Stochastic quantum trajectories demonstrate the Quantum Zeno Effect in an open spin system

We investigate the Quantum Zeno Effect in spin 1/2, spin 1 and spin 3/2 open quantum systems undergoing Rabi oscillations. The systems interact with an environment designed to perform continuous measurements of an observable, driving the systems stochastically towards one of the eigenstates of the corresponding operator. The system-environment coupling constant represents the strength of the measurement. Stochastic quantum trajectories are generated by unravelling a Markovian Lindblad master equation using the quantum state diffusion formalism. This is regarded as a better representation of system behaviour than consideration of the averaged evolution since the latter can mask the effect of measurement. Complete positivity is maintained and thus the trajectories can be considered as physically meaningful. Increasing the measurement strength leads to greater dwell by the system in the vicinity of the eigenstates of the measured observable and lengthens the time taken by the system to return to that eigenstate, thus demonstrating the Quantum Zeno Effect. For very strong measurement, the Rabi oscillations develop into randomly occurring near-instantaneous jumps between eigenstates. The stochastic measurement dynamics compete with the intrinsic, deterministic quantum dynamics of the system, each attempting to drive the system in the Hilbert space in different ways. As such, the trajectories followed by the quantum system are heavily dependent on the measurement strength which other than slowing down and adding noise to the Rabi oscillations, changes the paths taken in spin phase space from a circular precession into elaborate figures-of-eight