We investigate the stellar population properties of a sample of 24 massive quenched galaxies at 1.25 < z(spec) < 2.09 identified in the COSMOS field with our Subaru/Multi-object Infrared Camera and Spectrograph near-IR spectroscopic observations. Tracing the stellar population properties as close to their major formation epoch as possible, we try to put constraints on the star formation history, post-quenching evolution, and possible progenitor star-forming populations for such massive quenched galaxies. By using a set of Lick absorption line indices on a rest-frame optical composite spectrum, the average age, metallicity [Z/H], and alpha-to-iron element abundance ratio [alpha/Fe] are derived as log(age Gyr) = 0.04(-0.08)(+0.10-), [Z/H] = 0.24(-0.14)(+0.20), and [alpha/Fe] = 0.3(-0.12)(+0.12), respectively. If our sample of quenched galaxies at < z > = 1.6 is evolved passively to z = 0, their stellar population properties will align in excellent agreement with local counterparts at similar stellar velocity dispersions, which qualifies them as progenitors of local massive early-type galaxies. Redshift evolution of stellar population ages in quenched galaxies combined with low redshift measurements from the literature suggests a formation redshift of z(r) similar to 2.3, around which the bulk of stars in these galaxies have been formed. The measured [alpha/Fe] value indicates a star formation timescale of less than or similar to 1 Gyr, which can be translated into a specific star formation rate of similar or equal to 1 Gyr(-1) prior to quenching. Based on these findings, we discuss identifying possible progenitor star-forming galaxies at z similar or equal to 2.3. We identify normal star-forming galaxies, i.e., those on the star-forming main sequence, followed by a rapid quenching event, as likely precursors of the quenched galaxies at < z > = 1.6 presented here.
