Fall of ultra slow light under gravity

Abstract

Recent experiments on ultra slow light by several research groups reporting slowing down of the optical pulses down to speeds of a few metres per second encourage us to examine the intriguing possibility of detecting a fall of the ultra slow light under Earth's gravity, i.e., on the laboratory scale. In the absence of a usable general relativistic (e.g., post-Newtonian) theory of light waves propagating in the presence of a gravitational field in such a strongly dispersive optical medium, we present a geometrical-optics based derivation that incorporates 'the effective gravitational refractive index' additively to the usual optical dispersion. It gives a deflection, or the vertical fall Δ for a horizontal traversal L as Δ=L²/2(R_⊕G/R_⊕²)n_g(1/1+n_gR_⊕G/R_⊕), where R_⊕G/R_⊕ is the ratio of the gravitational Earth radius to its geometrical radius R_⊕, and n_g is the group refractive index of the strongly dispersive optical medium. The expression is essentailly that for the Newtonian fall of an object projected horizontally with the group speed v_g=c/n_g, and is tunable refractively thorugh the index n_g. For L~1 m and n_g = c/v_g ~10⁸ (corresponding to the ultra-slow pulse speed ~few × 1 ms^-1), we obtain a fall Δ~1μm, that should be measurable-in particular through its sensitive dependence on the frequency that tunes n_g.