  For finite chemical potential effective models of QCD predict a first order
phase transition. In favour for the search of such a phase transition in
nature, we construct an equation of state for strange quark matter based on the
MIT bag model. We apply this equation of state to highly asymmetric core
collapse supernova matter with finite temperatures and large baryon densities.
The phase transition is constructed using the general Gibbs conditions, which
results in an extended coexistence region between the pure hadronic and pure
quark phases in the phase diagram, i.e. the mixed phase. The supernovae are
simulated via general relativistic radiation hydrodynamics based on three
flavor Boltzmann neutrino transport in spherical symmetry. During the dynamical
evolution temperatures above 10 MeV, baryon densities above nuclear saturation
density and a proton-to-baryon ratio below 0.2 are obtained. At these
conditions the phase transition is triggered which leads to a significant
softening of the EoS for matter in the mixed phase. As a direct consequence of
the stiffening of the EoS again for matter in the pure quark phase, a shock
wave forms at the boundary between the mixed and the pure hadronic phases. This
shock is accelerated and propagates outward which releases a burst of neutrinos
dominated by electron anti-neutrinos due to the lifted degeneracy of the
shock-heated hadronic material. We discuss the radiation-hydrodynamic evolution
of the phase transition at the example of several low and intermediate mass
Fe-core progenitor stars and illustrate the expected neutrino signal from the
phase transition.
