Sub-Planck spots of Schroedinger cats and quantum decoherence

Wojciech Hubert Zurek

doi:10.1038/35089017

paper

Sub-Planck spots of Schroedinger cats and quantum decoherence

arXiv:quant-ph/0201118 · doi:10.1038/35089017

Abstract

Heisenberg's principle $^{1}$ states that the product of uncertainties of position and momentum should be no less than Planck's constant $ℏ$ . This is usually taken to imply that phase space structures associated with sub-Planck ( $≪ ℏ$ ) scales do not exist, or, at the very least, that they do not matter. I show that this deeply ingrained prejudice is false: Non-local "Schrödinger cat" states of quantum systems confined to phase space volume characterized by `the classical action' $A ≫ ℏ$ develop spotty structure on scales corresponding to sub-Planck $a = ℏ^{2} / A ≪ ℏ$ . Such structures arise especially quickly in quantum versions of classically chaotic systems (such as gases, modelled by chaotic scattering of molecules), that are driven into nonlocal Schrödinger cat -- like superpositions by the quantum manifestations of the exponential sensitivity to perturbations $^{2}$ . Most importantly, these sub-Planck scales are physically significant: $a$ determines sensitivity of a quantum system (or of a quantum environment) to perturbations. Therefore sub-Planck $a$ controls the effectiveness of decoherence and einselection caused by the environment $^{3 - 8}$ . It may also be relevant in setting limits on sensitivity of Schrödinger cats used as detectors.

Published in Nature 412, 712-717 (2001)

References in corpus (1)

Decoherence, einselection, and the quantum origins of the classical

Sub-Planck spots of Schroedinger cats and quantum decoherence

Abstract

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