AbstractWe consider the time evolution of a dynamic quantum system coupled to a repeatedly measured ancilla. Given the time lapse Δt between two subsequent measurements, the combined system may be described using a difference master equation whereas, in the Zeno-limit Δt → 0, the evolution of the dynamic system is unitary and defined by the state of the ancilla. For an arbitrary Δt, we also formulate a master equation that interpolates smoothly the exact evolution given by the difference equation.In the special case of a nondemolition interaction Hamiltonian, the master equation of the total system reduces to uncoupled systems of first order differential equations, whose dimensions are the same as the dimension Na of the ancilla Hilbert space.

After having traced over the ancilla state,the master equation of the dynamic system can be expressed either as Nath order differential equations in time or, equivalently, as Zwanzig equations with an explicit memory over the system evolution.The above results are applied to a harmonic oscillator coupled to a two-level system, that serves as the repeatedly measured ancilla. Relatively sparse measurements are shown to destroy the coherence of the oscillator whereas, in the Zeno-limit, the coherence is preserved for all times. This is demonstrated by a periodic generation of a Schr? dinger cat-like state. The decoherence process is highly nonlinear in the initial state amplitude and the decoherence time decreases rapidly for increasing amplitude.