  Since the original work on Bose-Einstein condensation, quantum degenerate
gases of atoms have allowed the quantum emulation of important systems from
condensed matter and nuclear physics, as well as the study of novel many-body
states with no analog in other fields of physics. Ultracold molecules in the
micro- and nano-Kelvin regimes promise to bring powerful new capabilities to
quantum emulation and quantum computing, thanks to their rich internal degrees
of freedom compared to atoms. They also open new possibilities for precision
measurement and the study of quantum chemistry. Quantum gases of atoms were
made possible by collision-based cooling schemes, such as evaporative cooling.
For ultracold molecules, thermalization and collisional cooling have not been
realized. With other techniques such as supersonic jets and cryogenic buffer
gases, studies have been limited to temperatures above 10 mK. Here we show
cooling of NaLi molecules at micro- and nano-Kelvin temperatures through
collisions with ultracold Na atoms, both prepared in their stretched hyperfine
spin states. We find a lower bound on the elastic to inelastic collision ratio
between molecules and atoms greater than 50 -- large enough to support
sustained collisional cooling. By employing two stages of evaporation, we
increase the phase-space density (PSD) of the molecules by a factor of 20,
achieving temperatures as low as 220 nK. The favorable collisional properties
of a Na and NaLi mixture show great promise for making deeply quantum
degenerate dipolar molecules and suggest the potential for such cooling in
other systems.
