime, the stable dynamics of the system is well-described in terms of Bloch waves. In the presence of nonlinearities, as in a high-density sample, the Bloch waves are not stable solutions of the Gross-Pitaevskii equation (GPE) and dynamical instability takes place.

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We present the results of experimental work on the dynamics of a Bose-Einstein condensate (BEC) loaded in a 1D moving optical lattice. The system is studied both in the regime of low atomic density (expanding BEC) and high atomic density (trapped BEC). In the low-density regime, the stable dynamics of the system is well-described in terms of Bloch waves. In the presence of nonlinearities, as in a high-density sample, the Bloch waves are not stable solutions of the Gross-Pitaevskii equation (GPE) and dynamical instability takes place.
We have experimentally studied the unstable dynamics of a harmonically trapped Bose-Einstein condensate loaded into a 1D moving optical lattice. The lifetime of the condensate in such a potential exhibits a dramatic dependence on the quasimomentum state. This is unambiguously attributed to the onset of dynamical instability, after a comparison with the predictions of the Gross-Pitaevskii theory. Deeply in the unstable region we observe the rapid appearance of complex structures in the atomic density profile, as a consequence of the condensate phase uniformity breakdown.
We report on the experimental characterization of energetic and dynamical instability, two mechanisms responsible for the breakdown of Bloch waves in a Bose-Einstein condensate interacting with a one-dimensional (1D) optical lattice. A clear separation of these two regimes is obtained by performing measurements at different temperatures of the atomic sample. The time scales of the two processes have been determined by measuring the losses induced in the condensate. A simple phenomenological model is introduced for energetic instability while a full comparison is made between the experiment and the 3D Gross-Pitaevskii theory that accounts for dynamical instability.
The physics of quantum particles in periodic potentials can be described in terms of Bloch waves and indeed many effects originally predicted for electrons moving in a lattice of ions have been observed for ultracold atoms in optical lattices. Interactions among the atoms forming the BEC are responsible for the nonlinear character of the Bloch waves, resulting in the onset of different kinds of instabilities, we have performed a detailed investigation of the stability regimes of a condensate in a moving optical lattice, separately addressing the effects and the timescales of energetic and dynamic instabilities. Spin-polarized Fermi gases are free from these effects and fundamental conduction phenomena, such as the crossover from a conducting to an insulating behaviour, the latter due to a localization of the particles in the lattice, can be observed
We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions.
By using a one-dimensional nonpolynomial nonlinear mean-field model, we numerically analyze the process of the loading of the Bose-Einstein condensate into a moving one-dimensional optical lattice. We demonstrate that the recently observed dynamical instability of the Bloch states of a repulsive condensate in a moving optical lattice can lead to formation of trains of spatially localized wave packets that can be associated with matter-wave gap solitons. We study the characteristic features of this matter-wave localization under realistic conditions by modeling the dynamics of the condensate beyond the onset of dynamical instability.
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.