Dresden 2020 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 7: Statistical Physics (General) I
DY 7.8: Talk
Monday, March 16, 2020, 12:00–12:15, ZEU 160
The quantum first detection problem — •Felix Thiel1,2, David A. Kessler2, and Eli Barkai2 — 1Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany — 2Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
An observer prepares a quantum particle at position xin on a lattice and wants to find its (random) time of arrival T in the target position xd. To avoid complications related to wave function collapse and the quantum Zeno effect, he must adhere to a detection protocol. That means he attempts to detect the particle in the target at the times τ, 2τ, 3τ, , where τ is the detection period, a free parameter. The time T of the first successful detection attempt is the first detection time that generalizes a classical random walker’s first-passage time to the quantum realm. Such a situation can easily be implemented in optical quantum walk or waveguide experiments.
In this contribution, we outline the quantum first detection theory and its similarities to first passage theory. We obtain the probability Fn of first detection at the n-th attempt and focus on its asymptotic decay for large times. We present numerical and analytical results for tight-binding quantum walks on one or higher-dimensional simple-cubic lattices.