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Physical Review Letters

Delocalizing Transition of Bose-Einstein Condensates in Optical Lattices

G. Kalosakas, Kim Ø. Rasmussen, A. R. Bishop

Published Jun 28, 2002• 37 citations
Publisher

Abstract

A Bose-Einstein condensate trapped in a two-dimensional optical lattice exhibits an abrupt transition manifested by the macroscopic wave function changing character from spatially localized to extended. Resulting from a bifurcation, this irreversible transition takes place as the interwell potential barrier is adiabatically decreased below a critical value. This is in sharp contrast to the corresponding one-dimensional case where such a bifurcation is absent and the extent of a localized mode is continuously tunable. We demonstrate how these phenomena can be experimentally explored.

DOI
10.1103/physrevlett.89.030402

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A Bose-Einstein condensate trapped in a two-dimensional optical lattice exhibits an abrupt transition manifested by the macroscopic wave function changing character from spatially localized to extended. Resulting from a bifurcation, this irreversible transition takes place as the interwell potential barrier is adiabatically decreased below a critical value. This is in sharp contrast to the corresponding one-dimensional case where such a bifurcation is absent and the extent of a localized mode is continuously tunable. We demonstrate how these phenomena can be experimentally explored.
Critical behavior of solitonic wave forms of Bose-Einstein condensates in optical lattices (OL's) has been studied in the framework of the continuous mean-field equation. In two and three-dimensions OL's bright matter-wave solitons undergo abrupt delocalization as the strength of the OL is decreased below some critical value. A similar delocalizing transition happens when the coefficient of nonlinearity crosses the critical value. As opposed, bright solitons in one-dimensional OL's retain their integrity over the whole range of parameter variations. An interpretation of this phenomenon in terms of quantum bound states in the effective potential is proposed.
It is shown that bifurcation of the mean-field dynamics of a Bose-Einstein condensate can be related to the quantum phase transition of the original many-body system. As an example we explore the intraband tunneling in the two-dimensional optical lattice. Such a system allows for easy control by the lattice depth as well as for macroscopic visualization of the phase transition. The system manifests switching between two self-trapping states or from a self-trapping state to a superposition of the macroscopically populated self-trapping states with a steplike variation of the control parameter about the bifurcation point. We have also observed the magnification of the microscopic difference between the even and odd number of atoms to a macroscopically distinguishable dynamics of the system.
It is shown that inhomogeneous nonlinear interactions in a Bose-Einstein condensate loaded in an optical lattice can result in a delocalizing transition in one dimension, which sharply contrasts to the known behavior of discrete and periodic systems with homogeneous nonlinearity. The transition can be originated either by decreasing the amplitude of the linear periodic potential or by the change of the mean value of the periodic nonlinearity. The dynamics of the delocalizing transition is studied.
Bose–Einstein condensate (BEC) exhibits a variety of fascinating and unexpected macroscopic phenomena, and has attracted sustained attention in recent years—particularly in the field of solitons and associated nonlinear phenomena. Meanwhile, optical lattices have emerged as a versatile toolbox for understanding the properties and controlling the dynamics of BEC, among which the realization of bright gap solitons is an iconic result. However, the dark gap solitons are still experimentally unproven, and their properties in more than one dimension remain unknown. In light of this, we describe, numerically and theoretically, the formation and stability properties of gap-type dark localized modes in the context of ultracold atoms trapped in optical lattices. Two kinds of stable dark localized modes—gap solitons and soliton clusters—are predicted in both the one- and two-dimensional geometries. The vortical counterparts of both modes are also constructed in two dimensions. A unique feature is the existence of a nonlinear Bloch-wave background on which all above gap modes are situated. By employing linear-stability analysis and direct simulations, stability regions of the predicted modes are obtained. Our results offer the possibility of observing dark gap localized structures with cutting-edge techniques in ultracold atoms experiments and beyond, including in optics with photonic crystals and lattices.
We study management of localized modes in two-component (spinor) Bose–Einstein condensates embedded in optical lattices by means of changing interspecies interactions. By numerical integration of the coupled Gross–Pitaevskii equations, we find three different regimes of the delocalizing transition: (i) the partial delocalization when the chemical potential of one of the components collapses with a gap edge and the respective component transforms into a Bloch state, while the other component remains localized; (ii) the partial delocalization as a consequence of instability of one of the components; and (iii) the situation where a vector soliton reaches the limits of the existence domain. It is shown that there exists a critical value for the interspecies scattering length, below which solutions can be manipulated and above which one of the components is irreversibly destroyed.
We report experimental results on the dynamics and phase evolution of Bose-Einstein condensates in 1D optical lattices. The dynamical behaviour is studied by adiabatically loading the condensate into the lattice and subsequently switching off the magnetic trap. In this case, the condensate is free to expand inside the periodic structure of the optical lattice. The phase evolution of the condensate, on the other hand, can be studied by non-adiabatically switching on the periodic potential. We observe decays and revivals of the interference pattern after a time-of-flight.