Driving quantum systems with periodic conditional measurements

We consider the effect of periodic conditional no-click measurements on a quantum system. What is the final state of such a driven system? When the system has some symmetry built into it, the final state is a dark state provided that the initial state overlaps with this nondetectable fragment of the Hilbert space. We find two classes of such states: generic dark states that are found also for nonperiodic measurements, and Floquet dark states that are directly controlled by the periodicity of the measurements and which do not rely on the underlying symmetry of the Hamiltonian. A different behavior is found in the absence of dark manifolds, where for specific periodicities of the measurements we find nontrivial oscillatory dynamics, controlled by the measurement rate. Finally, when the control parameters are tuned, the eigenvalues of the survival operator coalesce to zero, and then one finds exceptional points with a large degeneracy. The physical meaning of this special type of degeneracy is that the null measurement process becomes impossible, implying that detecting the state is guaranteed. We analyze these effects with a nonperturbative method based on a classical charge picture.