(9.7) Damping in the optical molasses technique
(a) For the particular case of a frequency detuning of δ = -Γ/2, the slope of the force versus velocity curve, shown in Fig. 9.6, at v = 0 equals the peak force divided by Γ/(2k). Use this to estimate ∂F/∂v and hence to determine the damping coefficient α for an atom in a pair of counter-propagating laser beams, under these conditions.
(b) Estimate the damping time for a sodium atom in the optical molasses technique when each laser beam has intensity I(sat) and δ = -Γ/2.
(a)
Fig. 9.6 The force as a function of the velocity in the optical molasses technique (solid lines) for δ = -Γ/2 and (b) δ = -I. The damping is proportional to the slope of the force curve at v = 0. Note that the force is negative for v > 0 and positive for v < 0, so the force decelerates atoms. The forces produced by each of the laser beams separately are shown as dotted lines - these curves have a Lorentzian line shape and they are drawn with an FWHM of Γ appropriate for low intensities. For δ = 0 (not shown in the figure), the forces from the two laser beams cancel each other for all velocities. The velocity capture range is approximately I/k.
(b)