Papers by Giuseppe Bimonte
It is commonly thought that thermal photons with transverse electric polarization cannot exist in... more 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 λT , 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, mF) → 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.
A recent experiment [J. L. Garrett, D. A. T. Somers, and J. N. Munday, Phys. Rev. Lett 120, 04040... more A recent experiment [J. L. Garrett, D. A. T. Somers, and J. N. Munday, Phys. Rev. Lett 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 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 conductors 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.
A recent experiment [Norte et al. Phys. Rev. Lett. 121, 030405 (2018)] probed the variation of th... more A recent experiment [Norte et al. Phys. Rev. Lett. 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 system used in the experiment the effect of the transition is over 250 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 system 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.
We describe an isoelectronic differential apparatus designed to observe the influence on the Casi... more 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 submicron 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, such as 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.
Physical Review D, 2018
A recent experiment [J.L. Garrett et al., Phys. Rev. Lett 120, 040401 (2018)] measured for the fi... more A recent experiment [J.L. Garrett et al., Phys. Rev. Lett 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.
Annual Review of Condensed Matter Physics, 2017
Quantum and thermal fluctuations of electromagnetic waves are the 2 Author et al.
Physical Review B, 2012
We present a detailed derivation of heat radiation, heat transfer, and (Casimir) interactions for... more We present a detailed derivation of heat radiation, heat transfer, and (Casimir) interactions for N arbitrary
objects in the framework of fluctuational electrodynamics in thermal nonequilibrium. The results can be expressed
as basis-independent trace formulas in terms of the scattering operators of the individual objects. We prove that
heat radiation of a single object is positive, and that heat transfer (for two arbitrary passive objects) is from
the hotter to a colder body. The heat transferred is also symmetric, exactly reversed if the two temperatures are
exchanged. Introducing partial wave expansions, we transform the results for radiation, transfer, and forces into
traces of matrices that can be evaluated in any basis, analogous to the equilibrium Casimir force. The method
is illustrated by (re)deriving the heat radiation of a plate, a sphere, and a cylinder. We analyze the radiation of
a sphere for different materials, emphasizing that a simplification often employed for metallic nanospheres is
typically invalid. We derive asymptotic formulas for heat transfer and nonequilibrium interactions for the cases
of a sphere in front a plate and for two spheres, extending previous results. As an example, we show that a hot
nanosphere can levitate above a plate with the repulsive nonequilibrium force overcoming gravity, an effect that
is not due to radiation pressure.
EPL, 2012
The proximity force approximation (PFA) relates the interaction between closely
spaced, smoothly ... more The proximity force approximation (PFA) relates the interaction between closely
spaced, smoothly curved objects to the force between parallel plates. Precision experiments on
Casimir forces necessitate, and spur research on, corrections to the PFA. We use a derivative
expansion for gently curved surfaces to derive the leading curvature modifications to the PFA. Our
methods apply to any homogeneous and isotropic materials; here we present results for Dirichlet
and Neumann boundary conditions and for perfect conductors. A Pad´e extrapolation constrained
by a multipole expansion at large distance and our improved expansion at short distances, provides
an accurate expression for the sphere/plate Casimir force at all separations.
Physical Review A, 2009
We develop an exact method for computing Casimir forces and the power of radiative heat transfer ... more We develop an exact method for computing Casimir forces and the power of radiative heat transfer between
two arbitrary nanostructured surfaces out of thermal equilibrium. The method is based on a generalization of
the scattering approach recently used in investigations on the Casimir effect. Analogously to the equilibrium
case, we find that also out of thermal equilibrium the shape and composition of the surfaces enter only through
their scattering matrices. The expressions derived provide exact results in terms of the scattering matrices of
the intervening surfaces.
APPLIED PHYSICS LETTERS, 2012
A widely used method for estimating Casimir interactions [H. B. G. Casimir, Proc. K. Ned. Akad.
W... more A widely used method for estimating Casimir interactions [H. B. G. Casimir, Proc. K. Ned. Akad.
