Phonon Scharnhorst effect: Acoustic analogue of the vacuum-fluctuation-boosted speed of light

arXiv:2609.14155v1 Announce Type: cross Abstract: The Scharnhorst effect in quantum electrodynamics predicts a superluminal velocity shift $\delta c>0$ at low photon frequencies due to vacuum fluctuations between two mirrors. Although theoretically robust (no causality violation), the effect is extraordinarily small ($\delta c/c\approx 10^{-32}$ for mirrors $1\,\mu{\rm m}$ apart) and outside current experimental reach. Here we propose a condensed matter analogue, replacing the photons in the electromagnetic vacuum by phonon excitations of a Bose-Einstein condensate. In an idealized geometry, the two-dimensional surface of a cylinder (circumference $L$) at zero temperature, the axial speed of sound is increased due to zero-point fluctuations of the condensate by $\delta c/c\simeq 5\times 10^{-3}\,\tilde{g}$ at $L\simeq 2\,\xi$, to first order in the dimensionless interaction constant $\tilde{g}\simeq 10^{-1}$ of the Bose gas of healing length $\xi\simeq 1\,\mu{\rm m}$. This is 28 orders of magnitude larger than the photonic effect, basically because phonons have a self-interaction while photons only interact via massive electrons. We discuss the prospects for observation of the acoustic Scharnhorst effect, the main restriction being the low-temperature requirement.

Abstract:The Scharnhorst effect in quantum electrodynamics predicts a superluminal velocity shift $\delta c>0$ at low photon frequencies due to vacuum fluctuations between two mirrors. Although theoretically robust (no causality violation), the effect is extraordinarily small ($\delta c/c\approx 10^{-32}$ for mirrors $1\,\mu{\rm m}$ apart) and outside current experimental reach. Here we propose a condensed matter analogue, replacing the photons in the electromagnetic vacuum by phonon excitations of a Bose-Einstein condensate. In an idealized geometry, the two-dimensional surface of a cylinder (circumference $L$) at zero temperature, the axial speed of sound is increased due to zero-point fluctuations of the condensate by $\delta c/c\simeq 5\times 10^{-3}\,\tilde{g}$ at $L\simeq 2\,\xi$, to first order in the dimensionless interaction constant $\tilde{g}\simeq 10^{-1}$ of the Bose gas of healing length $\xi\simeq 1\,\mu{\rm m}$. This is 28 orders of magnitude larger than the photonic effect, basically because phonons have a self-interaction while photons only interact via massive electrons. We discuss the prospects for observation of the acoustic Scharnhorst effect, the main restriction being the low-temperature requirement.

Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)

arXiv:2609.14155 [cond-mat.quant-gas]

(or arXiv:2609.14155v1 [cond-mat.quant-gas] for this version)

https://doi.org/10.48550/arXiv.2609.14155 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Phonon Scharnhorst effect: Acoustic analogue of the vacuum-fluctuation-boosted speed of light

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