We present a review of recent experimental and theoretical attempts to realize and investigate Bose-Einstein condensation in systems of cooled alkali atoms. We discuss a second quantized theory that describes quantum optics of such systems. We study in detail: (a) the weak field scattering off the condensate; and (b), the probing of the condensate with short laser pulses.
We discuss our numerical studies of the low energy excitations of trapped Bose condensates using a Bogoliubov-Hartree treatment. In the zero temperature limit, the lowest few excitation frequencies calculated within the Bogoliubov approximation agree well with the experimental data. Finite temperature results obtained using the Popov approximation display qualitative differences from the experimental data close to the critical temperature region. Details of our numerical approach are presented and comparison with other results is discussed.
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