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Università degli Studi di Milano
Dipartimento di Fisica
via Celoria 16, 20133 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 - 2012”, Milano
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
Introduction
Superradiant Rayleigh Scattering in free space (SRyS)
[ Collective Atomic Recoil Lasing in free space (CARL) ]
incident laser beam
Introduction
SRyS in free space
CARL in a ring cavity
2D CARL configuration
System: a BEC in a high-finesse ring cavity
X
Z
Φ
pump field
Experimental setup
•A
Bose-Einstein condensate is prepared
in an Ioffe-Pritchard type magnetic trap in a highfinesse 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.
Φ
• 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, 203601 (2011).
[2] S.Bux, H.Tomczyk, D.Schmidt, C.Zimmermann, N.Piovella, Ph.Courteille, New J. Phys., submitted (2012).
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
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.
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
Numerical Results
Numerical Results
- atom-number squeezing parameter
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.
Future Plans
BEC in optical lattice
Why is it so interesting?
Easy to realize
2D
Large variety of
optical lattices
Fascinating optical
effects
3D
Photonic band gaps
(PBG)
Future Plans
What is PBG?
We consider propagation of light through an optical lattice loaded with cold atoms
a
range of frequencies where
no propagation modes exist
in any directions
-π/a
π/a
The goal is to study photonic band gaps in cold atomic structures
Access to real time manipulations
Why?
Perfect long range order