The Abraham-Minkowski controversy and He-McKellar-Wilkens phase

Abstract

This thesis investigates the long-standing Abraham-Minkowski controversy concerning the momentum of light inside a dielectric medium. A revealing connection to the optical He-McKellar-Wilkens (HMW) phase is found upon studying the Langrangian describing the classical laser-atom interaction. This connection is further highlighted by moving into a semi-classical model in which the phase arises as a result of the transformation between the Abraham and Minkowski Hamiltonians. The HMW along with the Aharonov-Casher phases are found to be both dynamic and geometric depending on the representation. It is shown that an optical version of the HMW phase is acquired by a dipole moving in a laser beam, and I propose several interferometric schemes in order to observe the optical HMW effect. Finally, by moving into a cavity system, it is possible to account for the back action of the atoms on the light which changes the electromagnetic mode structure. This increase in model sophistication grants an alternative vantage from which to interpret the Abraham-Minkowski problem.