Cold atoms interacting with highly twisted laser beams mimic the forces involved in Millikan’s experiment

Abstract

This paper considers the analogy between the force exerted on cold atoms when they interact with a highly twisted tightly focused laser beam and the forces exerted on a charged dielectric particle inside a uniform electric field when we perform the Millikan’s experiment. In the later case the particle experiences its weight, a force due to the electric field which is arranged in the opposite direction of the weight, and a drag force due to the air proportional and opposite to the velocity of the particle. The force due to the electric field is ‘quantised’ since the charge of the particle is always an integer multiple of the electron charge. In the case of the cold atoms the total force is made up by three terms. The second term is quantised since it is proportional to the beam helicity which is an integer number. The sign of this term is opposite to the first. The third term is a damping force force proportional and opposite to the velocity of the atom. We present numerical calculations with parameters taken from experimental data which show an impressive analogy between the involved forces.