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Quantum phase transition and engineering in two-component BEC in optical lattices
In this paper we review recent progress in studying quantum phase transitions
in one- and two-component Bose-Einstein condensates (BEC) in optical lattices.
These phase transitions involve the emergence and disappearance of quantum
coherence over whole optical lattice and of linear superposition of macroscopic
quantum states. The latter may provide new means to engineer and to manipulate
novel macroscopic quantum states and novel coherent atomic beams for quantum
information processing, quantum computing etc.Comment: Format: LaTex2e. 7 pages, no figure. Talk at the Yang Symposium (in
honor of C.N. Yang's 80th birthday), Beijing, China, June 2002. To appear in
the Proceeding
Stable knots in the trapped Bose-Einstein condensates
The knot of spin texture is studied within the two-component Bose-Einstein
condensates which are described by the nonlinear Gross-Pitaevskii equations. We
start from the non-interacting equations including an axisymmetric harmonic
trap to obtain an exact solution, which exhibits a non-trivial topological
structure. The spin-texture is a knot with an integral Hopf invariant. The
stability of the knot is verified by numerically evolving the nonlinear
Gross-Pitaevskii equations along imaginary time.Comment: 4 pages, 5 figure
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