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)= ϵ_{R}(ω)+i ϵ_{I}(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.