arXiv subjects

Giuseppe Bimonte

Publications and source records attributed to Giuseppe Bimonte.

At least 19 recordsLinked to original sources

arXiv2025

Complex orientation dependence of Casimir-Polder interaction induced by curvature and optical properties of the surface and the surrounding medium

We employ a multiple scattering expansion to systematically derive curvature corrections to the Casimir-Polder (CP) interaction between small an-isotropic particles and general magneto-dielectric surfaces. Our results, validated against exact solutions, reveal a complex, distance-dependent interplay between material properties and surface curvature in determining stable particle orientations. We demonstrate that even small surface curvature can induce or eliminate switches in the preferred orientation, a quantum effect that is diminished by thermal fluctuations. This work provides a crucial understanding of how to engineer nano-particle orientation through tune-able parameters, offering significant implications for micro- and nano-mechanical device design.

quant-ph↗

arXiv2025

High-Resolution Casimir Force Sensing Across a Superconducting Transition

The Casimir effect and superconductivity are foundational quantum phenomena whose interplay is an open question in physics, with significant implications for electron physics, quantum gravity, and high-temperature superconductivity. Determining how Casimir forces behave across a superconducting transition remains elusive due to the difficulty of realizing precise alignment, cryogenic operation, and isolating small force changes from competing effects. Recent theories predict milli-Pascal jumps in Casimir pressure across the transition, motivating experiments capable of reaching well below this regime. Here, we demonstrate an on-chip superconducting nanomechanical platform that overcomes these long-standing challenges, achieving the most parallel Casimir configurations to date. Our microchip-based parallel plates reach unprecedented area-to-separation ratios, exceeding past experiments across superconducting transitions by three orders of magnitude and yielding the strongest Casimir forces generated between compliant surfaces. Scanning tunneling microscopy (STM) directly detects the resonant motion of a suspended nanoscale plate with subatomic precision in lateral positioning and displacement, enabling suppression of van der Waals, electrostatic, and thermal effects. With verified micro-Pascal pressure resolution, our platform provides a credible entry point into a new field of quantum experiments, enabling exploration of Casimir-superconductivity interactions with the stability, parallelism, and sensitivity required to access this regime of physics.

quant-ph↗

arXiv2025

Proposal to measure the Casimir Effect Across the Superconducting Transition

The influence of the superconducting transition on the Casimir effect remains experimentally elusive. We propose a novel approach to address this challenge, exploiting the first-order superconducting transition induced in a thick film by a parallel magnetic field. Our calculations for a Au sphere opposite a Pb film, based on the Mattis-Bardeen theory, predict a jump in the Casimir force across the transition. By periodically modulating the magnetic field, we induce a corresponding modulation of the Casimir force that should be readily detectable with existing micro-torsional oscillator technology, opening a promising pathway to finally observe the long-sought Casimir-superconductivity coupling. A successful measurement of this effect would provide crucial insights into the fundamental nature of the Casimir force and its interaction with macroscopic quantum phenomena.

quant-ph↗

arXiv2025

Casimir force inadequacy in explaining a strong attractive force in a micrometer-sized narrow-gap re-entrant cavity

Pate et al. \cite{pate} investigated a macroscopic opto-mechanical system with a narrow-gap re-entrant cavity coupled to a SiN membrane resonator coated with Au or Nb. They observed a significant increase in the membrane's effective spring constant $k_{\rm eff}$ for sub-2-micron gaps $x$. This increase scales roughly with $x^{-4}$, suggesting an attractive force pulling the membrane towards the re-entrant Al post, with an $x^{-3}$ dependence. Attributing this force solely to the thermal Casimir effect is challenged by our detailed calculations (presented below). These calculations reveal that the Casimir force, at the investigated gap sizes, is orders of magnitude weaker than the observed force. This significant discrepancy necessitates an alternative explanation for the observed attraction.

quant-ph↗

arXiv2023

Casimir and Casimir-Polder Interactions for Magneto-dielectric Materials: Surface Scattering Expansion

