  An atom placed in a focused laser beam will experience a dipole force due to
the gradient in the interaction energy, which is analogous to the well-known
optical tweezers effect. This force will be dependent on the velocity of the
atom due to the Doppler effect, which could potentially be used to implement a
Maxwell's demon. Photon scattering and other forms of dissipation can be
negligibly small, which would seem to contradict quantum information proofs
that a Maxwell's demon must dissipate a minimum amount of energy. We show that
the velocity dependence of the dipole force is cancelled out by another force
that is related to the gradient in the phase of the laser beam. As a result, a
Maxwell's demon cannot be implemented in this way.
