  Quenching, the cessation of star formation, is one of the most significant
events in the life cycle of galaxies. We show here the first evidence that the
Milky Way experienced a generalised quenching of its star formation at the end
of its thick disk formation $\sim$9 Gyr ago. Elemental abundances of stars
studied as part of the APOGEE survey reveal indeed that in less than $\sim$2
Gyr the star formation rate in our Galaxy dropped by an order-of-magnitude.
Because of the tight correlation between age and alpha abundance, this event
reflects in the dearth of stars along the inner disk sequence in the
[Fe/H]-[$\alpha$/Fe] plane. Before this phase, which lasted about 1.5 Gyr, the
Milky Way was actively forming stars. Afterwards, the star formation resumed at
a much lower level to form the thin disk. These events are very well matched by
the latest observation of MW-type progenitors at high redshifts. In late type
galaxies, quenching is believed to be related to a long and secular exhaustion
of gas. In our Galaxy, it occurred on a much shorter time scale, while the
chemical continuity before and after the quenching indicates that it was not
due to the exhaustion of the gas. While quenching is generally associated with
spheroids, our results show that it also occurs in galaxies like the Milky Way,
possibly when they are undergoing a morphological transition from thick to thin
disks. Given the demographics of late type galaxies in the local universe, in
which classical bulges are rare, we suggest further that this may hold true
generally in galaxies with mass lower than or approximately $M^*$, where
quenching could be directly a consequence of thick disk formation. We emphasize
that the quenching phase in the Milky Way could be contemporaneous with, and
related to, the formation of the bar. We sketch a scenario on how a strong bar
may inhibit star formation.
