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arXiv:quant-ph/0009068 · Physica A Statistical Mechanics and its Applications

Quantum Zeno-like effect and spectra of particles in cascade transition

Alexander D Panov

Published Nov 1, 2000• 3 citations
arXivHTMLPDF
DOI
10.1016/s0378-4371(00)00316-2

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Shr\\"odinger equation for two-step spontaneous cascade transition in a three-level quantum system is solved by means of Markovian approximation for non-Markovian integro-differential evolution equations for amplitudes of states. It is shown that both decay constant and radiation shift of initial level are affected by instability of intermediate level of the cascade. These phenomena are interpreted as the different manifestations of quantum Zeno-like effect. The spectra of particles emitted during the cascade transition are calculated in the general case and, in particular, for an unusual situation when the initial state is lower than the intermediate one. It is shown that the spectra of particles do not have a peak-like shape in the latter case.
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.