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?