We develop a general multiple scattering expansion (MSE) for computing Casimir forces between magneto-dielectric bodies and Casimir-Polder forces between polarizable particles and magneto-dielectric bodies. The approach is based on fluctuating electric and magnetic surface currents and charges. The surface integral equations for these surface fields can be formulated in terms of surface scattering operators (SSO). We show that there exists an entire family of such operators. One particular member of this family is only weakly divergent and allows for a MSE that appears to be convergent for general magneto-dielectric bodies. We proof a number of properties of this operator, and demonstrate explicitly convergence for sufficiently low and high frequencies, and for perfect conductors. General expressions are derived for the Casimir interaction between macroscopic bodies and for the Casimir-Polder interaction between particles and macroscopic bodies in terms of the SSO, both at zero and finite temperatures. An advantage of our approach above previous scattering methods is that it does not require the knowledge of the scattering amplitude (T-operator) of the bodies. A number of simple examples are provided to demonstrate the use of the method. Some applications of our approach have appeared previously [T. Emig, G. Bimonte, Phys. Rev. Lett. 130, 200401 (2023)]. Here we provide additional technical aspects and details of our approach.

quant-ph↗

arXiv2023

Multiple scattering expansion for dielectric media: Casimir effect

Recent measurements of Casimir forces have provided evidence of an intricate modification of quantum fluctuations of the electromagnetic field in complex geometries. Here we introduce a multiple scattering description for Casimir interactions between bodies of arbitrary shape and material composition, admitting an expansion as a sequence of inter- and intra-body wave scatterings. Interactions in complex geometries can be computed within the current experimental resolution from typically a few wave scatterings, notably without any a priori knowledge of the scattering amplitudes of the bodies. Some first applications demonstrate the power of the approach.

quant-ph↗

arXiv2022

Something Can Come of Nothing: Surface Approaches to Quantum Fluctuations and the Casimir Force

The Casimir force provides a striking example of the effects of quantum fluctuations in a mesoscopic system. Because it arises from the objects' electromagnetic response, the necessary calculations in quantum field theory are most naturally expressed in terms of electromagnetic scattering from each object. In this review we illustrate a variety of such techniques, with a focus on those that can be expressed in terms of surface effects, including both idealized boundary conditions and their physical realization in terms of material properties.

quant-ph↗

arXiv2021

Unifying Theory for Casimir Forces: Bulk and Surface Formulations

The principles of the electromagnetic fluctuation-induced phenomena such as Casimir forces are well understood. However, recent experimental advances require universal and efficient methods to compute these forces. While several approaches have been proposed in the literature, their connection is often not entirely clear, and some of them have been introduced as purely numerical techniques. Here we present a unifying approach for the Casimir force and free energy that builds on both the Maxwell stress tensor and path integral quantization. The result is presented in terms of either bulk or surface operators that describe corresponding current fluctuations. Our surface approach yields a novel formula for the Casimir free energy. The path integral is presented both within a Lagrange and Hamiltonian formulation yielding different surface operators and expressions for the free energy that are equivalent. We compare our approaches to previously developed numerical methods and the scattering approach. The practical application of our methods is exemplified by the derivation of the Lifshitz formula.

quant-ph↗

arXiv2021

Casimir-Polder shift of ground-state hyperfine Zeeman sub-levels of hydrogen isotopes in a micron-sized metallic cavity at finite temperature

The frequencies of transitions between hyperfine levels of ground-state atoms can be measured with exquisite precision using magnetic-resonance techniques. This makes hyperfine transitions ideal probes of QED effects originating from the interaction of atoms with the quantized electromagnetic field. One of the most remarkable effects predicted by QED is the Casimir-Polder shift experienced by the energy levels of atoms placed near one or more dielectric objects. Here we compute the Casimir-Polder shift and the width of hyperfine transitions between ground-state Zeeman sub-levels of an hydrogen atom placed in a micron-sized metallic cavity, over a range of temperatures extending from cryogenic temperatures to room temperature. Results are presented also for deuterium and tritium. We predict shifts of the hyperfine transitions frequencies of a few tens of Hz that might be measurable with present-day magnetic resonance apparatus.

quant-ph↗

arXiv2021

Measurement of the Casimir Force between 0.2 and 8 mum: Experimental Procedures and Comparison with Theory

