Nonlocality of the energy density for all single-photon states
- URL: http://arxiv.org/abs/2306.09793v3
- Date: Fri, 27 Oct 2023 13:01:20 GMT
- Title: Nonlocality of the energy density for all single-photon states
- Authors: Maxime Federico and Hans-Rudolf Jauslin
- Abstract summary: Nonlocality of single-photon states has been analyzed from several different but interrelared perspectives.
We propose a demonstration based on the electromagnetic energy density observable and on the anti-local property of the frequency operator $Omega=c(-Delta)1/2$.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The nonlocality of single-photon states has been analyzed from several
different but interrelared perspectives. In this article, we propose a
demonstration based on the electromagnetic energy density observable and on the
anti-local property of the frequency operator $\Omega=c(-\Delta)^{1/2}$. The
present proof is based on the standard quantization of the electromagnetic
field, which can be formulated equivalently in the momentum representations or
in the position representations of Landau and Peierls [Z. Phys. {\bf 62}, 188
(1930)] and of Bia{\l}ynicki-Birula [\textit{Progress in Optics}, edited by E.
Wolf (Elsevier, Amsterdam, 1996)]. Our proof extends to all single-photon
states the results of Bia{\l}ynicki-Birula, which were formulated for two
particular classes of states, those involving a uniform localization [Phys.
Rev. Lett. {\bf80}, 5247 (1998)] or alternatively states that are electrically
or magnetically localized [Phys.Rev. A {\bf79}, 032112 (2009)]. Our approach is
formulated in terms of Knight's definition of strict localization [J. Math.
Phys. {\bf 2}, 459 (1961)], based on the comparison of expectation values of
single-photon states of local observables with those of the vacuum.
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