Andrew Hilliard 

Title: Collective Rayleigh scattering in a Bose Einstein condensate

A thesis submitted for the degree of Doctor of Philosophy on October, 2008.  

Danish National Research Foundation, Center for Quantum Optics – Quantop, Niels Bohr Institute

Academic supervisors: Eugene S. Polzik
Jörg Helge Müller

Abstract

Collective Rayleigh scattering in a Bose Einstein condensate 

This thesis describes the construction of a machine to generate Bose Einstein condensates in ⁸⁷Rb and the first experiments performed with this machine on superradiant Rayleigh scattering.

Bose Einstein condensates of ⁸⁷Rb are produced by evaporatively cooling atoms in a magnetic trap of the quadrupole-Ioffe configuration. The atoms are loaded
into the magnetic trap in a region of ultra-high vacuum from a double Magneto- Optical trap set-up. The evaporative cooling is achieved by selectively driving radiofrequency transitions to untrapped magnetic substates. During the evaporation, the magnetic trap is relaxed so that density dependent heating does not substantially reduce the number of atoms in the condensate. With a duty cycle of about a minute,
we produce pure, prolate condensates containing up to a few million atoms.

The application of an off-resonant beam of light along the long axis of the condensate leads to a form of collective Rayleigh scattering analogous to the superradiance that occurs in electronically inverted samples. One can think of this process as the amplification of quantum noise: photons are spontaneously scattered out of the pump beam, and due to the extended optical depth along the long axis of the BEC, the modes that propagate along this axis see the most gain. In the end-pumped geometry, the strongest superradiant mode is the one where photons are back-scattered by the atoms.

The overlap of stationary and recoiling atoms recoil produces a density modulation - a Bragg grating - which amplifies the back-scattering. We have performed a systematic study of the effects of pump detuning on the process while keeping the single particle scattering rate constant. In this way, we move between the case where the pump beam functions as a reservoir of photons to the situation where superradiance is clamped by a lack of photons in the pump beam.

Our experimental results are strongly supported by simulations of the system based on 1D Maxwell-Schrödinger equations. We demonstrate that the dynamics result from the structures that build up in the light and matter fields along the long axis of the condensate. In particular, we find that the emission of the first superradiant pulse may be understood in terms of the overlap of light and matter wave gratings. Finally, the random nature of the spontaneous scattering that initiates the collective scattering is manifest at later times in the distribution of arrival times and photon numbers of the first superradiant pulse.