Quantum Zeno effect: Quantum shuffling and Markovianity

Instituto de Física Fundamental (IFF-CSIC), Serrano 123, 28006 Madrid, Spain
Annals of Physics (Impact Factor: 3.32). 12/2011; 327(4):1277-1289. DOI: 10.1016/j.aop.2011.12.012
Source: arXiv

ABSTRACT The behavior displayed by a quantum system when it is perturbed by a series of von Neumann measurements along time is analyzed. Because of the similarity between this general process with giving a deck of playing cards a shuffle, here it is referred to as quantum shuffling, showing that the quantum Zeno and anti-Zeno effects emerge naturally as two time limits. Within this framework, a connection between the gradual transition from anti-Zeno to Zeno behavior and the appearance of an underlying Markovian dynamics is found. Accordingly, although a priori it might result counterintuitive, the quantum Zeno effect corresponds to a dynamical regime where any trace of knowledge on how the unperturbed system should evolve initially is wiped out (very rapid shuffling). This would explain why the system apparently does not evolve or decay for a relatively long time, although it eventually undergoes an exponential decay. By means of a simple working model, conditions characterizing the shuffling dynamics have been determined, which can be of help to understand and to devise quantum control mechanisms in a number of processes from the atomic, molecular and optical physics.Graphical abstractHighlights► The concept of quantum shuffling process is introduced. ► The quantum Zeno and anti-Zeno effects are seen as time limits of this process. ► The quantum shuffling induces a Markovian dynamics in the quantum Zeno limit. ► Analytical results are found for a non-stationary Gaussian wave packet. ► A link between the two Zeno regimes and the wave-packet natural time scales is found.

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