Presentations available in PDF format:

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Vortices in Superfluid Helium and Bose-Einstein Condensates (Sandy Fetter)

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Synthetic Gauge Fields in Bose-Einstein Condensates (Sandy Fetter)

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Quantum Kinetic Theory (Crispin Gardiner)

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Confined Spin-Orbit Coupled Electron Systems (Roland Winkler)

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Fragility of the Fractional Quantum Spin Hall Effect in Quantum Gases (Ulrich Zuelicke)

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Stirapping Atoms Through an Occupational Dark State (Murray Olsen)

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Calorimetry and Thermalisation of a Bose Gas (Maarten Hoogerland)

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Dynamics of solitonic vortices and Chladni solitons in confined quantum gases (Joachim Brand, Antonio Mateo)

Introductory Lecture

Synthetic Gauge Fields in Bose-Einstein Condensates

Sandy Fetter, Stanford University 

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I review the physics of two-component trapped spin-orbit coupled Bose Einstein condensates as created by the NIST group. Specifically, I focus on the dynamics of a vortex in such a two-component condensate.

I then consider synthetic gauge fields in optical lattices, dealing with three particular mechanisms: (1) time-dependent modulations (“shaken lattice”), (2) laser-assisted tunneling to create Harper-Hofstadter square two-dimensional lattice in an applied magnetic field with flux  1/2 per plaquette, and (3) synthetic dimensions involving internal atomic states. In each case, I explain the synthetic vector potential and the associated complex phase of a hopping amplitude in the tight-binding Hamiltonian.

Introductory Lecture

Vortices in Superfluid Helium and Bose-Einstein Condensates

Sandy Fetter, Stanford University 

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I review the basic physics of superfluid 4He, especially quantized vortices, and then describe dilute quantum gases, particularly Bose-Einstein condensates (BECs). The dynamical motion of an off-axis single vortex in a BEC provides a clear test of theoretical predictions; experiments confirm these ideas in considerable detail at the 5-10% level. I review various experiments that create and detect vortices in BECs.

With increasing external rotation of the condensate, the BEC has many vortices, typically arranged in a triangular lattice. If the vortices are well separated, a simple mean-field description suffices. For more rapid rotation, the vortex cores start to overlap, and a “lowest-Landau-level” picture becomes appropriate; it includes the local variation of the particle density.

For sufficiently rapid rotation, the system is predicted to undergo a quantum phase transition to a highly correlated state, similar to a bosonic analog of the Laughlin 1/3 state for the fractional quantum Hall state of an electron gas in a strong magnetic field. Such a correlated state would not have a condensate wave function and hence would not be superfluid. This transition has not yet been observed, but it would be highly interesting.