New limits on time-reversal invariance from the hyperfine structure of thallium fluoride

We have made a very precise test of time-reversal invariance using nuclear-spin resonance in a thallium fluoride molecular beam. We searched for a shift of the 120-kHz Tl resonance when an external electric field was reversed relative to the nuclear spin and found it to be (-2.2\ifmmode\pm\else\textpm\fi{}2.1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ Hz, less than 0.02 ppm and a fivefold improvement over any previous measurement. Our result imposes new constraints on the proton electric dipole moment and on CP nonconservation in strong and weak interactions.