Localizing an atom via quantum interference

The subwavelength localization of an atom using laserinduced schemes has been actively studied @1–9#. Several models have been proposed using, for example, the measurement of the phase shift due to an off-resonant standing-wave field @1–3#, the entanglement between the atom’s position to its internal state @4#, and others @5,6#. Recently, Zubairy and co-workers @7–9# have proposed two simple localization schemes using either the measurement of Autler-Townes split spontaneous emission in a three-level system @7,8# or the resonant fluorescence in a two-level system @9#. The main advantage of these schemes is that the localization of the atom occurs immediately in the subwavelength domain of the standing-wave field as spontaneous emission is recorded during the atom’s motion in the standing-wave field. In this article we describe a related method for localizing an atom in a standing-wave field. We use a three-level L-type atom that interacts with two fields, a probe laser field and a classical standing-wave coupling field. If the probe field is weak then the measurement of the population in the upper level can lead to subwavelength localization of the atom during its motion in the standing wave. The degree of localization is dependent on the parameters of interaction, especially on the detunings and the Rabi frequencies of the atom-field interactions. The atomic system under consideration is shown in Fig. 1. It consists of three atomic levels in a L-type configuration. The atom is assumed to be initially in state u0&. The transition u1&↔u2& is taken to be nearly resonant with a classical standing-wave field aligned along the x direction. In addition, the atom interacts with a probe laser field near resonant with the u0&↔u2& transition. We assume that the center-ofmass position of the atom is nearly constant along the direction of the standing wave. Hence, we apply the Raman-Nath approximation @10# and neglect the kinetic part of the atom from the Hamiltonian. Then, the Hamiltonian of the laserdriven part of the system in the interaction picture and the rotating wave approximation reads