Quantum Phase Transitions in Cavity QED

Overview

The fully quantum interaction between light and atoms has been studied extensively ever since the idea of a quantized electromagnetic field was dreamed up by Dirac in the late 1920s. A whole host of interesting phenomena and applications as been theorized and observed including Rabi flopping, stimulated and spontaneous emission, the laser, laser trapping and cooling, and squeezed coherent states, among others.

Systems involving atom-laser interactions have proven useful in study the behavior of other, non-tractable systems such as those from solid-state physics where control over parameters can be difficult (not to mention reaching near-zero temperatures!) Because the parameters of lasers (frequency and amplitude) are essentially fully adjustable, it can be possible to simulate a given Hamiltonian and subsequently study its dynamics.

We are interested in two Hamiltonians in particular - the Dicke and the Lipkin-Meshkov-Glick (LMG). Why are they so interesting? Each exhibits a quantum phase transition, an abrupt change in a macroscopic property at zero temperature, when a parameter in the Hamiltonian is tuned through a critical value.

Our task is to realize the Dicke and LMG Hamiltonians with cesium atoms in a trapped in a high finesse optical cavity using far detuned Raman lasers and we are now working toward that goal. Thanks to the control we have over the lasers, we expect to be able to tune through the critical value in order to investigate the dynamics before, during, and after passing through the quantum phase transition.

Cavity QED for Quantum Phase Transitions

In an optical cavity a very intense light field can develop. That is to say, when highly reflective mirrors point at each other, light bounces around for a relatively long time, building up a very intense field. If the volume between the mirrors becomes very small a single photon can make a substantial change in the cavity's electric field. Cavity Quantum Electrodynamics (QED) is the study of how the quantum nature of individual photons in a cavity interacting with the quantum nature of individual atoms.

We want to realize the LMG quantum phase transition by trapping a sample of cesium atoms within a high finesse optical cavity. Each atom in the sample will be individually coupled to the cavity mode. In turn the photons in the cavity will couple back to the atoms in a coherent way. With the assistance of externally applied lasers, the cavity photons will mediate interactions that are symmetrically distributed across the atomic sample. When various parameters are properly tuned, the cavity mediated interactions have the same form as the interactions in the LMG collective spin model.

Preparing the Atomic Sample

Laser cooling and trapping allows for the collection of cold atomic gases with temperatures on the order of microkelvin. Starting from a room temperature background vapor the number of atoms collected in a magneto-optical trap (MOT) increases with background pressure. However, the number of atoms lost from the sample because of collisions with untrapped atoms also increases with the pressure.

In order to obtain a large number of atoms in the cavity but with a low background pressure, Our apparatus funnels atoms from a higher pressure chamber though a small aperture tube into a science chamber with a lower background pressure. The funnel is a MOT which cools on the two dimensions which are transverse to the connecting aperture but not on the transverse axis, a so called 2D-MOT. The beam of funneled atoms are then trapped in a conventional 3D-MOT in the science chamber. From the 3D-MOT the atoms will be transfered to an intracavity optical lattice.