  The Dicke model describes the collective behavior of a sub-wavelength--size
ensemble of two-level atoms (i.e., spin-1/2) interacting identically with a
single quantized radiation field of a cavity. Across a critical coupling
strength it exhibits a zero-temperature phase transition from the normal state
to the superradiant phase where the field is populated and the collective spin
acquires a nonzero $x$-component, which can be imagined as ferromagnetic
ordering of the atomic spins along $x$. Here we introduce a variant of this
model where two sub-wavelength--size ensembles of spins interact with a single
quantized radiation field with different strengths. Subsequently, we restrict
ourselves to a special case where the coupling strengths are opposite (which is
unitarily equivalent to equal-coupling strengths). Due to the conservation of
the total spin in each ensemble individually, the system supports two distinct
superradiant states with $x$-ferromagnetic and $x$-ferrimagnetic spin ordering,
coexisting with each other in a large parameter regime. The stability and
dynamics of the system in the thermodynamic limit are examined using a
semiclassical approach, which predicts non-stationary behaviors due to the
multistabilities. At the end, we also perform small-scale full
quantum-mechanical calculations, with results consistent with the semiclassical
ones.
