Light-induced motion of trapped ions. I. Low-intensity limit

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Abstract
Derives a Fokker-Planck equation for the Wigner function describing the centre-of-mass motion of a trapped ion in a monochromatic travelling wave of light. The driving term and the coefficients of diffusion are found by solving certain sets of ordinary differential equations. In the low-intensity limit, the author investigates the rate of change of the mechanical energy of the ion and analyse a linearised Fokker-Planck equation valid in the vicinity of the steady state. The quantum mechanical properties of the harmonic oscillator implicit in the equations for the Wigner functions are discussed.