Equivalence of the Abraham momentum and the Minkowski momentum of photons in media

The century-long debate on the momentum of light in a medium involves two rival forms of momentum, namely those of Abraham and Minkowksi. In this Letter, we analyze this dilemma from the view of the quantum theory of light, the result of which can be easily extended to the classical level. It is found that the Abraham momentum of one polariton mode in linear and dispersive dielectrics differs from its Minkowski momentum, by a considerable factor. However, after taking all branches into consideration, we find the two lead to the same end, which unifies the two rival forms of momentum. The sum rule is traditional, but our conclusion provides a new perspective on the Abraham-Minkowski dilemma, and is consistent with existing experiments including a recent measurement of recoil momentum of atoms using an atom interferometer with Bose-Einstein Condensates G. K. Campbell et al. Phys. Rev. Lett. 94, 170403 (2005).], the Cerenkov effect, the Doppler effect and the phase matching conditions in nonlinear optical processes.