Using ~5000 spectroscopically-confirmed galaxies drawn from the Observations of Redshift Evolution in Large Scale Environments (ORELSE) survey we investigate the relationship between color and galaxy density for galaxy populations of various stellar masses in the redshift range $0.55 le z le 1.4$. The fraction of galaxies with colors consistent with no ongoing star formation ($f_q$) is broadly observed to increase with increasing stellar mass, increasing galaxy density, and decreasing redshift, with clear differences observed in $f_q$ between field and group/cluster galaxies at the highest redshifts studied. We use a semi-empirical model to generate mock group/cluster galaxies unaffected by environmental processes and compare them to observed populations to constrain the environmental quenching efficiency ($Psi_{convert}$). High-density environments from $0.55 le z le 1.4$ appear capable of efficiently quenching galaxies with $log(M_{ast}/M_{odot})>10.45$. Lower stellar mass galaxies also appear efficiently quenched at the lowest redshifts, but this efficiency drops precipitously with increasing redshift. Quenching efficiencies, combined with simulated group/cluster accretion histories and results from a companion ORELSE study, are used to constrain the average time from group/cluster accretion to quiescence and the time between accretion and the inception of quenching. These timescales were constrained to be <$t_{convert}$>=$2.4pm0.3$ and <$t_{delay}$>=$1.3pm0.4$ Gyr, respectively, for galaxies with $log(M_{ast}/M_{odot})>10.45$ and <$t_{convert}$>=$3.3pm0.3$ and <$t_{delay}$>=$2.2pm0.4$ Gyr for lower stellar mass galaxies. These quenching efficiencies and associated timescales are used to rule out certain environmental mechanisms as being those primarily responsible for transforming the star-formation properties of galaxies over this 4 Gyr window in cosmic time.
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