università degli studi di milano dipartimento di fisica via celoria 16, 20133 milano, italy quantum...
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Università degli Studi di MilanoDipartimento di Fisica
via Celoria 16, 20133 Milano, Italy
Quantum Theory of Collective Atomic Recoil in Ring Cavities
16th October 2012“Mini Workshop - 2012”, Milano
PhD School in Physics, Astrophysics and Applied Physics
Thesis advisor:Dr. Nicola Piovella
Marina Samoylova
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
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
SRyS in free space CARL in a ring cavity
2D CARL configuration
System: a BEC in a high-finesse ring cavity
X
Z
pump fieldΦ
Experimental setup
• 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, 203601 (2011).
[2] S.Bux, H.Tomczyk, D.Schmidt, C.Zimmermann, N.Piovella, Ph.Courteille, New J. Phys., submitted (2012).
Φ
Results of the experiment
N=80000 is the number of atoms,
t= 200μs is the duration of the pump laser pulse
At certain conditions only 4 momentum states can be populated
individual momentum state
The semi-classical model
closed systems of equations !
In the semi-classical limit the four states configuration can be solved in termsof two independent two-level systems for the left and right cavity modes.
We are interested in a 4-level system
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.
The general state of the system: , where
and
tt
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
Why is it so interesting?BEC in optical lattice
2D
3D
Easy to realize
Large variety of optical lattices
Fascinating optical effects
Photonic band gaps (PBG)
Future Plans
What is PBG?We consider propagation of light through an optical lattice loaded with cold atoms
The goal is to study photonic band gaps in cold atomic structures
range of frequencies where no propagation modes existin any directions
a
-π/a π/a
Access to real time manipulations
Perfect long range order
Why?
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