Analytic model for elastic scattering losses from colliding condensates M. Trippenbach P. Zin, J....

Analytic model for elastic scattering losses from colliding condensates

M. TrippenbachP. Zin, J. Chwedenczuk, A. Perez Physics Department, Warsaw University,Yehuda BandChemistry Department, Ben Gurion University

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

Outline

Parametric down conversion

aaaaH *

Superradiance

Bragg Scattering

Elastic collisions

Model - 1

..),(ˆ),(ˆ),(ˆ),(ˆ),(ˆ2

ˆ),(ˆˆ 3

23 cHtrtrtrtrrdgtr

m

ptrrdH ee

),(ˆ),(),(),(ˆ trtrtrtr eQQ

..),(),(),(ˆ),(ˆ),(ˆ2

ˆ),(ˆˆ 3

23 cHtrtrtrtrrdgtr

m

ptrrdH QQeeee

Model - 2

222

2

2

32/3 2

1

2exp

2),( zy

m

Qtx

Rm

tQiiQx

R

NtrQ

2222

2

2

32/3

1exp

2),(),(

m

Qtzyx

Rm

tQi

R

Ntrtr QQ

..),(),(),(ˆ),(ˆ),(ˆ2

ˆ),(ˆˆ 3

23 cHtrtrtrtrrdgtr

m

ptrrdH QQeeee

mlnmln

mllne taYrRtr ,,,,

,, )(),()(),(

),(ˆ),(),(2),(ˆ2

),(ˆ2

trtrtrgtrm

trdt

di eQQee

Model - 3

2222

2

2

32/3

1exp

2),(),(

m

Qtzyx

Rm

tQi

R

Ntrtr QQ

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