A Measurement of the Cosmic Microwave Background Lensing Potential and Power Spectrum from 500 deg$^2$ of SPTpol Temperature and Polarization Data

We present a measurement of the cosmic microwave background (CMB) lensing potential using 500 deg$^2$ of 150 GHz data from the SPTpol receiver on the South Pole Telescope. The lensing potential is reconstructed with signal-to-noise per mode greater than unity at lensing multipoles $L lesssim 250$, using a quadratic estimator on a combination of CMB temperature and polarization maps. We report measurements of the lensing potential power spectrum in the multipole range of $100< L < 2000$ from sets of temperature-only, polarization-only, and minimum-variance estimators. We measure the lensing amplitude by taking the ratio of the measured spectrum to the expected spectrum from the best-fit $Lambda$CDM model to the $textit{Planck}$ 2015 TT+lowP+lensing dataset. For the minimum-variance estimator, we find $A_{rm{MV}} = 0.944 pm 0.058{rm (Stat.)}pm0.025{rm (Sys.)}$; restricting to only polarization data, we find $A_{rm{POL}} = 0.906 pm 0.090 {rm (Stat.)} pm 0.040 {rm (Sys.)}$. Considering statistical uncertainties alone, this is the most precise polarization-only lensing amplitude constraint to date (10.1 $sigma$), and is more precise than our temperature-only constraint. We perform null tests and consistency checks and find no evidence for significant contamination.