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 no-result continuous measurement would not affect these transitions. We demonstrate that it holds only for Markovian reservoirs (infinite bandwidth ). In the case of finite , the probability of the particle's interwell transition is a function of the ratio , where is the frequency of measurements. This scaling tells us that in the limit , the measurement freezes the initial state (the quantum Zeno effect), whereas for 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 energy-time uncertainty relation, with no explicit use of the projection postulate. Experimental tests of our predictions are discussed.
- Received 14 January 2014
- Revised 6 June 2014
DOI:https://doi.org/10.1103/PhysRevA.90.022108
©2014 American Physical Society