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Analytic model for elastic scattering losses from colliding condensates M. Trippenbach P. Zin, J. Chwedenczuk, A. Perez Physics Department, Warsaw University, Yehuda Band Chemistry Department, Ben Gurion University Outline Spontaneous & Stimulated – processes Examples from Quantum Optics Examples from BEC (elastic scattering) Stochastic Approach Benchmark – our simple quantum model to study properties of the scattered atoms Parametric down conversion * H aa a a Superradiance Bragg Scattering Elastic collisions Model - 1 2 ˆ p ˆ (r , t ) ˆ (r , t ) g d 3r ˆ (r , t ) ˆ (r , t ) ˆ (r , t ) ˆ (r , t ) H .c. Hˆ d 3r e e 2m ˆ (r , t ) (r , t ) (r , t ) ˆ (r , t ) Q Q e 2 ˆ p ˆ (r , t ) ˆ (r , t ) g d 3r ˆ (r , t ) ˆ (r , t ) (r , t ) (r , t ) H .c. Hˆ d r e e Q Q e 2m 3 e Model - 2 2 ˆ p ˆ (r , t ) ˆ (r , t ) g d 3r ˆ (r , t ) ˆ (r , t ) (r , t ) (r , t ) H .c. Hˆ d r e e Q Q e 2m 3 e 2 i Q t 1 Q (r , t ) exp iQx 2 3/ 2 3 2 R 2m 2 R N iQ 2t 1 Q (r , t )Q (r , t ) 3 / 2 3 exp 2 2 R m R N 2 Qt 2 2 y z x m 2 2 Qt 2 2 x y z m Model - 3 d ˆ 2 ˆ ˆ i e (r , t ) e (r , t ) 2 gQ (r , t ) Q (r , t )e (r , t ) dt 2m iQ 2t 1 Q (r , t )Q (r , t ) 3 / 2 3 exp 2 2 R m R N e (r , t ) R n ,l n ,l , m 2 2 Qt 2 2 x y z m (r )Yl ,m ( , ) a (t ) n ,l ,m Summary We presented FULL quantum model (multimodel) to study how spontaneously initiated emission can get into stimulated mode Scattered atoms form a squeezed state that can be viewed as a multi-component condensate. Not only are we able to calculate the dynamics of mode occupation, but also the full statistics of scattered atoms. Test ground for other (stochastic) methods