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We use South Pole Telescope data from 2008 and 2009 to detect thenon-Gaussian signature in the cosmic microwave background (CMB) produced bygravitational lensing and to measure the power spectrum of the projectedgravitational potential. We constrain the ratio of the measured amplitude ofthe lensing signal to that expected in a fiducial LCDM cosmological model to be0.86 +/- 0.16, with no lensing disfavored at 6.3 sigma. Marginalizing over LCDMcosmological models allowed by the WMAP7 results in a measurement ofA_lens=0.90+/-0.19, indicating that the amplitude of matter fluctuations overthe redshift range 0.5 <~ z <~ 5 probed by CMB lensing is in good agreementwith predictions. We present the results of several consistency checks. Theseinclude a clear detection of the lensing signature in CMB maps filtered to haveno overlap in Fourier space, as well as a "curl" diagnostic that is consistentwith the signal expected for LCDM. We perform a detailed study of bias in themeasurement due to noise, foregrounds, and other effects and determine thatthese contributions are relatively small compared to the statisticaluncertainty in the measurement. We combine this lensing measurement withresults from WMAP7 to improve constraints on cosmological parameters whencompared to those from WMAP7 alone: we find a factor of 3.9 improvement in themeasurement of the spatial curvature of the Universe, Omega_k=-0.0014+/-0.0172;a 10% improvement in the amplitude of matter fluctuations within LCDM,sigma_8=0.810+/ 0.026; and a 5% improvement in the dark energy equation ofstate, w=-1.04+/-0.40. When compared with the measurement of w provided by thecombination of WMAP7 and external constraints on the Hubble parameter, theaddition of the lensing data improve the measurement of w by 15% to givew=-1.087+/-0.096.

A measurement of gravitational lensing of the microwave background using South Pole Telescope data