Analyzing the Quantum Zeno and anti-Zeno effects using optimal projective measurements

Measurements in quantum mechanics can not only effectively freeze the state of the quantum system (the quantum Zeno effect) but also accelerate the time evolution of the system (the quantum anti-Zeno effect). In studies of the quantum Zeno and anti-Zeno effects, a quantum state, usually an excited state of the system, is prepared repeatedly by projecting the quantum state onto the initial state again and again. In this paper, we repeatedly prepare the initial quantum state in a different manner. Instead of only performing projective measurements, we allow unitary operations to be performed, on a very short time-scale, after each measurement. We can then repeatedly prepare the initial quantum state by performing some projective measurement and thereafter, after each measurement, performing a suitable unitary operation to repeatedly end up with the initial state. Our objective thereafter is to find the projective measurements that need to repeatedly performed such that we obtain the minimum possible effective decay rate of the quantum state. Consequently, the quantum state is maximally protected from its environment. We find that these optimized projective measurements keep on changing depending on the measurement time interval. We explicitly find the projective measurements that need to be performed, as well as the optimized effective decay rate, for a variety of system-environment models such as the population decay model, the pure dephasing model, the spin-boson model, and the large spin-boson model. We find that there can be considerable differences between this optimized effective decay rate and the usual decay rate obtained by repeatedly projecting onto the initial state. In particular, the Zeno and anti-Zeno regimes can be considerably modified.