Exponential decay in Quantum Mechanics, spectral meaning of resonances, quantum Zeno effect

Petr Hruška

Kofman, Kurizki

Vladimir I. Kruglov, Konstantin A. Makarov, B. S. Pavlov +1 more

Yuichiro Matsuzaki, Hirotaka Tanaka

We theoretically propose a scheme for verification of quantum Zeno effect (QZE) to suppress a decay process with Nuclear Magnetic Resonance (NMR). Nuclear spins are affected by low frequency noise, and so one can naturally observe non-exponential decay behavior, which is prerequisite in observing QZE. We also describe that a key component for QZE, namely measurements on the nuclear spin, can be realized with NMR in the current technology

Elena Rufeil Fiori, Horacio M. Pastawski

S. Longhi [1] studied the survival probability P(t) of an unstable state coupled to a tight-binding lattice finding an exact analytical solution that describes the nonexponential decay. When the first coupling is smaller than the others, he shows that P(t) has a natural decomposition into two terms; one is the exponential decay, consistent with the Gamow's approach, and the other is the correction to this decay. The first purpose of this Comment is to show that the condition imposed on the system; the site energy of the first site is set in the center of the band, limits the generality of the results. A decomposition based on the spectral properties of the system removes this restriction [2]. Other point of this Comment is that, for the weak coupling limit, the author stated that a Zeno effect occurs for t less than t*, where t* is the smallest root of the equation g_eff(t*)=g_0, and for the strong coupling limit an anti-Zeno effect occurs for t close to t**, where t** is the first peak of g_eff. By using a spectral formulation we show that, the anti-Zeno effect not only requires a strong coupling limit, also is necessary to choose the resonance energy and width such that a destructive interference can occur. We present this interference and give an analytical expression and physically interpretation for t* and t**.

Hayato Goto, Kouichi Ichimura

The quantum Zeno effect for exponentially decaying systems predicted by Koshino Shimizu [Phys. Rev. Lett. 92, 030401 (2004)] is reexamined. A formula for the instantaneous decay rate reduced by the quantum Zeno effect is derived in the case of an exponentially decaying system. The present approach is based on the standard approaches in quantum optics: a master equation and a quantum Langevin equation. This approach provides a phenomenological interpretation of the Koshino-Shimizu model.