Gravitational redshift and deflection of slow light

We explore the nature of the classical propagation of light through media with strong frequency-dependent dispersion in the presence of a gravitational field. In the weak field limit, gravity causes a redshift of the optical frequency, which the slow-light medium converts into a spatially varying index of refraction. This results in the bending of a light ray in the medium. We further propose experimental techniques to amplify and detect the phenomenon using weak value measurements. Independent heuristic and rigorous derivations of this effect are given.

Figure 1

Experimental setup. A laser beam enters a Sagnac interferometer. If no other optical element is in the system and for perfect alignment all of the light exits out the input port of the interferometer and goes back to the laser. Using a combination of a half $(\lambda ∕2)$ wave plate and a Soleil Babinet compensator (SBC), one can tune the relative phase acquired for each direction in the interferometer. This allows us to tune between the dark and bright ports, which is necessary for weak value measurements. The slow-light medium of the interferometer allows us to couple the “which-way” information of the interferometer to the transverse deflection of the light beam. A quadrant detector, which measures beam deflections, is in the dark port of the interferometer. The gravitational field $g$ is perpendicular to the plane of the figure.