  We investigate the stellar populations of 25 massive, galaxies
($\log[M_\ast/M_\odot] \geq 10.9$) at $1.5 < z < 2$ using data obtained with
the K-band Multi-Object Spectrograph (KMOS) on the ESO VLT. Targets were
selected to be quiescent based on their broadband colors and redshifts using
data from the 3D-HST grism survey. The mean redshift of our sample is $\bar{z}
= 1.75$, where KMOS YJ-band data probe age- and metallicity-sensitive
absorption features in the rest-frame optical, including the $G$ band, Fe I,
and high-order Balmer lines. Fitting simple stellar population models to a
stack of our KMOS spectra, we derive a mean age of $1.03^{+0.13}_{-0.08}$ Gyr.
We confirm previous results suggesting a correlation between color and age for
quiescent galaxies, finding mean ages of $1.22^{+0.56}_{-0.19}$ Gyr and
$0.85^{+0.08}_{-0.05}$ Gyr for the reddest and bluest galaxies in our sample.
Combining our KMOS measurements with those obtained from previous studies at
$0.2 < z < 2$ we find evidence for a $2-3$ Gyr spread in the formation epoch of
massive galaxies. At $z < 1$ the measured stellar ages are consistent with
passive evolution, while at $1 < z \lesssim2$ they appear to saturate at
$\sim$1 Gyr, which likely reflects changing demographics of the (mean)
progenitor population. By comparing to star-formation histories inferred for
"normal" star-forming galaxies, we show that the timescales required to form
massive galaxies at $z \gtrsim 1.5$ are consistent with the enhanced
$\alpha$-element abundances found in massive local early-type galaxies.

Astrophysics of Galaxies