We present results on the determination of the differential Casimir force between an Au-coated sapphire sphere and the top and bottom of Au-coated deep silicon trenches performed by means of the micromechanical torsional oscillator in the range of separations from 0.2 to 8 $\upmu$m. The random and systematic errors in the measured force signal are determined at the 95\% confidence level and combined into the total experimental error. The role of surface roughness and edge effects is investigated and shown to be negligibly small. The distribution of patch potentials is characterized by Kelvin probe microscopy, yielding an estimate of the typical size of patches, the respective r.m.s. voltage and their impact on the measured force. A comparison between the experimental results and theory is performed with no fitting parameters. For this purpose, the Casimir force in the sphere-plate geometry is computed independently on the basis of first principles of quantum electrodynamics using the scattering theory and the gradient expansion. In doing so, the frequency-dependent dielectric permittivity of Au is found from the optical data extrapolated to zero frequency by means of the plasma and Drude models. It is shown that the measurement results exclude the Drude model extrapolation over the region of separations from 0.2 to 4.8~$\upmu$m, whereas the alternative extrapolation by means of the plasma model is experimentally consistent over the entire measurement range. A discussion of the obtained results is provided.

quant-ph↗

arXiv2019

Probing the non-Planckian spectrum of thermal radiation in a micron-sized cavity with a spin-polarized atomic beam

It is commonly thought that thermal photons with transverse electric polarization cannot exist in a planar metallic cavity whose size $a$ is smaller than the thermal wavelength $λ_T$, due to absence of modes with $λ< 2a$. Computations based on a realistic model of the mirrors contradict this expectation, and show that a micron-sized metallic cavity is filled with non-resonant radiation having transverse electric polarization, following a non-Planckian spectrum, whose average density at room temperature is orders of magnitudes larger than that of a black-body. We show that the spectrum of this radiation can be measured by observing the transition rates between hyperfine ground-state sub-levels $1S_{1/2}(F,m_F) \rightarrow 1S_{1/2}(F',m'_F)$ of D atoms passing in the gap between the mirrors of a Au cavity. Such a measurement would also shed light on a puzzle in the field of dispersion forces, regarding the sign and magnitude of the thermal Casimir force. Recent experiments with Au surfaces led to contradictory results, whose interpretation is much controversial.

quant-ph↗

arXiv2019

Apparatus to probe the influence on the Casimir effect of the Mott-Anderson metal-insulator transition in doped semiconductors

We describe an isoelectronic differential apparatus designed to observe the influence on the Casimir force of the Mott-Anderson metal-insulator transition in doped semiconductors. Alternative theories of dispersion forces lead to different predictions for this effect. The investigation of this problem by standard apparatus, based on absolute measurements of the Casimir force, is very difficult because the effect is small in the region of sub-micron separations, where the Casimir force can be measured precisely. The differential apparatus described here is immune by design to several sources of error that blur the interpretation of Casimir experiments, like electrostatic patches, inaccurate determination of plates separation, surface roughness and errors in the optical data. With the help of the proposed setup it should be possible to establish conclusively which among the alternative theories of the Casimir effect for semiconducting test bodies is correct.

cond-mat.mes-hall↗

arXiv2019

On the Casimir effect between superconductors

A recent experiment [R. A. Norte et al. Phys. Rev. Lett. {\bf 121}, 030405 (2018)] probed the variation of the Casimir force between two closely spaced thin Al films, as they transition into a superconducting state, observing a null result. We present here computations of the Casimir effect for superconductors, based on the Mattis-Bardeen formula for their optical response. We show that for the Al cavity used in the experiment the effect of the transition is over two hundred and fifty times smaller than the experimental sensitivity, in agreement with the observed null result. We demonstrate that a large enhancement of the effect can be achieved by using a cavity consisting of a Au mirror and a superconducting NbTiN film. We estimate that the effect of the superconducting transition would be observable with the proposed Au-NbTiN configuration, if the sensitivity of the apparatus could be increased by an order of magnitude.

quant-ph↗

arXiv2018

Beyond-proximity-force-approximation Casimir force between two spheres at finite temperature II: plasma versus Drude modeling, grounded versus isolated spheres

