Nonlinear Pressure Shifts of 87Rb and 133Cs in Ar and Kr

We demonstrated the nonlinear dependence of the microwave resonance frequencies of ground-state Rb or Cs atoms on the pressure of the buffer gases Ar and Kr. No nonlinearities were observed in the gases He or N₂. These observations strongly suggest that the nonlinearities are due to the van der Waals molecules that form in Ar and Kr, but not in He or N₂. We developed a simple model, parameterized by the effective three-body formation rate of molecules and by the effective product of the collisionally-limited lifetime times the shift of the hyperfine coupling coefficient in the molecule, and it explained the data very well.