Laser frequency stabilization by modulation transfer spectroscopy and balanced detection of molecular iodine for laser cooling of ${}^{174}$Yb

We report laser frequency stabilization by the combination of modulation transfer spectroscopy and balanced detection of a relatively weak hyperfine transition of the R(158)25-0 line of molecular iodine (${}^{127}$I${}_2$), which is used as a new frequency reference for laser trapping and cooling of ${}^{174}$Yb on the ${}^1{S}_0-{}^3{P}_1$ transition. The atomic cloud is characterized by time-of-flight measurements, and an on-resonance optical depth of up to 47 is obtained. We show laser noise reduction and characterize the short-term laser frequency instability by the Allan deviation of the laser fractional frequency. The minimum measured value is 3.9 x ${10}^{-13}$ at 0.17 s of averaging time.