Eur. Phys. J. Plus (2022) 137: 778
https://doi.org/10.1140/epjp/s13360-022-02986-z

Regular Article

Uncertainties and entropic uncertainties for nonstatic light waves: periodic uncertainty enhancement/collapse and their statistical effects

Department of Nanoengineering, Kyonggi University, Yeongtong-gu, 16227, Suwon, Gyeonggi-do, Republic of Korea

^a choiardor@hanmail.net

Received: 20 March 2022
Accepted: 22 June 2022
Published online: 6 July 2022

Abstract

Nonstatic light waves appear when the electromagnetic parameters in a medium vary in time. Recent reports show that nonstatic waves can also take place even in the static environment, where the electromagnetic parameters do not vary. Albeit there are no changes of electromagnetic parameters in this case, the nonstatic waves exhibit a periodic behavior which is that a belly and a node emerge in turn successively in the evolution of the wave in quadrature space. We investigate Heisenberg’s uncertainty products, Schrödinger–Robertson’s, and entropy-based uncertainties for such quantum waves in the Fock states. Interestingly, all kinds of the uncertainties including entropy-based ones and the joint uncertainties for quadratures q and p exhibit periodic behaviors over time according to the appearance of bellies and nodes in the wave evolution. Both the uncertainties and entropic uncertainties for each quadrature are maximum when the wave packet in the corresponding space constitutes a belly, while they are minimum when the wave in the same space constitutes a node. However, joint uncertainties are minimum not only when the wave constitutes a node but when a belly as well. These uncertainty profiles are manifestation of the wave nonstaticity. The corresponding statistical complexity measures also reflect the nonstaticity of waves.