Hydrogen maser frequency shifts due to coherently excited Δm F =±1 transitions betweenF=1 levels of the atomic hydrogen ground state

Hydrogen maser frequency shifts, caused by the multiple quantum transition nonlinearities of a resonant multiple frequency excitation of the atomic hydrogen four level ground state system have been investigated. The oscillation characteristics of hydrogen maser operation with simultaneously excited, low frequencyΔm _F =±1 transitions between theF=1 states of the atomic hydrogen ground state have been analysed theoretically and explicit formulas for hydrogen maser frequency shifts and amplitude response have been derived for arbitrary maser oscillation amplitude and a small signal approximation for theΔm _F =±1 “Zeeman” transitions. The comparison with experimentally observed hydrogen maser frequency shifts was specialized to small magnetic fields, for which the difference between the resonance frequencies of the two low frequency,Δm _F =±1 Zeeman transitions is small compared to the linewidth. Special emphasis was placed on the evaluation of frequency pulling effects for a Zeeman transition excitation at off-resonance conditions. For this case the theoretical formulation of frequency pulling effects becomes insensitive against simplifying assumptions about the radiation damping phenomena and a particular good agreement between experiment and theory can therefore be expected. Experimental conditions have been specified, for which the uncertainty of hydrogen maser frequency due to Zeeman transition induced frequency shifts does not restrict the present frequency stability of a hydrogen maser frequency standard.