Bose-Einstein Condensation in a Dilute Gas: Measurement of Energy and Ground-State Occupation

We measure the ground-state occupation and energy of a dilute Bose gas of ${}^{87}\mathrm{Rb}$ atoms as a function of temperature. The ground-state fraction shows good agreement with the predictions for an ideal Bose gas in a 3D harmonic potential. The measured transition temperature is $0.94\left(5\right)T_o$, where $T_o$ is the value for a noninteracting gas in the thermodynamic limit. We determine the energy from a model-independent analysis of the velocity distribution, after ballistic expansion, of the atom cloud. We observe a distinct change in slope of the energy-temperature curve near the transition, which indicates a sharp feature in the specific heat.