Light Propagation in Ultracold Atomic Gases

Ultracold atomic systems are ideal candidates for simulating more complex quantum systems due to their high experimental controllability and also for applications in quantum information and quantum computation. A crucial point for comparing experiment with theoretical predictions is the characterization of the many-body state of the atoms. In the present text we study ultracold bosonic gases interacting dispersively with the electromagnetic field, and analyse the kind of information about the many-body state of the atoms that may be obtained by measuring the scattered photons. In an introductory part the basic theory describing the intreraction of the electromagnetic field with a gas of ultracold atoms and the dynamics of ultracold atoms in optical lattices is reviewed. In the main part we study the response of the ultracold atomic system to a weak probe field and its signatures in the scattered light. We show how to measure the density-density correlation function and the excitation spectrum of the atomic gas, as well as the mean value of the atomic field operator. Each chapter has a separate introduction and summary giving a clear picture of the physical system considered.