Quantum transfer through a non-Markovian environment under frequent measurements and Zeno effect

Luting Xu, Yunshan Cao, Xin-Qi Li, YiJing Yan, and Shmuel Gurvitz
Phys. Rev. A 90, 022108 – Published 11 August 2014

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 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 energy-time uncertainty relation, with no explicit use of the projection postulate. Experimental tests of our predictions are discussed.

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  • Received 14 January 2014
  • Revised 6 June 2014

DOI:https://doi.org/10.1103/PhysRevA.90.022108

©2014 American Physical Society

Authors & Affiliations

Luting Xu1, Yunshan Cao1, Xin-Qi Li1,*, YiJing Yan2, and Shmuel Gurvitz3,4,†

  • 1Department of Physics, Beijing Normal University, Beijing 100875, China
  • 2Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong
  • 3Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 76100, Israel
  • 4Beijing Computational Science Research Center, Beijing 100084, China

  • *lixinqi@bnu.edu.cn
  • shmuel.gurvitz@weizmann.ac.il

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Issue

Vol. 90, Iss. 2 — August 2014

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