We report a 4.8$sigma$ measurement of the cross-correlation signal between the cosmic microwave background (CMB) lensing convergence reconstructed from measurements of the CMB polarization made by the POLARBEAR experiment and the infrared-selected galaxies of the Herschel-ATLAS survey. This is the first measurement of its kind. We infer a best-fit galaxy bias of $b = 5.76 pm 1.25$, corresponding to a host halo mass of $log_{10}(M_h/M_odot) =13.5^{+0.2}_{-0.3}$ at an effective redshift of $z sim 2$ from the cross-correlation power spectrum. Residual uncertainties in the redshift distribution of the sub-mm galaxies are subdominant with respect to the statistical precision. We perform a suite of systematic tests, finding that instrumental and astrophysical contaminations are small compared to the statistical error. This cross-correlation measurement only relies on CMB polarization information that, differently from CMB temperature maps, is less contaminated by galactic and extra-galactic foregrounds, providing a clearer view of the projected matter distribution. This result demonstrates the feasibility and robustness of this approach for future high-sensitivity CMB polarization experiments.
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