Quantum Trajectory method for the Quantum Zeno and anti-Zeno effects

Abstract

We perform stochastic simulations of the quantum Zeno and anti-Zeno effects for two level system and for the decaying one. Instead of simple projection postulate approach, a more realistic model of a detector interacting with the environment is used. The influence of the environment is taken into account using the quantum trajectory method. The simulation of the measurement for a single system exhibits the probabilistic behavior showing the collapse of the wave-packet. When a large ensemble is analysed using the quantum trajectory method, the results are the same as those produced using the density matrix method. The results of numerical calculations are compared with the analytical expressions for the decay rate of the measured system and a good agreement is found. Since the analytical expressions depend on the duration of the measurement only, the agreement with the numerical calculations shows that otherparameters of the model are not important.