Optical excitations in cold gases

Abstract

In this thesis, we study the effects of interparticle interactions on the optical spectrum of cold gases. We first consider homogenous gas in the weak excitation regime and find that the optical spectrum of a system of Bosons is highly sensitive to interactions. We find that optical excitations, at temperatures low enough for the thermal de Broglie wavelength to be larger than the scattering length, become collective modes. We study collective affects in the optical spectrum both above and below Bose-Einstein condensation, and show that the spectrum acquires a doublet structure when the condensate forms. We present a detailed theory of spectral shift and an estimate of some of the broadening effects. We derive a sum rule for the average frequency shift of an optical spectrum and investigate the basic conservation laws and symmetries of the system lying at the basis of this sum rule. We also compare the sum rule for the optical spectrum with the f-sum rule for the density-density correlation function. Finally we derive a transport equation for the optical modes in a dilute Bose system, which allows us to study the non-linear response to the excitation field. We map the problem onto the dynamics of two interacting anisotropic spins, and calculate the precession frequencies exactly both below and above Bose condensation. We demonstrate a relation between Rabi oscillations and internal Josephson oscillations, and find that an analogue of the internal Josephson effect exists in a non-condensed system.

(cont.) We also derive the transport equation for a dilute Fermi system and find that the dependence of the precession frequencies on interparticle interactions is very weak for fermions.