Quantum Motion of Trapped Atom Interacting with a Quantized Cavity Mode

Abstract

Recent advances in a laser cooling and trapping of atoms and ions have enabled an experimental observation of a quantized center-of-mass motion of trapped two-level ions (atoms) [1]. Trapped particles cooled down to a zero-point kinetic energy can be used for the ultimate frequency, time and length standard or for a single-atom spectroscopy experiments [2,3]. Blockley et al. [4] have proposed a simple model describing dynamics of an ion in a trap: a single two-level atom (ion) exhibiting quantized vibrational motion within a harmonic trapping potential and interacting with a classical single-mode traveling light field. Cirac et al. [3] have analyzed the quantized atomic motion stimulated by the standing wave near a node of the field. In both of these models the ‘notion the center-of-mass of the particle within the optical potential is described quantum-mechanically but the standing or traveling waves are treated classically. We focus our attention on the case when the field mode is considered to be quantized. This model corresponds to a situation when the trap is placed within a resonator which supports just one particular mode of the electromagnetic field.