Wet. 51, 793 (1948)] between gently curved material surfaces at short distances is the proximity
force approximation (PFA). While this approximation is asymptotically exact at vanishing
separations, quantifying corrections to PFA has been notoriously difficult. Here, we use a
derivative expansion to compute the leading curvature correction to PFA for metals (gold) at room
temperature. We derive an explicit expression for the amplitude ^h 1 of the PFA correction to the
force gradient for axially symmetric surfaces. In the non-retarded limit, the corrections to the
Casimir free energy are found to scale logarithmically with distance. For gold, ^h 1 has an unusually
large temperature dependence.
Physical Review B, 2016
Differential force measurements between spheres coated with either nickel or gold and rotating di... more Differential force measurements between spheres coated with either nickel or gold and rotating disks with periodic distributions of nickel and gold are reported. The rotating samples are covered by a thin layer of titanium and a layer of gold. While titanium is used for fabrication purposes, the gold layer (nominal thicknesses of 21, 37, 47, and 87 nm) provides an isoelectronic environment, and is used to nullify the electrostatic contribution but allow the passage of long wavelength Casimir photons. A direct comparison between the experimental results and predictions from Drude and plasma models for the electrical permittivity is carried out. In the models, the magnetic permeability of nickel is allowed to change to investigate its effects. Possible sources of errors, both in the experimental and theoretical sides, are taken into account. It is found that a Drude response with magnetic properties of nickel taken into account is unequivocally ruled out. The full analysis of the data indicates that a dielectric plasma response with the magnetic properties of Ni included shows good agreement with the data. Neither a Drude nor a plasma dielectric response provide a satisfactory description if the magnetic properties of nickel are disregarded.
Physical Review B, 2015
Isoelectronic differential force measurements provide a unique opportunity to probe controversial... more Isoelectronic differential force measurements provide a unique opportunity to probe controversial features of
the thermal Casimir effect that are still much debated in the current literature. Isolectronic setups offer two major
advantages over conventional Casimir setups. On the one hand, they are immune from electrostatic forces caused
by potential patches on the plates surfaces that plague present Casimir experiments, especially for separations in
the micron range. On the other hand, they can strongly enhance the discrepancy between alternative theoretical
models that have been proposed to estimate the thermal Casimir force for metallic and magnetic surfaces. Thanks
to these two features, isoelectronic differential experiments should allow one to establish conclusively which
among these models correctly describes the thermal Casimir force.
Physical Review Letters, 2014
We describe a Casimir setup consisting of two aligned sinusoidally corrugated Ni surfaces, one of... more We describe a Casimir setup consisting of two aligned sinusoidally corrugated Ni surfaces, one of which
is “hidden” by a thin opaque layer of gold with a flat exposed surface. The gold layer acts as a low-pass
filter that allows for a clean observation of the controversial thermal Casimir force between the
corrugations, with currently available Casimir apparatuses. The proposed scheme of measurement, based
on the phase-dependent modulation of the Casimir force, requires no electrostatic calibrations of the
apparatus, and is unaffected by uncertainties in the knowledge of the optical properties of the surfaces. This
scheme should allow for an unambiguous discrimination between alternative theoretical prescriptions that
have been proposed in the literature for the thermal Casimir effect.
Physical Review Letters, 2014
We describe a Casimir apparatus based on a differential force measurement between a Au-coated sph... more We describe a Casimir apparatus based on a differential force measurement between a Au-coated sphere
and a planar slab divided in two regions, one of which is made of high-resistivity (dielectric) Si, and the
other of Au. The crucial feature of the setup is a semitransparent plane parallel conducting overlayer,
covering both regions. The setup offers two important advantages over existing Casimir setups. On one
hand, it leads to a large amplification of the difference between the Drude and the plasma prescriptions that
are currently used to compute the thermal Casimir force. On the other hand, thanks to the screening power
of the overlayer, it is in principle immune from electrostatic forces caused by potential patches on the plates
surfaces, that plague present large distance Casimir experiments. If a semitransparent conductive overlayer
with identical patch structure over the Au-Si regions of the plate can be manufactured, similar to the opaque
overlayers used in recent searches of non-Newtonian gravitational forces based on the isoelectronic
technique, the way will be paved for a clear observation of the thermal Casimir force up to separations of
several microns, and an unambiguous discrimination between the Drude and the plasma prescriptions.
