Induced Dipole Forces in a Radiation Field

When an atom with the polarizability a is brought into an inhomogeneous electric field E a dipole moment p = oE is induced and the force 

For Au) the polarizability a u)) increases nearly linear with the detuning Aw. From (14.20 and 22) it follows that in an intense laser beam (S 1) with the intensity I = ocE the force on an induced atomic dipole is 

This reveals that in a homogeneous field (e.g., an extended plane wave) VI = 0 and the dipole force becomes zero. For a Gaussian beam with the beam waist w, propagating in the z-direction, the intensity I(r) in the xy plane is according to (5.32) 

The intensity gradient VI = -(4r/w2)I(r)r points into the radial direction and the dipole force F is then directed towards the axis r = 0 for Aw 0 and radially outwards for Aw 0. 

For Aw 0 the z-axis of an intense Gaussian laser beam with l(r=0) = Tq represents a minimum of the potential energy 

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