Matter wave lensing to picokelvin temperatures

Using a matter wave lens and a long time-of-flight, we cool an ensemble of Rb-87 atoms in two dimensions to an effective temperature of less than $50^{+50}_{-30}$~pK. A short pulse of red-detuned light generates an optical dipole force that collimates the ensemble. We also report a three-dimensional magnetic lens that substantially reduces the chemical potential of evaporatively cooled ensembles with high atom number. By observing such low temperatures, we set limits on proposed modifications to quantum mechanics in the macroscopic regime. These cooling techniques yield bright, collimated sources for precision atom interferometry.