  It is well known that the rotational motion does not induce Unruh effect,
because the Minkowski vacuum coincides with the vacuum state defined by the
pure rotating observers. However, are there Rindler particles carrying orbital
angular momentum (OAM), and do they produce observable effect? To answer these
questions, we need an accelerated observer having a vortex structure in the
transverse dimensions and carrying well-defined OAM. Here we consider the
angular momentum characteristics of Unruh effect in the theory of scalar field
and electromagnetic field for the first time. We find that the rotation and
vortex structure of a uniformly accelerated observer lead to the definite
angular momentum correlation between Rindler particles and their counterparts
in Minkowski vacuum. When interacting with the Unruh thermal bath, the
accelerated vortex observer carrying the OAM of l can absorb and emit Rindler
particles with the same OAM, and the particle energy is determined by the
angular velocity of the rotation. The absorption rate is not equal to the
emission rate in general. Both the absorption and emission processes in the
thermal bath are correlated with the emission process of particles with OAM of
+l or -1 in Minkowski vacuum. This effect may promote a potential scheme to
detect the Unruh effect. The OAM provides a potential approach to filter out
the background noise so that the signal particles could be extracted
sufficiently.
