Passage-time distributions from a spin-boson detector model

Details Passage-time distributions from a spin-boson detector model Passage-time distributions from a spin-boson detector model

2006-10-06

arxiv.org/abs/quant-ph/0610041v2

Physical Review A 75, 012108 (2007)

Physics

Quantum Physics

11 pages, 6 figures; minor changes, references corrected; accepted for publication in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.75.012108

The passage-time distribution for a spread-out quantum particle to traverse a specific region is calculated using a detailed quantum model for the detector involved. That model, developed and investigated in earlier works, is based on the detected particle's enhancement of the coupling between a collection of spins (in a metastable state) and their environment. We treat the continuum limit of the model, under the assumption of the Markov property, and calculate the particle state immediately after the first detection. An explicit example with 15 boson modes shows excellent agreement between the discrete model and the continuum limit. Analytical expressions for the passage-time distribution as well as numerical examples are presented. The precision of the measurement scheme is estimated and its optimization discussed. For slow particles, the precision goes like $E^{-3/4}$, which improves previous $E^{-1}$ estimates, obtained with a quantum clock model.

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