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arXiv:cond-mat/0206543 · Physical Review Letters

Creation of Solitons and Vortices by Bragg Reflection of Bose-Einstein Condensates in an Optical Lattice

R. G. Scott, A. Martin, T. M. Fromhold, Sylwia Bujkiewicz, F. W. Sheard, M. L. Leadbeater

Published Mar 21, 2003• 65 citations
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Abstract

We study the dynamics of Bose-Einstein condensates in an optical lattice and harmonic trap. The condensates are set in motion by displacing the trap and initially follow simple semiclassical paths, shaped by the lowest energy band. Above a critical displacement, the condensate undergoes Bragg reflection. For high atom densities, the first Bragg reflection generates a train of solitons and vortices, which destabilize the condensate and trigger explosive expansion. At lower densities, soliton and vortex formation requires multiple Bragg reflections, and damps the center-of-mass motion.

DOI
10.1103/physrevlett.90.110404

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We study the dynamics of Bose-Einstein condensates in an optical lattice and harmonic trap. The condensates are set in motion by displacing the trap and initially follow simple semiclassical paths, shaped by the lowest energy band. Above a critical displacement, the condensate undergoes Bragg reflection. For high atom densities, the first Bragg reflection generates a train of solitons and vortices, which destabilize the condensate and trigger explosive expansion. At lower densities, soliton and vortex formation requires multiple Bragg reflections, and damps the center-of-mass motion.
We present theoretical and experimental studies of the dynamics of Bose-Einstein condensates in a one-dimensional optical lattice and a three-dimensional harmonic trap. For low atom densities and inertial forces, the condensate performs regular Bloch oscillations, and its center-of-mass motion closely follows semiclassical single-particle trajectories, shaped by the lowest-energy band. But in other regimes, the center-of-mass motion disrupts the internal structure of the condensate by generating solitons and vortex rings, which can trigger explosive expansion of the atom cloud. We use images of the atom cloud to provide experimental evidence for this internal disruption, and find that the process occurs most readily in high-density condensates undergoing slow Bloch oscillations.
We investigate the effect of solitons and vortices, with a range of different topologies, on the dynamics of Bose-Einstein condensates in a one-dimensional optical lattice and a three-dimensional harmonic trap. The solitons and vortices are imposed on the initial state of the atom cloud, which is set in oscillatory motion by a sudden displacement of the harmonic trap. We study this motion using both quantum-mechanical calculations, based on the nonlinear Schr\"odinger equation, and a semiclassical model for transport through the lowest energy band of the optical lattice. We demonstrate that the geometry of the vortices and solitons in the initial state plays a crucial role in the evolution of the atom cloud. In particular, we find that the center-of-mass motion of a condensate containing a vortex is only weakly damped if the vortex core lies parallel to the optical lattice direction, but is strongly damped when the core is orientated perpendicular to the lattice direction. Severe damping is observed for a condensate containing a soliton whose nodal plane is perpendicular to the optical lattice.
This thesis describes the behaviour of cold atoms in optical lattices. In particular, it explores how transport through the energy bands of the optical lattice can be used to study quantum chaos and Bose-Einstein condensation.\n\nFirstly, this study examines the dynamics of ultra-cold sodium atoms in a one-dimensional optical lattice and a three-dimensional harmonic trap, using both semi-classical and quantum-mechanical analyses. The atoms show mixed stable-chaotic classical dynamics, which originate from the intrinsically quantum-mechanical nature of the energy band. \nThe quantised energy levels exhibit Gutzwiller fluctuations, and the wavefunctions are scarred by an unstable periodic orbit. Distinct types of wavefunction are identified and related directly to particular parts of the classical phase space via a Wigner function analysis.\n\nSecondly, this report studies the dynamics of a rubidium Bose-Einstein condensate in a one-dimensional optical lattice and three-dimensional harmonic trap. The condensates are set in motion by displacing the trap and initially follow simple semi-classical paths, shaped by the lowest energy band. Above a critical displacement, the condensate undergoes Bragg reflection, and performs Bloch oscillations. After multiple Bragg reflections, solitons and vortices form which damp the centre-of-mass motion.\n\nFinally, the dynamics of Bose-Einstein condensates in optical lattices are investigated for different parameter regimes, as realised in recent experiments. The results reveal how the experiments can be understood, and identify regimes in which vortices trigger explosive expansion of the condensate.
We experimentally realize an atom cavity consisting of a magnetic trap and an optical lattice that extends over the whole trap. When displaced sufficiently from the center of the magnetic trap, dynamics of the atoms are characterized by magnetic confinement on one side of the cavity and Bragg reflection due to the optical lattice on the other side. We demonstrate this atom cavity by recording the momentum-space oscillation of a Bose-Einstein condensate inside the cavity as a function of time. This atom-cavity configuration presents the possibility of realizing a Mach-Zehnder-type atom interferometer.