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Photonic Crystals for Matter Waves: BEC in Optical Lattices

Photonic Crystals for Matter Waves: BEC in Optical Lattices. Elena Ostrovskaya and Yuri Kivshar. Nonlinear Physics Group, Australian Research Council Centre of Excellence for Quantum-Atom Optics, Australian National University. http://wwwrsphysse.anu.edu.au/nonlinear. Vortices in BEC.

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Photonic Crystals for Matter Waves: BEC in Optical Lattices

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  1. Photonic Crystals for Matter Waves: BEC in Optical Lattices Elena Ostrovskaya and Yuri Kivshar Nonlinear Physics Group, Australian Research Council Centre of Excellence for Quantum-Atom Optics, Australian National University http://wwwrsphysse.anu.edu.au/nonlinear

  2. Vortices in BEC 2m phase change Vortices exist in a harmonic trap in the presence of repulsive atom-atom interactions Density Vortices described by GP equation

  3. Two-dimensional optical lattice What is the effect of periodicity on the condensate?

  4. (k)  X M 2D band-gap structure Stationary states: Bloch states:

  5. Gap solitons • Nonlinearity allows energy transmission in the linear bandgap in the form of gap solitons • Envelope of gap soliton is described in terms of Bloch states near the lower band edge • Critical power for self-focusing of the envelope (Townes) soliton in 2D (1960s), • Strongly localized in the gap

  6. (k)  X M Imprinting a phase: BEC vortex in-band Bloch vortex at k=0: Bloch vortex at k=kM:

  7. Discrete Vortices • A vortex which has discrete steps in its phase profile • Approximated by coupled gap solitons • Energy flow in the system determined by the phase and coupling between lobes 0

  8. Vortices in the gap (a) (b) (c) (a) Off-site vortex (b) On-site vortex (c) Wide off-site vortex

  9. Evolution of gap vortices: robust Off-site vortex with initial perturbation ~ 5% of the wavefunction density On-site vortex displays similar dynamics t=0 t=2 ms t=4 ms t=6 ms

  10. Evolution of gap vortices: unstable Off-site wide vortex with initial perturbation ~ 5% of the wavefunction density t=0 t=2 ms t=4 ms

  11. Evolution of wide gap vortices On-site wide vortex with initial perturbation ~ 5% of the wavefunction density t=2 ms t=4 ms t=6 ms

  12. Further directions • Gap vortices may also exist in robust states with • reduced symmetry, including: • Rhomboidal vortices • Triangular vortices Existence depends on coupling between the “lobes”

  13. Summary • In-band vortices exist with Bloch wave tails • Localised vortices with a discrete phase profile may exist in the gap • Energy flow between the lobes is determined by the phase and coupling of the lobes • Demonstrated the existence of both robust and unstable discrete vortex solitons • Showed the existence of reduced-symmetry vortices.

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