We report on a laser based $^{199}$Hg co-magnetometer deployed in an experiment searching for a permanent electric dipole moment of the neutron. We demonstrate a more than five times increased signal to-noise-ratio in a direct comparison measurement with its $^{204}$Hg discharge bulb-based predecessor. An improved data model for the extraction of important system parameters such as the degrees of absorption and polarization is derived. Laser- and lamp-based data-sets can be consistently described by the improved model which permits to compare measurements using the two different light sources and to explain the increase in magnetometer performance. The laser-based magnetometer satisfies the magnetic field sensitivity requirements for the next generation nEDM experiments.
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