Continuous measurement with traveling wave probes

We consider the use of a traveling wave probe to continuously measure the quantum state of an atom in free space. Unlike the more familiar cavity QED geometry, the traveling wave is intrinsically a multimode problem. Using an appropriate modal decomposition we determine the effective measurement strength for different atom-field interactions and different initial states of the field. These include the interaction of a coherent-state pulse with an atom, the interaction of a Fock-state pulse with an atom, and the use of Faraday rotation of a polarized laser probe to perform a QND measurement on an atomic spin.