Kerr effect studies of the Heavy Fermion URu$_2$Si$_2$

In the heavy fermion metal URu$_2$Si$_2$ the very large entropy carried by the 5f electrons is released at $\sim 17.5$ K via a second-order phase transition to a ``hidden order'' state. Below $\sim 1.5$K superconductivity emerges with a yet unknown gap structure adding to the mystery associated with this material. In this talk we present polar Kerr effect measurements of URu$_2$Si$_2$ crystals using a Sagnac interferometer. We find a weak magnetic signal in the ``hidden order'' phase that seems to not influence superconductivity. Finite Kerr signal below $T_c$ provides strong evidence that time reversal symmetry is broken in the superconducting state. The relation between the magnetic response in the ``hidden order'' phase and superconductivity is also studied.