Quantum transfer through a nonMarkovian environment under frequent measurements and Zeno effect
Abstract
We study transitions of a particle between two wells, separated by a reservoir, under the condition that the particle is not detected in the reservoir. Conventional quantum trajectory theory predicts that such noresult continuous measurement would not affect these transitions. We demonstrate that it holds only for Markovian reservoirs (infinite bandwidth Λ). In the case of finite Λ, the probability of the particle's interwell transition is a function of the ratio Λ /ν, where ν is the frequency of measurements. This scaling tells us that in the limit ν →∞, the measurement freezes the initial state (the quantum Zeno effect), whereas for Λ →∞ it does not affect the particle's transition across the reservoir. The scaling is proved analytically by deriving a simple formula, which displays two regimes, with the Zeno effect and without the Zeno effect. It also supports a simple explanation of the Zeno effect entirely in terms of the energytime uncertainty relation, with no explicit use of the projection postulate. Experimental tests of our predictions are discussed.
 Publication:

Physical Review A
 Pub Date:
 August 2014
 DOI:
 10.1103/PhysRevA.90.022108
 arXiv:
 arXiv:1401.3159
 Bibcode:
 2014PhRvA..90b2108X
 Keywords:

 03.65.Xp;
 03.65.Yz;
 73.63.b;
 73.40.Gk;
 Tunneling traversal time quantum Zeno dynamics;
 Decoherence;
 open systems;
 quantum statistical methods;
 Electronic transport in nanoscale materials and structures;
 Tunneling;
 Quantum Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 5 pages, 2 figures