Persistent oscillations induced by a decoherence-free subspace in open quantum systems

Open quantum systems described by the Gorini–Kossakowski–Sudarshan–Lindblad master equation either converge to steady states or exhibit persistent oscillations in the long-time limit. It is well known that steady states always exist; however, the conditions for the occurrence of oscillations and their frequencies are nontrivial. We show that oscillations indeed occur under the condition that the steady-state manifold forms a decoherence-free subspace of dimension two or higher. In this case, the spectrum of the oscillations can be explicitly determined from the system Hamiltonian, and the dynamics can be represented by unitary time evolution.