EPL, 2017
– Quantum fluctuations of the electromagnetic field in the medium surrounding two discharged macr... more – 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.
EUROPEAN PHYSICAL JOURNAL C, 2007
The low-temperature asymptotic expressions for the Casimir interaction between two real metals
de... more The low-temperature asymptotic expressions for the Casimir interaction between two real metals
described by the Leontovich surface impedance are obtained in the framework of thermal quantum field theory.
It is shown that the Casimir entropy computed using the impedance of infrared optics vanishes in the
limit of zero temperature. By contrast, the Casimir entropy computed using the impedance of the Drude
model attains at zero temperature a positive value, which depends on the parameters of a system, i.e., the
Nernst heat theorem is violated. Thus, the impedance of infrared optics withstands the thermodynamic test,
whereas the impedance of the Drude model does not. We also perform a phenomenological analysis of the
thermal Casimir force and of the radiative heat transfer through a vacuum gap between real metal plates.
The characterization of a metal by means of the Leontovich impedance of the Drude model is shown to be
inconsistent with experiment at separations of a few hundred nanometers. A modification of the impedance
of infrared optics is suggested taking into account relaxation processes. The power of radiative heat transfer
predicted from this impedance is several times less than previous predictions, due to different contributions
from the transverse electric evanescent waves. The physical meaning of low frequencies in the Lifshitz formula
is discussed. It is concluded that new measurements of radiative heat transfer are required to find the
adequate description of a metal in the theory of electromagnetic fluctuations.
Physical Review D, 2017
We study the Casimir interaction between perfectly conducting sphere and plate in the classical l... more 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.
Physical Review Letters, 2012
Analytic expressions that describe Casimir interactions over the entire range of separations have... more Analytic expressions that describe Casimir interactions over the entire range of separations have been
limited to planar surfaces. Here we derive analytic expressions for the classical or high-temperature limit
of Casimir interactions between two spheres (interior and exterior configurations), including the sphereplane
geometry as a special case, using bispherical coordinates. We consider both Dirichlet boundary
conditions and metallic boundary conditions described by the Drude model. At short distances, closedform
expansions are derived from the exact result, displaying an intricate structure of deviations from the
commonly employed proximity force approximation
Physical Review A, 2016
We study the shift of rotational levels of a diatomic polar molecule due to its van der Waals (vd... more 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.
Physical Review A, 2017
A differential measurement scheme is proposed which allows for a clear observation of the giant t... more A differential measurement scheme is proposed which allows for a clear observation of the giant thermal effect for the Casimir force, that was recently predicted to occur in graphene systems at short separation distances. The difference among the Casimir forces acting between a metal-coated sphere and the two halves of a dielectric plate, one uncoated and the other coated with graphene, is calculated in the framework of the Dirac model using the rigorous formalism of the polarization tensor. It is shown that in the proposed configuration both the difference among the Casimir forces and its thermal contribution can be easily measured using already existing experimental setups. An observation of the giant thermal effect should open opportunities for modulation and control of dispersion forces in micromechanical systems based on graphene and other novel 2D-materials.
