Generalized theory of double-resonance optical pumping of ⁴He

We present extensions to the theory of double-resonance laser pumping of ⁴He in the context of magnetometer instrumentation. This extended theory allows for arbitrary optical polarization, magnetic resonance (H₁) coil orientation, and overall instrument orientation relative to the ambient magnetic field. Steady-state solutions are presented for portions of the extended parameter space. These calculations are used to analyze the shot-noise-limited sensitivities for helium magnetometers for selected parameter values, and we find that linearly polarized light can have a relatively simple orientational dependence for a particular choice of angle between the H₁ coils and the light polarization vector. Calculations are also compared to experimentally measured magnetic resonance curves, and a shot-noise limit on sensitivity of 6 fT/√Hz is determined for a particular magnetometer apparatus using a cell 2.4 cm in diameter and 7.5 cm in length. This extended theory can be utilized to select optimal operational parameter values and obtain ideal sensitivities for helium magnetometers.