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Unification of quantum Zeno-anti Zeno effects and parity-time symmetry breaking transitions
The decay of any unstable quantum state can be inhibited or enhanced by
carefully tailored measurements, known as the quantum Zeno effect (QZE) or
anti-Zeno effect (QAZE). To date, studies of QZE (QAZE) transitions have since
expanded to various system-environment coupling, in which the time evolution
can be suppressed (enhanced) not only by projective measurement but also
through dissipation processes. However, a general criterion, which could extend
to arbitrary dissipation strength and periodicity, is still lacking. In this
letter, we show a general framework to unify QZE-QAZE effects and parity-time
(PT) symmetry breaking transitions, in which the dissipative Hamiltonian
associated to the measurement effect is mapped onto a PT-symmetric non-
Hermitian Hamiltonian, thus applying the PT symmetry transitions to distinguish
QZE (QAZE) and their crossover behavior. As a concrete example, we show that,
in a two-level system periodically coupled to a dissipative environment, QZE
starts at an exceptional point (EP), which separates the PT-symmetric (PTS)
phase and PT-symmetry broken (PTB) phase, and ends at the resonance point (RP)
of the maximum PT-symmetry breaking; while QAZE extends the rest of PTB phase
and remains the whole PTS phase. Such findings reveal a hidden relation between
QZE-QAZE and PTS-PTB phases in non-Hermitian quantum dynamics