  We study the nonequilibrium dynamic behaviors in a driven-dissipative
single-atom cavity electromagnetically induced transparency. The optical
bistability and multistability beyond a Kerr nonlinearity are observed
utilizing the optical Stark shift induced strong nonlinearity. We show that the
nonequilibrium dynamical phase transition between bistability and
multistability is highly tunable by the system parameters in a large parameter
region. The first-order dissipative optical bistability (multistability) always
corresponds to the photon-bunching quantum statistics, which indicates that the
quantum fluctuations and correlations play important roles in nonequilibrium
dynamics.Interestingly, bistability and multistability with photon-bunching
quantum statistics occurring at extremely low steady-state cavity photon number
are observed, even under a very strong cavity driven field. Furthermore, we
demonstrate that the unique cavity steady-state solution of the full quantum
calculation is excellently consistent with the lowest solution based on the
semiclassical mean-field approach in bistability and multistability regimes
when the cavity photon number is much less than unity, albeit these
nonclassical quantum states should possess strong quantum fluctuations in this
parameter regime. Our results pave the way to exploring nonclassical correlated
optical multistability in quantum regime, which may bring exciting
opportunities for potential applications from quantum information processing to
quantum metrology.
