Zeno And Anti-zeno Effects In Classical Noise

The quantum Zeno effect and anti-Zeno effect is closely linked with the applications of the basic theory in quantum mechanics and quantum technology,so they have raised and continue to gather widespread interest in terms of theory and experiment for years.Most of the existing studies are devoted to the quantum Zeno and anti-Zeno effects in open quantum systems under quantization environment,little attention has been paid to the quantum Zeno dynamics behavior under classical noise.In this paper,we analyze the quantum Zeno and anti-Zeno dynamics under the random telegraph noise and the family of low-frequency noise with 1/f~αspectrum.We use effective decay rate to describe the transition between zeno effect and anti-Zeno effect of a two-level system under the frequent measurements quanti-tatively.Based on qualitative analysis of effective decay rate,we find that the two kinds of classical noise under different conditions have significant influence on the Zeno and anti-Zeno dynamics.For random telegraph noise,when the switching rateγ>2,the coupling strength between the system and the environment is small,the dynamic behavior of the sys-tem presents the Markovian characteristics,the transition between Zeno effect and anti-Zeno effect occurs when the measurement time interval increases.On the contrary,whenγ<2,the coupling strength between the system and the environment is large,the dynamic behav-ior of the system presents the non-Markovian characteristics,the effective decay rate shows damped oscillation as the measurement time interval increases,which indicates that the quan-tum Zeno effect and anti-Zeno effect appear alternately.In the case of colored noise,different coefficientαand number of fluctuators N_fwill make the effective decay rate change.We find that for fixed N_f,whenαis small,the oscillation of effective decay rate is not obvious,which indicates that the quantum anti-Zeno effect is not obvious,whenαincreases,the os-cillation of effective decay rate begin to appear and gradually obvious,which indicates that quantum anti-Zeno effect appear significantly and quantum Zeno effect and anti-Zeno effect appear alternately with the measurement time interval increases.For fixedα,the coupling strength between the system and the environment weakens with the increase of N_f,the oscil-lation of effective decay rate disappear gradually.This is because when the N_fincreases,a number of independent noise and collective behavior will show Gaussian features according to the central limit theorem of probability theory.Therefore,with the increase of N_f,the evolution of the system gradually changed from non-Gaussian to Gaussian.