  We demonstrate the emergence of nonreciprocal superradiant phase transitions
and novel multicriticality in a cavity quantum electrodynamics (QED) system,
where a two-level atom interacts with two counter-propagating modes of a
whispering-gallery-mode (WGM) microcavity. The cavity rotates at a certain
angular velocity, and is directionally squeezed by a unidirectional parametric
pumping $\chi^{(2)}$ nonlinearity. The combination of cavity rotation and
directional squeezing leads to nonreciprocal first- and second-order
superradiant phase transitions. These transitions do not require ultrastrong
atom-field couplings and can be easily controlled by the external pump field.
Through a full quantum description of the system Hamiltonian, we identify two
types of multicritical points in the phase diagram, both of which exhibit
controllable nonreciprocity. These results open a new door for all-optical
manipulation of superradiant transitions and multicritical behaviors in
light-matter systems, with potential applications in engineering various
integrated nonreciprocal quantum devices
