  Quantum phase transitions with multicritical points are fascinating phenomena
occurring in interacting quantum many-body systems. However, multicritical
points predicted by theory have been rarely verified experimentally; finding
multicritical points with specific behaviors and realizing their control
remains a challenging topic. Here, we propose a system that a quantized light
field interacts with a two-level atomic ensemble coupled by microwave fields in
optical cavities, which is described by a generalized Dicke model.
Multicritical points for the superradiant quantum phase transition are shown to
occur. We determine the number and position of these critical points and
demonstrate that they can be effectively manipulated through the tuning of
system parameters. Particularly, we find that the quantum critical points can
evolve into a Lifshitz point if the Rabi frequency of the light field is
modulated periodically in time. Remarkably, the texture of atomic pseudo-spins
can be used to characterize the quantum critical behaviors of the system. The
magnetic orders of the three phases around the Lifshitz point, represented by
the atomic pseudo-spins, are similar to those of an axial
next-nearest-neighboring Ising model. The results reported here are beneficial
for unveiling intriguing physics of quantum phase transitions and pave the way
towards to find novel quantum multicritical phenomena based on the generalized
Dicke model.
