Superluminal light propagation?
It is really interesting that we, the physicists, can entangle two light pulses separated by 100s of km from each other, but we unable to identify the propagation velocity of a pulse even in an ordinary dye solution. Even in linear optics, which is widely explored, defining the motion of a pulse analytically or measuring it experimentally is a fundamental problem due to the following reasons.
When there exists a frequency dependent absorption in a linear dielectric medium, i.e. ϵ(ω)= ϵR(ω)+i ϵI(ω), the shape of the pulse in the frequency space (hence also in the direct space) distorts due to the nonuniform absorption. One cannot define the velocity by tracking the peak or the center of the pulse. Because, the peak (or the center) of the pulse shifts forward or backward in space due to the spectral modification of the absorption. The original pulse is lost (or hidden).
In a ground breaking experiment, conducted in 2000 [Wang et al. Nature, 406, 277 (2000)], scientists announced the observation of superluminal (v>c) of Gaussian pulses in ordinary dye solutions. Such an observation was surprising to occur, since it violated the theory of relativity.
In a recent publication [Tasgin, Phys. Rev. A, 86, 033833 (2012)], we demonstrated that the superluminal speed, measured in this famous experiment, cannot be considered as a reliable measure for the pulse propagation velocity. In order to determine the reliability of a velocity definition (e.g. with respect to displacement of the pulse peak or center), we use the following fundamental and indisputable approach. Given a velocity definition, we calculate the two values for the velocity using real-ω and real-k Fourier spaces. If the definition for propagation is reliable —i.e. if it indeed corresponds to a physical flow, but not a shape distortion— the two values for the velocity must be close (or identical) to each other. However, we show that; even though in the luminal regime (v≤c) the two velocities overlap, in the superluminal region they differ significantly. In a recent paper [Phys. Rev. Lett., 112, 093903 (2014)], Talukder and colleagues confirmed that superluminal propagation emerges indeed owing to (absorptive) distorted shift of the pulse center.
The reliability of a velocity definition cannot be deduced experimentally, unlike other physical quantities. Because, experiments also measure the pulse peak or pulse center. In other words, one has to define the quantity to measure. Therefore, the method we introduced is the single way to check if a velocity indeed corresponds to a physical flow, or the correct description of the propagation.