  We study quantum dynamics of many-qubit systems strongly coupled to a
quantized electromagnetic cavity mode, in the presence of decoherence and
dissipation for both fermions and cavity photons. The analytic solutions are
derived for a broad class of open quantum systems in Lindblad approximation.
They include identical qubits, an ensemble of qubits with a broad distribution
of transition frequencies, and multi-level electron systems. Compact analytic
solutions for time-dependent quantum state amplitudes and observables become
possible with the use of the stochastic equation of evolution for the state
vector. We show that depending on the initial quantum state preparation, the
systems can evolve into a rich variety of entangled states with destructive or
constructive interference between the qubits. In particular, dissipation in a
cavity can drive the system into the dark states completely decoupled from the
cavity modes. We also find the regimes in which multi-electron systems with a
broad distribution of transition frequencies couple to the quantized cavity
field as a giant collective dipole.
