High Resolution Polar Kerr Effect Measurements of High-Temperature Superconductors: Evidence for Broken Time Reversal Symmetry Below the Pseudogap temperature

High resolution Polar Kerr Effect (PKE) measurements were performed on YBa$_2$Cu$_3$O$_{7-\delta}$ as a function of temperature for variety of doping levels. In order be able to measure effects beyond our old search for anyon superconductivity, we devised a new technique based on a fiber Sagnac interferometer with a zero-area Sagnac loop. With this technique we show a shotnoise-limited sensitivity of 100 nanorad/$\sqrt{Hz}$ with incident photon power of $\sim$ 10 $\mu$-Watt, in a wide temperature range from 0.3 K to room temperature. Our results indicate that a Time Reversal Symmetry Breaking (TRSB) signal appears in all underdoped YBa$_2$Cu$_3$O$_{7-\delta}$~ samples below the doping dependent pseudogap temperature. The effect increases with decreasing temperature and seems to saturate at a lower temperature close to $T_c$. The saturated size of the effect increases with increasing $\delta$. We will discuss possible origins of this effect and its presence in other high-Tc superconductors.