Excerpt from a paper, "Quantized Motion of an Atom in a Gaussian-Laguerre Beam", Twamley, Imperial College, London, to be printed 3/16/99.
Recently there has been a growing interest, both in theory and experiment, in the interaction between matter and light fields possessing orbital angular momentum. The typical light fields used in these works are the Gaussian-Laguerre modes (G-L). The theoretical work so far has solely concentrated on the semi-classical description of the motion of matter in G-L beams. As neutral atom cooling improves, a truly quantum description becomes necessary. Indeed, recent experiments in atomic guiding using evanescent waves within a hollow optical fibre verge on the quantum regime . In this paper we examine the quantised motion of a neutral atom in a Gaussian-Laguerre 10 mode, taking into account the spontaneous recoil while in the far de-tuned limit. We are primarily interested in the quantised transfer of the orbital angular momentum to the centre-of-mass (COM) of the atom and how this appears in the quantal evolution. In the limit where the incident light is far detuned from the atom's natural frequency, we find that the transfer of angular momentum is imparted through the dissipation suffered by the atom through spontaneous recoil. We derive a master equation for the COM motion in the limit of large detuning for motion near the centre of the beam which includes the momentum kick from spontaneous recoil. We select the beam and atomic parameters which give an atom that can be easily cooled to the lowest COM eigenstate of the G-L beam and which suffers a large amount of spontaneous recoil. This results in a rapid increase of angular momentum over the orbital time of the atom around the center of the beam.
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