  The Collider Detector at Fermilab (CDF) experiment performed the first
measurement of the time-evolution of flavor-tagged B0s->J/psiphi decays, which
probes mixing-induced CP-violation in the B0s sector. Any sizable deviation
from zero of the phase beta_s, accessible through interference of the bbar\to
cbar c sbar quark-level process accompanied or not by B0s-aB0s mixing, would be
unambiguous indication of physics beyond the Standard Model. I report CDF
results obtained in 1.35/fb, a recent extension to a larger dataset
corresponding to 2.8/fb, and future projections.
