We study quantum dynamics of many-qubit systems strongly coupled to a quantized electromagnetic cavity field in the presence of decoherence and dissipation for both fermions and cavity photons, and taking into account the nonuniform cavity field and the spread of qubit transition frequencies. Analytic solutions for quantum state amplitudes and observables are derived for a broad class of open quantum systems. We show that depending on the initial state preparation, the dissipation in a cavity may drive the system into many-qubit entangled dark states that live much longer than the decay time of the cavity field.
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