Time Reversal Symmetry Breaking in the B Phase of the Heavy Fermion Superconductor PrOs$_4$Sb$_{12}$

We present polar Kerr effect measurements of the filled skutterudite superconductor PrOs$_4$Sb$_{12}$. Simultaneous AC susceptibility measurements allow us to observe the superconducting transition under the influence of heating from the optical beam. A nonzero Kerr angle $theta_K$ develops below the superconducting transition, saturating at $sim 300$ nrad at low temperatures. This result is repeated across several measurements of multiple samples. By extrapolating the measured $theta_K(T)$ to zero optical power, we are able to show that the Kerr angle onset temperature in one set of measurements is consistent with the transition to the B phase at $T_{C2}$. We discuss the possible explanations for this result and its impact on the understanding of multi-phase and inhomogeneous superconductivity in PrOs$_4$Sb$_{12}$.