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Papers by Giuseppe Bimonte
objects in the framework of fluctuational electrodynamics in thermal nonequilibrium. The results can be expressed
as basis-independent trace formulas in terms of the scattering operators of the individual objects. We prove that
heat radiation of a single object is positive, and that heat transfer (for two arbitrary passive objects) is from
the hotter to a colder body. The heat transferred is also symmetric, exactly reversed if the two temperatures are
exchanged. Introducing partial wave expansions, we transform the results for radiation, transfer, and forces into
traces of matrices that can be evaluated in any basis, analogous to the equilibrium Casimir force. The method
is illustrated by (re)deriving the heat radiation of a plate, a sphere, and a cylinder. We analyze the radiation of
a sphere for different materials, emphasizing that a simplification often employed for metallic nanospheres is
typically invalid. We derive asymptotic formulas for heat transfer and nonequilibrium interactions for the cases
of a sphere in front a plate and for two spheres, extending previous results. As an example, we show that a hot
nanosphere can levitate above a plate with the repulsive nonequilibrium force overcoming gravity, an effect that
is not due to radiation pressure.
spaced, smoothly curved objects to the force between parallel plates. Precision experiments on
Casimir forces necessitate, and spur research on, corrections to the PFA. We use a derivative
expansion for gently curved surfaces to derive the leading curvature modifications to the PFA. Our
methods apply to any homogeneous and isotropic materials; here we present results for Dirichlet
and Neumann boundary conditions and for perfect conductors. A Pad´e extrapolation constrained
by a multipole expansion at large distance and our improved expansion at short distances, provides
an accurate expression for the sphere/plate Casimir force at all separations.
two arbitrary nanostructured surfaces out of thermal equilibrium. The method is based on a generalization of
the scattering approach recently used in investigations on the Casimir effect. Analogously to the equilibrium
case, we find that also out of thermal equilibrium the shape and composition of the surfaces enter only through
their scattering matrices. The expressions derived provide exact results in terms of the scattering matrices of
the intervening surfaces.
Wet. 51, 793 (1948)] between gently curved material surfaces at short distances is the proximity
force approximation (PFA). While this approximation is asymptotically exact at vanishing
separations, quantifying corrections to PFA has been notoriously difficult. Here, we use a
derivative expansion to compute the leading curvature correction to PFA for metals (gold) at room
temperature. We derive an explicit expression for the amplitude ^h 1 of the PFA correction to the
force gradient for axially symmetric surfaces. In the non-retarded limit, the corrections to the
Casimir free energy are found to scale logarithmically with distance. For gold, ^h 1 has an unusually
large temperature dependence.
the thermal Casimir effect that are still much debated in the current literature. Isolectronic setups offer two major
advantages over conventional Casimir setups. On the one hand, they are immune from electrostatic forces caused
by potential patches on the plates surfaces that plague present Casimir experiments, especially for separations in
the micron range. On the other hand, they can strongly enhance the discrepancy between alternative theoretical
models that have been proposed to estimate the thermal Casimir force for metallic and magnetic surfaces. Thanks
to these two features, isoelectronic differential experiments should allow one to establish conclusively which
among these models correctly describes the thermal Casimir force.
is “hidden” by a thin opaque layer of gold with a flat exposed surface. The gold layer acts as a low-pass
filter that allows for a clean observation of the controversial thermal Casimir force between the
corrugations, with currently available Casimir apparatuses. The proposed scheme of measurement, based
on the phase-dependent modulation of the Casimir force, requires no electrostatic calibrations of the
apparatus, and is unaffected by uncertainties in the knowledge of the optical properties of the surfaces. This
scheme should allow for an unambiguous discrimination between alternative theoretical prescriptions that
have been proposed in the literature for the thermal Casimir effect.
and a planar slab divided in two regions, one of which is made of high-resistivity (dielectric) Si, and the
other of Au. The crucial feature of the setup is a semitransparent plane parallel conducting overlayer,
covering both regions. The setup offers two important advantages over existing Casimir setups. On one
hand, it leads to a large amplification of the difference between the Drude and the plasma prescriptions that
are currently used to compute the thermal Casimir force. On the other hand, thanks to the screening power
of the overlayer, it is in principle immune from electrostatic forces caused by potential patches on the plates
surfaces, that plague present large distance Casimir experiments. If a semitransparent conductive overlayer
with identical patch structure over the Au-Si regions of the plate can be manufactured, similar to the opaque
overlayers used in recent searches of non-Newtonian gravitational forces based on the isoelectronic
technique, the way will be paved for a clear observation of the thermal Casimir force up to separations of
several microns, and an unambiguous discrimination between the Drude and the plasma prescriptions.
described by the Leontovich surface impedance are obtained in the framework of thermal quantum field theory.
