Unification of quantum Zeno–anti Zeno effects and parity-time symmetry breaking transitions

Abstract

The decay of an unstable quantum state can be inhibited or enhanced by tailored measurements, known as quantum Zeno effect (QZE) or anti Zeno effect (QAZE). QZE(QAZE) has been intensively explored in terms of the cases of various system-environment couplings, where the time evolution can be affected either by the projective measurements, or through the dissipative couplings to the environment. A general relation between QZE(QAZE) and the dissipation, for arbitrary dissipation strength and periodicity, is yet to be developed. In this paper, we show a framework to unify the QZE(QAZE) and the parity-time (𝒫𝒯) symmetry breaking transition, where the pure dissipative Hamiltonian is mapped onto a 𝒫𝒯 symmetric non-Hermitian Hamiltonian. This method uses the 𝒫𝒯 symmetry transitions to distinguish QZE and QAZE, and can be applied to analyze the crossover behavior between these two effects. Using a heuristic example of a two-level system which is coupled to environment by periodical dissipation, we show the relation diagram between the QZE(QAZE) and the 𝒫𝒯 symmetry breaking transition, in which the QZE appears at an exceptional point that separates the 𝒫𝒯 symmetric (PTS) phase and the 𝒫𝒯 symmetry broken (PTSB) phase, and ends at the resonance point of the maximum 𝒫𝒯 symmetry breaking; after that, QAZE exists at the rest of the PTSB phase and remains in the next PTS phase. This interesting finding reveals a hidden relation between the QZE–QAZE and PTS-PTSB phases in a non-Hermitian quantum system.