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Journal of Mathematical Physics

Revisiting quantum Zeno effect and anti-Zeno effect: Universality vs non-universality

Kyungsun Na

Published Dec 1, 2021• 1 citation
Publisher

Abstract

Universality vs non-universality on the quantum Zeno effect and the anti-Zeno effect is discussed. It is well-known that the Zeno effect is a result of the branch point effect based on the constraint that the energy spectrum is bounded from below. On the other hand, we show that the anti-Zeno effect arises from the interference of multiple complex poles in the lower half energy plane on a larger time scale compared with the Zeno time. Since the production of extra complex poles depends on the characteristics of the interaction Hamiltonian, we emphasize that the anti-Zeno effect is model-dependent and non-universal, while the Zeno effect is a universal phenomenon independent of the form of the interaction.

DOI
10.1063/5.0050473

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We investigate the quantum Zeno and anti-Zeno effects in quantum dissipative systems by employing a hierarchical equations of motion approach which is beyond the usual Markovian approximation, the rotating wave approximation, and the perturbative approximation. The quantum Zeno and anti-Zeno dynamics of a biased qubit-boson model and a biased qutrit-boson model are provided as illustrative examples. It is found that (i) there exists multiple Zeno--anti-Zeno crossover phenomena, (ii) the non-Markovian characteristic of the bath may be favorable for the accessibility of the Zeno dynamics, and (iii) high bath temperature may add the difficulty in observing the quantum Zeno effect in quantum dissipative systems.
In this work, we study the decay behavior of a two-level system under the competing influence of a dissipative environment and repetitive measurements. The sign of the second derivative of the environmental spectral density function with respect to the system transition frequency is found to be a sufficient condition to distinguish between the quantum Zeno (negative) and the anti-Zeno (positive) effects raised by the measurements. We check our criterion for practical measurement intervals, which are larger than the conceptual Zeno time, in various environments. In particular, with the Lorentzian spectrum, the quantum Zeno and anti-Zeno phenomena are found to emerge respectively in the near-resonant and off-resonant cases. For the interacting spectra of hydrogenlike atoms, the quantum Zeno effect usually occurs and the anti-Zeno effect can rarely occur unless the transition frequency is close to the cut-off frequency. With a power-law spectrum, we find that sub-Ohmic and super-Ohmic environments lead to the quantum Zeno and anti-Zeno effects, respectively.