Many Body Effects in Atomic Systems.

Abstract

This thesis summarizes work on the theory of many-body effects in atomic systems. The modification of emission rates and spectra for a single impurity atom embedded in a many-body system is studied. In addition, the physics of two, cold atom systems is investigated.

We first study the spontaneous decay of a source atom inside a dielectric. In a microscopic picture, the photon radiated by the source atom is scattered by the medium atoms. This scattered photon is absorbed by the source atom, which results in a modification of the atom's decay rate. The calculation is carried out to second order in the medium density and we find a result that differs from the one obtained in macroscopic calculations.

Using the same microscopic model, we carry out a microscopic calculation for the recoil momentum acquired by a radiating atom in a medium. In our microscopic calculation, the average value of the photon momentum is modified by its scattering with the source atoms. This gives a modification to the recoil momentum of the source atom. The calculated correction agrees with the experimental observations.

In the second part of the thesis, we study two, ultra-cold atomic systems. An exactly solvable model, a Tonks-Girardeau gas with a local potential, is explain first. Such a one dimensional quantum gas has been realized recently. The spectrum of the single particle density matrix is evaluated exactly. We find the "condensate density" as a function of the potential strength. We also propose to use time-of-flight imaging to detect experimental observables.

The possibility of modulating the interaction strength in space using a Feshbach resonance in a degenerate Fermi gas is examined in the last part of the thesis. Using a periodic modulation, we find that the ground state of the system contains Cooper pairs with non-zero center-of-mass momenta. The resultant single particle spectrum is found to have an additional gap along particular directions. We propose experimental schemes to detect properties of both the ground state and the quasi-particle excitations.