1. Quantum Theory of Collective Atomic Recoil in Ring Cavities
Università degli Studi di Milano
Dipartimento di Fisica via Celoria 16, Milano, Italy
PhD School in Physics, Astrophysics and Applied Physics
Quantum Theory of Collective Atomic Recoil in Ring Cavities
Marina Samoylova
Thesis advisor:
Dr. Nicola Piovella
16th October 2012
“Mini Workshop ”, Milano

2. Outline
The advantages of studying a Bose-Einstein Condensate (BEC) in a ring cavity
A possible experimental realization of such a system
The semi-classical and quantum models of the system
The numerical analysis of the exact solution
The summary of the results
Future doctoral research

3. Introduction Superradiant Rayleigh Scattering in free space (SRyS)
[ Collective Atomic Recoil Lasing in free space (CARL) ]
incident laser beam

4. Introduction SRyS in free space CARL in a ring cavity
Scattered photons can be recycled many times
Coherence time is enhanced
BEC + thermal clouds (100μK)
Scattered photons rapidly leave
the interaction region
Bose-Einstein Condensate (BEC) only

5. 2D CARL configuration X Z System: a BEC in a high-finesse ring cavity X Z
pump field Φ

6. Experimental setup Φ
A Bose-Einstein condensate is prepared in an Ioffe-Pritchard type magnetic trap in a high-finesse ring cavity (F=135000).
The BEC is illuminated by s-polarized pump light incident under the angle Φ=37˚. The pump beam is provided by a Ti:sapphire laser.
The condensate scatters the light superradiantly into two counter-propagating cavity modes.
The atomic momentum distribution is taken via absorption imaging.
A single-photon counter records the photons transmitted through one of the cavity mirrors.
[1] S. Bux, C. Gnahm, R. Maier, C. Zimmermann and Ph. Courteille, Phys. Rew. Lett. 106, (2011).
[2] S.Bux, H.Tomczyk, D.Schmidt, C.Zimmermann, N.Piovella, Ph.Courteille, New J. Phys., submitted (2012).

7. Results of the experiment
N=80000 is the number of atoms,
t= 200μs is the duration of the pump laser pulse
individual momentum state
At certain conditions only 4 momentum states can be populated

8. The semi-classical model
We are interested in a 4-level system
closed systems of equations !
In the semi-classical limit the four states configuration can be solved in terms
of two independent two-level systems for the left and right cavity modes.

9. The Quantum Model
The Hamiltonian of the system in the interaction picture:
where and are constants of motion representing the sum of excitations for the systems 1 and 2, respectively. t t
The general state of the system: , where
and

10. Numerical Results

11. Numerical Results
- atom-number squeezing parameter

12. Summary
we consider CARL-type dynamics
we investigate 4-level system
In the semi classical limit the four states configuration can be represented in terms of two independent two-level systems.
The quantum problem can be solved exactly where its full quantum properties are determined.

13. Future Plans BEC in optical lattice Why is it so interesting?
Easy to realize
Large variety of optical lattices
Fascinating optical effects 2D 3D
Photonic band gaps (PBG)

14. Future Plans What is PBG? Why?
We consider propagation of light through an optical lattice loaded with cold atoms
range of frequencies where
no propagation modes exist
in any directions a
-π/a
π/a
The goal is to study photonic band gaps in cold atomic structures
Access to real time manipulations
Perfect long range order
Why?