  Traditional approach on quantum Zeno effect (QZE) and quantum anti-Zeno
effect (QAZE) in open quantum systems (implicitly) assumes the bath
(environment) state returning to its original state after each instantaneous
projective measurement on the system and thus ignores the cross-correlations of
the bath operators between different Zeno intervals. However, this assumption
is not generally true, especially for a bath with a considerably non-negligible
memory effect and for a system repeatedly projected into an initial general
superposition state. We find that in stark contrast to the result of a constant
value found in the traditional approach, the scaled average decay rate in unit
Zeno interval of the survival probability is generally time-dependent or has an
oscillatory behavior. In the case of strong bath correlation, the transition
between the QZE and QAZE depends sensitively on the number of measurements $N$.
For a fixed $N$, a QZE region predicted by the tradition approach may be in
fact already in the QAZE region. We illustrate our findings using an exactly
solvable open qubit system model with a Lorentzian bath spectral density, which
is directly related to realistic circuit cavity quantum electrodynamics
systems. Thus the results and dynamics presented here can be verified by
current superconducting circuit technology.
