Localization of Atoms by Homodyne Measurement

Abstract

An atom passing through a standing electromagnetic wave inside an optical cavity couples via its dipole moment to the cavity field. The state of the combined system is an entangled state of atom and field; consequently, a measurement on one of the subsystems, on either the atom or the field, will provide information about the other. In particular, the position of the atom in the standing wave becomes strongly correlated with the phase of the field, since in the presence of the field the atom becomes polarized and thus changes the phase of the field through its refractive index; the magnitude of this phase change depends on the local light intensity and hence on the position of the atom. A measurement of the phase change due to the atom traversing the cavity can be made, for example, by balanced homodyne detection, and yields information about the position of the atom relative to the nodes and anti-nodes of the standing wave^1,2. The information gain implies a localization of an initially extended atomic wave-packet. We have made a detailed investigation of this measurement-induced localization, where the influence of the measurement on the state of the system is described by the method of quantum trajectories³, which links measurement theory with quantum jump simulations. The quantum trajectory method allowed us to calculate the time evolution of the system wave function, conditioned on the measurement record made by the homodyne detector.