A recent experiment [J. L. Garrett, D. A. T. Somers, and J. N. Munday, Phys. Rev. Lett {\bf 120}, 040401 (2018)] measured for the first time the gradient of the Casimir force between two gold spheres in vacuum at room temperature, and placed a bound on the magnitude of the deviation of the measured force from the proximity force approximation (PFA). The present work extends a previous theoretical analysis of this experiment [G. Bimonte, Phys. Rev. D {\bf 97}, 085011 (2018)], by analyzing in detail how the magnitude of the deviation from PFA is affected by the inclusion or neglect of ohmic dissipation at zero frequency, a much debated issue in the current Casimir literature, which goes by the name of the Drude vs plasma controversy. We analyze as well the effect of connecting the plates to charge reservoirs, which is the standard configuration used in Casimir experiments. We describe a simple and effective decimation procedure, allowing for a faster computation of the Casimir force for large aspect ratios of the system.

quant-ph↗

arXiv2018

Beyond-PFA Casimir Force between two spheres at finite temperature

A recent experiment [J.L. Garrett et al., Phys. Rev. Lett {\bf 120}, 040401 (2018)] measured for the first time the gradient of the Casimir force between two gold spheres at room temperature. The theoretical analysis of the data was carried out using the standard Proximity Force Approximation (PFA). A fit of the data, using a parametrization of the force valid for the sphere-plate geometry, was used by the authors to place a bound on deviations from PFA. Motivated by this work, we compute the Casimir force between two gold spheres at finite temperature. The semi-analytic formula for the Casimir force that we construct is valid for all separations, and can be easily used to interpret future experiments in both the sphere-plate and sphere-sphere configurations. We describe the correct parametrization of the corrections to PFA for two spheres that should be used in data analysis.

quant-ph↗

arXiv2017

Going beyond PFA: a precise formula for the sphere-plate Casimir force

Quantum fluctuations of the electromagnetic field in the medium surrounding two discharged macroscopic polarizable bodies induce a force between the two bodies, the so called Casimir force. In the last two decades many experiments have accurately measured this force, and significant efforts are made to harness it in the actuation of micro and nano machines. The inherent many body character of the Casimir force makes its computation very difficult in non-planar geometries, like the standard experimental sphere-plate configuration. Here we derive an approximate semi-analytic formula for the sphere-plate Casimir force, which is both easy to compute numerically and very accurate at all distances. By a comparison with the fully converged exact scattering formula, we show that the error made by the approximate formula is indeed much smaller than the uncertainty of present and foreseeable Casimir experiments.

quant-ph↗

arXiv2017

Classical Casimir interaction of perfectly conducting sphere and plate

We study the Casimir interaction between perfectly conducting sphere and plate in the classical limit of high temperatures. By taking the small-distance expansion of the exact scattering formula, we compute the leading correction to the Casimir energy beyond the commonly employed proximity force approximation. We find that for a sphere of radius $R$ at distance $d$ from the plate the correction is of the form $\ln^2 (d/R)$, in agreement with indications from recent large-scale numerical computations. We develop a fast-converging numerical scheme for computing the Casimir interaction to high precision, based on bispherical partial waves, and we verify that the short-distance formula provides precise values of the Casimir energy also for fairly large distances.

quant-ph↗

arXiv2016

Spectroscopic Probe of the van der Waals Interaction between Polar Molecules and a Curved Surface

We study the shift of rotational levels of a diatomic polar molecule due to its van der Waals (vdW) interaction with a gently curved dielectric surface at temperature $T$, and submicron separations. The molecule is assumed to be in its electronic and vibrational ground state, and the rotational degrees are described by a rigid rotor model. We show that under these conditions retardation effects and surface dispersion can be neglected. The level shifts are found to be independent of $T$, and given by the quantum state averaged classical electrostatic interaction of the dipole with its image on the surface. We use a derivative expansion for the static Green's function to express the shifts in terms of surface curvature. We argue that the curvature induced line splitting is experimentally observable, and not obscured by natural line widths and thermal broadening.

quant-ph↗