  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.

Quantum Physics;Statistical Mechanics