  Most of the successful physical theories rely on the constancy of few
fundamental quantities (such as the speed of light, $c$, the fine-structure
constant, \alpha, the proton to electron mass ratio, \mu, etc), and
constraining the possible time variations of these fundamental quantities is an
important step toward a complete physical theory. Time variation of \alpha can
be accurately probed using absorption lines seen in the spectra of distant
quasars. Here, we present the results of a detailed many-multiplet analysis
performed on a new sample of Mg II systems observed in high quality quasar
spectra obtained using the Very Large Telescope. The weighted mean value of the
variation in \alpha derived from our analysis over the redshift range 0.4<z<2.3
is \Delta\alpha/\alpha = (-0.06+/-0.06) x 10^{-5}. The median redshift of our
sample (z=1.55) corresponds to a look-back time of 9.7 Gyr in the most favored
cosmological model today. This gives a 3\sigma limit, -2.5 x 10^{-16} yr^-1
<(\Delta\alpha/\alpha\Delta t) <+1.2x10^{-16} yr^-1, for the time variation of
\alpha, that forms the strongest constraint obtained based on high redshift
quasar absorption line systems.
