Nonlinear wave mixing between atomic and optical fields

The interaction between Bose Einstein condensates (BECs) and coherent light fields is treated within the framework of nonlinear wave mixing and studied using techniques developed in the fields of nonlinear and quantum optics. We focus in particular on two situations involving a BEC driven by a strong off-resonant 'pump' laser. First, we consider the case where the laser light is scattered into a single mode of an optical ring cavity. We then consider the case where the light is scattered into the continuum of vacuum modes of the electric field. The first problem is an extension of recent theoretical and experimental work on the so-called collective atomic recoil laser (CARL), whereas the second corresponds to a recent condensate-superradiance experiment performed at MIT. In the cavity situation, we develop a CARL model in which both the atomic and optical fields are treated fully quantum mechanically. We first show that the previous CARL model, which treats the atomic motion classically, breaks down at the recoil temperature due to the effects of matter-wave diffraction. We then show that when combined with a BEC the CARL can be viewed as a device which parametrically amplifies atomic and optical fields. The existence of entanglement and non-classical intensity correlations between the amplified atomic and optical fields is demonstrated, as well as the ability to manipulate the quantum statistical properties of the matter and light waves by injecting a weak laser field into the optical cavity to trigger the device. By replacing the cavity mode with a continuum of modes, we are able to formulate a quantum theory of condensate superradiance in which the scattered light field is eliminated in the Markov approximation. This model shows that condensate depletion leads to mode competition which prevents light scattering in all but the preferred direction(s). The outcome of the mode-competition is highly sensitive to the quantum fluctuations which trigger the phenomenon, resulting in large run-to-run variations in the angular pattern of the superradiant light pulse, an effect which is observed experimentally