Quantum backaction in spinor-condensate magnetometry

We provide a theoretical treatment of the quantum backaction of Larmor frequency measurements on a spinor Bose-Einstein condensate by an off-resonant light field. Two main results are presented; the first is a quantum jump operator description that reflects the abrupt change in the spin state of the atoms when a single photon is counted at a photodiode. The second is the derivation of a conditional stochastic master equation relating the evolution of the condensate density matrix to the measurement record. We provide a few examples of the application of this formalism and comment on its application to metrology.