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