Cold-atom clock based on a diffractive optic

Clocks based on cold atoms offer unbeatable accuracy and long-term stability, but their use in portable quantum technologies is hampered by a large physical footprint. Here, we use the compact optical layout of a grating magneto-optical trap (gMOT) for a precise frequency reference. The gMOT collects ${10}^7$ ${}^{87}$Rb atoms, which are subsequently cooled to $20\mu$K in optical molasses. We optically probe the microwave atomic ground-state splitting using lin$\perp$lin polarised coherent population trapping and a Raman-Ramsey sequence. With ballistic drop distances of only $0.5$mm, the measured short-term fractional frequency stability is $2\times {10}^{-11}\mathrm{/}\sqrt{\tau }$.