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arXiv:2602.07116

Revealing quantum geometry of solids through vacuum fluctuations

Yugo Onishi, Liang Fu

cond-mat.mes-hallcond-mat.str-elquant-phSubmitted Feb 6, 2026• Announced Feb 10, 2026• Revised Sep 1, 2026 (v2)
v1 · Feb 6, 2026v2 · Sep 1, 2026
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Abstract

We show that quantum fluctuations of electromagnetic fields induce an extensive zero-point energy in insulators. The zero-point energy density is proportional to the quantum fluctuation of electric polarization in the many-body ground state, a fundamental quantum geometric property of solids known as the quantum weight. For fields produced by a superconducting LC circuit, the zero-point energy results in a repulsive force between the circuit and the material and an attractive force on the capacitor plates, which we call quantum geometric force. The force on the capacitor plates is proportional to the quantum weight, inversely proportional to the plate area, and independent of the plate distance. The proposed effects provide direct experimental access to the many-body quantum geometry and reveal a new quantum geometric effect in macroscopic solids induced by vacuum fluctuation.

Comments
5 pages, 2 figures + Ref + SM

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We show that quantum fluctuations of electromagnetic fields induce an extensive zero-point energy in insulators. The zero-point energy density is proportional to the quantum fluctuation of electric polarization in the many-body ground state, a fundamental quantum geometric property of solids known as the quantum weight. For fields produced by a superconducting LC circuit, the zero-point energy results in a repulsive force between the circuit and the material and an attractive force on the capacitor plates, which we call quantum geometric force. The force on the capacitor plates is proportional to the quantum weight, inversely proportional to the plate area, and independent of the plate distance. The proposed effects provide direct experimental access to the many-body quantum geometry and reveal a new quantum geometric effect in macroscopic solids induced by vacuum fluctuation.
The fluctuations in the phonon vacuum state can lead to zero point density fluctuations in a material, which in turn lead to local zero point fluctuations of the dielectric properties of the material. We argue that the density fluctuations lead to a fluctuating force on a test charge, such as an electron, located a short distance outside of the material. This force is due to fluctuating dipole moments inside the material, and produces Brownian motion of the electron. We calculate the mean squared velocity of the electron in both the normal and transverse direction relative to the boundary of the material. The result is nonzero in both directions, but larger in the normal case. We estimate the magnitude of this quantum Brownian motion and find that, in some cases, it can exceed the effects of both thermal motion and quantum momentum uncertainty. This suggests that the effect may be observable, and could constitute a source of quantum noise in nanoscale devices. It also potentially offers a means to remotely sense zero point density fluctuations in a material.
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A broadband electromagnetic source is important for scientific and technological applications. Quantum vacuum fluctuations, which manifest most prominently in the Casimir effect, provide a fundamentally broadband electromagnetic source. Here we explore a potential consequence of the broadband nature of quantum vacuum fluctuations, by showing that such fluctuations can enable measurement of material permittivity over a broad frequency range. Specifically, we consider the Casimir force in a parallel-plate geometry, with one plate covered by a nanoscopic thin film. Using a machine learning approach, we show that one can infer both the thickness of the film and its permittivity over a broad frequency range, starting from the dependency of the Casimir forces on the spacing between the two plates. Our work highlights the application potential of using vacuum fluctuations as a naturally-existing broadband electromagnetic source for material characterization, and shows that the inverse problem in Casimir force calculation can be solved with machine learning.
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Quantum fluctuations associated with the ground state of a system exist as a consequence of Heisenberg's uncertainty principle. These fluctuating fields manifest themselves indirectly through their influence on matter which has been extensively studied by considering e.g. the Casimir and Casimir-Polder force. More recently, these ground state fluctuations have been measured directly using nonlinear crystals by means of electro-optical sampling. Despite their common origin, these direct versus indirect evidence of ground-state fluctuations remain disjoint phenomena to date. Here we develop a theoretical framework for describing propagation of a quantized electric field through a nonlinear crystal, allowing for arbitrarily-shaped dispersive and absorptive environments. It can be used in different contexts, one of which is to forge the missing link between the different approaches to observing the quantum vacuum mentioned above. To demonstrate this we show that the change of the vacuum fluctuations induced by a macroscopic object can be directly observed using electro-optical sampling.