Slow photons as charged quasi-particles, and photonic Aharonov-Bohm effect

Recently we have proposed the method of Raman Adiabatic Transfer of Optical States (RATOS) to manipulate the optical state of light [1]. In this method a four-level atomic medium in double-Lambda configuration is interacting with two pump fields and a signal photon, which can be in a superposition of two modes with different frequencies. Depending on the intensity of the pump fields, only a particular superposition will experience electromagnetically induced transparency and thus can be slowed down. An adiabatic change in time of the pump fields can then change this superposition dynamically. Here we theoretically analyze the influence of an adiabatic change in the spatial form of the pump fields. We demonstrate that the signal photon then behaves like a charged quasi-particle: in paraxial approximation its dynamics is governed by a Schroedinger-like equation that includes a scalar and a vector quasi-potential whose form is determined by the shape of the pump fields. We suggest pump field configurations that generate potentials corresponding to a constant electric and a constant magnetic quasi-field and show that the magnetic quasi-field suppresses spatial dispersion of the signal photon. Furthermore we devise a scheme of pump fields that generates a vector potential of Aharonov-Bohm type. This induces a topological phase shift on the signal field. [1] J. Appel, K.-P. Marzlin and A.I. Lvovsky, Phys. Rev. A 73, 013804 (2006).