Frequency shift of the hyperfine transition of atomic hydrogen by two coherent perturbations: Effect of relaxation

A two-level quantum system is considered in which relaxation processes with characteristic time constants T
1
and T
2
are present. The shift in frequency due to perturbations at two different frequencies is calculated. The general result is experimentally verified for the
\DeltaF = 1, \Deltam_{F} = 0
transition of atomic hydrogen, when the frequency of the external perturbations is close to the unperturbed two-level transition frequency.