Some Studies about Quantum Zeno Effecta

A. G. Klein

Hiromichi Nakazato, Mikio Namiki, Saverio Pascazio +1 more

Zhenbo Ni, Yonggang Peng, Yujun Zheng

The quantum Zeno effect (QZE) is widely employed in quantum engineering due to the issue of frequent measurements freezing a quantum system. In this study, the quantum Zeno factor is introduced to characterize the quantum Zeno capacity of a quantum system. The quantum Zeno factor reveals that the quantum Zeno effect is dependent on the evolution mode of quantum states, which is semi-irrelevant to conventional energy uncertainty and extends the QZE domain. The Zeno factor provides a new consideration to qualify the (anti-)Zeno capacity of a quantum system for its applications: a large quantum Zeno factor value indicates that a quantum system is of a QZE quality. The numerical results of the quantum Zeno capacity are shown using two typical examples: tailing the dynamic evolution modes using the quantum Zeno factor in a three-level system, and quantifying the message exchange between qubits in a coupled qubit system using a quantum Zeno factor.

Hiromichi Nakazato, Mikio Namiki, Saverio Pascazio +1 more

Kishore Thapliyal, Anirban Pathak, Jan Peřina

Quantum Zeno and anti-Zeno effects are studied in a symmetric nonlinear optical coupler, which is composed of two nonlinear (${\ensuremath{\chi}}^{\left(2\right)}$) waveguides that are interacting with each other via the evanescent waves. Both waveguides operate under second harmonic generation. However, to study quantum Zeno and anti-Zeno effects one of them is considered as the system and the other one is considered as the probe. Considering all the fields involved as weak, a completely quantum mechanical description is provided, and the analytic solutions of Heisenberg's equations of motion for all the field modes are obtained using a perturbative technique. Photon number statistics of the second harmonic mode of the system is shown to depend on the presence of the probe, and this dependence is considered as quantum Zeno and anti-Zeno effects. Further, it is established that as a special case of the momentum operator for ${\ensuremath{\chi}}^{\left(2\right)}\ensuremath{-}{\ensuremath{\chi}}^{\left(2\right)}$ symmetric coupler we can obtain momentum operator of ${\ensuremath{\chi}}^{\left(2\right)}\ensuremath{-}{\ensuremath{\chi}}^{\left(1\right)}$ asymmetric coupler with linear (${\ensuremath{\chi}}^{\left(1\right)}$) waveguide as the probe, and, in such a particular case, the expressions obtained for Zeno and anti-Zeno effects with nonlinear probe (which we referred to as nonlinear quantum Zeno and anti-Zeno effects) may be reduced to the corresponding expressions with linear probe (which we referred to as the linear quantum Zeno and anti-Zeno effects). Linear and nonlinear quantum Zeno and anti-Zeno effects are rigorously investigated, and it is established that, in the stimulated case, we may switch between quantum Zeno and anti-Zeno effects just by controlling the phase of the second harmonic mode of the system or probe.

Baidyanath Misra, Ioannis E. Antoniou