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.