  We analyse the evolution of environmental quenching efficiency, the fraction
of quenched cluster galaxies that would be star-forming if they were in the
field, as a function of redshift in 14 spectroscopically confirmed galaxy
clusters with 0.87 < z < 1.63 from the Spitzer Adaptation of the Red-Sequence
Cluster Survey (SpARCS). The clusters are the richest in the survey at each
redshift. Passive fractions rise from $42_{-13}^{+10}$\% at z ~ 1.6 to
$80_{-9}^{+12}$\% at z ~ 1.3 and $88_{-3}^{+4}$\% at z < 1.1, outpacing the
change in passive fraction in the field. Environmental quenching efficiency
rises dramatically from $16_{-19}^{+15}$ at z ~ 1.6 to $62_{-15}^{+21}\% at z ~
1.3 and $73_{-7}^{+8}$\% at z $\lesssim$ 1.1. This work is the first to show
direct observational evidence for a rapid increase in the strength of
environmental quenching in galaxy clusters at z ~ 1.5, where simulations show
cluster-mass halos undergo non-linear collapse and virialisation.
