Trapping of Single Atoms with Single Photons in Cavity QED

Two recent experiments have reported the trapping of individual atoms inside optical resonators by the mechanical forces associated with single photons [Hood et al., Science 287, 1447 (2000) and Pinkse et al., Nature 404, 365 (2000)]. Here we analyze the trapping dynamics in these settings, focusing on two points of interest. Firstly, we investigate the extent to which light-induced forces in these experiments are distinct from their free-space counterparts. Secondly, we explore the quantitative features of the resulting atomic motion and how these dynamics are mapped onto variations of the intracavity field. Not surprisingly, qualitatively distinct atomic dynamics arise as the coupling and dissipative rates are varied. For the experiment of Hood et al., we show that atomic motion is largely conservative and is predominantly in radial orbits transverse to the cavity axis. A comparison with the free-space theory demonstrates that the fluctuations of the dipole force are suppressed by an order of magnitude. This effect is based upon the Jaynes-Cummings eigenstates of the atom-cavity system and represents qualitatively new physics for optical forces at the single-photon level. By contrast, even in a regime of strong coupling in the experiment of Pinkse et al., there are only small quantitative distinctions between the free-space theory and the quantum theory, so it is not clear that description of this experiment as a novel single-quantum trapping effect is necessary. The atomic motion is strongly diffusive, leading to an average localization time comparable to the time for an atom to transit freely through the cavity and to a reduction in the ability to infer aspects of the atomic motion from the intracavity photon number.