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Optical bistability in strong-coupling cavity QED with a few atoms

We present exact numerical solutions of the damped-driven Jaynes--Cummings model adapted to describe absorptive optical bistability in the limit of a few atoms strongly coupled to a high-finesse resonator. We show that the simplifying semiclassical result for many physical quantities of interest is well reproduced by the quantum model including even with only a few atoms in the strongly coupled system. Nontrivial atom-field quantum cross-correlations show up in the strong-driving limit.