It is shown that the Casimir entropy computed using the impedance of infrared optics vanishes in the
limit of zero temperature. By contrast, the Casimir entropy computed using the impedance of the Drude
model attains at zero temperature a positive value, which depends on the parameters of a system, i.e., the
Nernst heat theorem is violated. Thus, the impedance of infrared optics withstands the thermodynamic test,
whereas the impedance of the Drude model does not. We also perform a phenomenological analysis of the
thermal Casimir force and of the radiative heat transfer through a vacuum gap between real metal plates.
The characterization of a metal by means of the Leontovich impedance of the Drude model is shown to be
inconsistent with experiment at separations of a few hundred nanometers. A modification of the impedance
of infrared optics is suggested taking into account relaxation processes. The power of radiative heat transfer
predicted from this impedance is several times less than previous predictions, due to different contributions
from the transverse electric evanescent waves. The physical meaning of low frequencies in the Lifshitz formula
is discussed. It is concluded that new measurements of radiative heat transfer are required to find the
adequate description of a metal in the theory of electromagnetic fluctuations.
limited to planar surfaces. Here we derive analytic expressions for the classical or high-temperature limit
of Casimir interactions between two spheres (interior and exterior configurations), including the sphereplane
geometry as a special case, using bispherical coordinates. We consider both Dirichlet boundary
conditions and metallic boundary conditions described by the Drude model. At short distances, closedform
expansions are derived from the exact result, displaying an intricate structure of deviations from the
commonly employed proximity force approximation
objects in the framework of fluctuational electrodynamics in thermal nonequilibrium. The results can be expressed
as basis-independent trace formulas in terms of the scattering operators of the individual objects. We prove that
heat radiation of a single object is positive, and that heat transfer (for two arbitrary passive objects) is from
the hotter to a colder body. The heat transferred is also symmetric, exactly reversed if the two temperatures are
exchanged. Introducing partial wave expansions, we transform the results for radiation, transfer, and forces into
traces of matrices that can be evaluated in any basis, analogous to the equilibrium Casimir force. The method
is illustrated by (re)deriving the heat radiation of a plate, a sphere, and a cylinder. We analyze the radiation of
a sphere for different materials, emphasizing that a simplification often employed for metallic nanospheres is
typically invalid. We derive asymptotic formulas for heat transfer and nonequilibrium interactions for the cases
of a sphere in front a plate and for two spheres, extending previous results. As an example, we show that a hot
nanosphere can levitate above a plate with the repulsive nonequilibrium force overcoming gravity, an effect that
is not due to radiation pressure.
spaced, smoothly curved objects to the force between parallel plates. Precision experiments on
Casimir forces necessitate, and spur research on, corrections to the PFA. We use a derivative
expansion for gently curved surfaces to derive the leading curvature modifications to the PFA. Our
methods apply to any homogeneous and isotropic materials; here we present results for Dirichlet
and Neumann boundary conditions and for perfect conductors. A Pad´e extrapolation constrained
by a multipole expansion at large distance and our improved expansion at short distances, provides
an accurate expression for the sphere/plate Casimir force at all separations.
two arbitrary nanostructured surfaces out of thermal equilibrium. The method is based on a generalization of
the scattering approach recently used in investigations on the Casimir effect. Analogously to the equilibrium
case, we find that also out of thermal equilibrium the shape and composition of the surfaces enter only through
their scattering matrices. The expressions derived provide exact results in terms of the scattering matrices of
the intervening surfaces.
