  To advance precise inertial navigation, we present a compact quantum sensor
which is based on novel quantum phenomenon of the angular Bloch oscillations
and measures solely the angular acceleration of slow external rotation. We
investigate the dynamics of ultra-cold atoms confined in a toroidal trap with a
ring-lattice along the azimuth angle, realized with the superposition of two
copropagating Laguerre-Gaussian beams. In the presence of external rotation of
small angular acceleration, or prescribed linear chirp between the two beams,
the measured angular momentum of trapped atoms displays a specific periodic
behaviour in time, which we name as the angular Bloch oscillations. This
discovered quantum phenomenon is shown to be a key element of fruitful
applications for (i) an efficient transfer of quantized angular momentum from
light field to atoms by controlling the chirp, and (ii) the direct
determination of the angular acceleration of external rotation by measuring the
Bloch period.
