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
Critical fluctuations of an attractive Bose gas in a double well potential (no molecules here) Marek Trippenbach, with B. Malomed, P. Ziń, J. Chwedeńczuk,
Dec 22, 2015
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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 ONCOLD 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, 150405 (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, 200401 (2005)J. Chwedeńczuk et al., Phys. Rev. Lett. 97, 170404 (2006)P. Ziń, J. Chwedeńczuk and M. Trippenbach, Phys. Rev. A 73, 033602 (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 momentaopposite momenta
BEC in 1D double wellby Markus Oberhaler
Experiment: Double well structureMarkus Oberthaler, 2005
Oberthaler data
Why are we surprized:linear case
Linear case: tunneling only
Mean Field Approach
Mean Field Approach
Energy diagram
Phase Space Dynamics
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 welleffects of higher dimensions
Two channel potential
422** uuuuuuuiL yxzz
)()(
)(2exp)( 2
2
2
zirzibzW
rzAu
3
W
AW
2222222 2/22
WbAWWbWAL
Hysteresis
Two channel solitons
Gap solitons
Two channel potential + lattice
Two channel potentail + lattice
Experimental Proposal:Hysteresis
Wieslaw KrolikowskiPawel ZinJan Chwedenczuk
Experimental Proposal:Collisions
Nguen Viet HungPawel ZinCzesław Radzewicz
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