Critical fluctuations of an attractive Bose gas in a double well potential (no molecules here) Marek Trippenbach, with B. Malomed, P. Ziń, J. Chwedeńczuk,

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Presentation transcript:

Critical fluctuations of an attractive Bose gas in a double well potential (no molecules here) Marek Trippenbach, with B. Malomed, P. Ziń, J. Chwedeńczuk, B. Oleś, K. Sacha, Ngien Viet Hung, M. Matuszewski, J. Gocałek EUROQUAM SATELLITE MEETING ON COLD AND ULTRACOLD MOLECULES

Plan Introducing CIGMA and BEC collisions BEC in double well Effects of higher dimensions Instability during collisions

Elastic collisions

BEC collision – the experiment A. Perrin et al. PRL 99, (2007) 2-nd order corelation

Theoretical model for collision Hamiltonian Bogoliubov approximation Condensate wave-function

Spontaneous versus Stimulated P. Ziń et al., Phys. Rev Lett. 94, (2005) J. Chwedeńczuk et al., Phys. Rev. Lett. 97, (2006) P. Ziń, J. Chwedeńczuk and M. Trippenbach, Phys. Rev. A 73, (2006)

Equations of motion the condensate: Gross-Pitaevskii Equation field of scattered atoms: time-dependent Bogoliubov approximation small 1st order perturbation theory

Theory versus experiment Close momenta opposite momenta

BEC in 1D double well by Markus Oberhaler

Experiment: Double well structure Markus Oberthaler, 2005

Oberthaler data

Why are we surprized: linear case

Linear case: tunneling only

Mean Field Approach

Energy diagram

Phase Space Dynamics

Dynamics

Two body interactions: Hamiltonian Introducing interactions Noninteracting particles … Localized states

Schrodinger Equation … and approximation

Continuum approximation Effective one dimensional equation

Effective potential

Fluctuations … can be done even in the repulsive case, if multicomponent

Wigner Function

BEC in double well effects of higher dimensions

Two channel potential

Hysteresis

Two channel solitons

Gap solitons

Two channel potential + lattice

Two channel potentail + lattice

Experimental Proposal: Hysteresis Wieslaw Krolikowski Pawel Zin Jan Chwedenczuk

Experimental Proposal: Collisions Nguen Viet Hung Pawel Zin Czesław Radzewicz