Wet. 51, 793 (1948)] between gently curved material surfaces at short distances is the proximity
force approximation (PFA). While this approximation is asymptotically exact at vanishing
separations, quantifying corrections to PFA has been notoriously difficult. Here, we use a
derivative expansion to compute the leading curvature correction to PFA for metals (gold) at room
temperature. We derive an explicit expression for the amplitude ^h 1 of the PFA correction to the
force gradient for axially symmetric surfaces. In the non-retarded limit, the corrections to the
Casimir free energy are found to scale logarithmically with distance. For gold, ^h 1 has an unusually
large temperature dependence.
the thermal Casimir effect that are still much debated in the current literature. Isolectronic setups offer two major
advantages over conventional Casimir setups. On the one hand, they are immune from electrostatic forces caused
by potential patches on the plates surfaces that plague present Casimir experiments, especially for separations in
the micron range. On the other hand, they can strongly enhance the discrepancy between alternative theoretical
models that have been proposed to estimate the thermal Casimir force for metallic and magnetic surfaces. Thanks
to these two features, isoelectronic differential experiments should allow one to establish conclusively which
among these models correctly describes the thermal Casimir force.
is “hidden” by a thin opaque layer of gold with a flat exposed surface. The gold layer acts as a low-pass
filter that allows for a clean observation of the controversial thermal Casimir force between the
corrugations, with currently available Casimir apparatuses. The proposed scheme of measurement, based
on the phase-dependent modulation of the Casimir force, requires no electrostatic calibrations of the
apparatus, and is unaffected by uncertainties in the knowledge of the optical properties of the surfaces. This
scheme should allow for an unambiguous discrimination between alternative theoretical prescriptions that
have been proposed in the literature for the thermal Casimir effect.
and a planar slab divided in two regions, one of which is made of high-resistivity (dielectric) Si, and the
other of Au. The crucial feature of the setup is a semitransparent plane parallel conducting overlayer,
covering both regions. The setup offers two important advantages over existing Casimir setups. On one
hand, it leads to a large amplification of the difference between the Drude and the plasma prescriptions that
are currently used to compute the thermal Casimir force. On the other hand, thanks to the screening power
of the overlayer, it is in principle immune from electrostatic forces caused by potential patches on the plates
surfaces, that plague present large distance Casimir experiments. If a semitransparent conductive overlayer
with identical patch structure over the Au-Si regions of the plate can be manufactured, similar to the opaque
overlayers used in recent searches of non-Newtonian gravitational forces based on the isoelectronic
technique, the way will be paved for a clear observation of the thermal Casimir force up to separations of
several microns, and an unambiguous discrimination between the Drude and the plasma prescriptions.
described by the Leontovich surface impedance are obtained in the framework of thermal quantum field theory.
It is shown that the Casimir entropy computed using the impedance of infrared optics vanishes in the
limit of zero temperature. By contrast, the Casimir entropy computed using the impedance of the Drude
model attains at zero temperature a positive value, which depends on the parameters of a system, i.e., the
Nernst heat theorem is violated. Thus, the impedance of infrared optics withstands the thermodynamic test,
whereas the impedance of the Drude model does not. We also perform a phenomenological analysis of the
thermal Casimir force and of the radiative heat transfer through a vacuum gap between real metal plates.
The characterization of a metal by means of the Leontovich impedance of the Drude model is shown to be
inconsistent with experiment at separations of a few hundred nanometers. A modification of the impedance
of infrared optics is suggested taking into account relaxation processes. The power of radiative heat transfer
predicted from this impedance is several times less than previous predictions, due to different contributions
from the transverse electric evanescent waves. The physical meaning of low frequencies in the Lifshitz formula
is discussed. It is concluded that new measurements of radiative heat transfer are required to find the
adequate description of a metal in the theory of electromagnetic fluctuations.
limited to planar surfaces. Here we derive analytic expressions for the classical or high-temperature limit
of Casimir interactions between two spheres (interior and exterior configurations), including the sphereplane
geometry as a special case, using bispherical coordinates. We consider both Dirichlet boundary
conditions and metallic boundary conditions described by the Drude model. At short distances, closedform
expansions are derived from the exact result, displaying an intricate structure of deviations from the
commonly employed proximity force approximation