The Casimir effect results from alterations of the zero-point electromagnetic energy introduced by boundary-conditions. For ferromagnetic layers separated by vacuum (or a dielectric) such boundary-conditions are influenced by the magneto-optical Kerr effect. We will show that this gives rise to a long-range magnetic interaction and discuss the effect for two different configurations (magnetization parallel and perpendicular to the layers). Analytical expressions are derived for two models and compared to numerical calculations. Numerical calculations of the effect for Fe are also presented and the possibility of an experimental observation of the Casimir magnetic interaction is discussed.
We consider the Casimir interaction between a ferromagnetic and a non-magnetic mirror, and show how the Casimir effect gives rise to a magnetic anisotropy in the ferromagnetic layer. The anisotropy is out-of-plane if the non-magnetic plate is optically isotropic. If the non-magnetic plate shows a uniaxial optical anisotropy (with optical axis in the plate plane), we find an in-plane magnetic anisotropy. In both cases, the energetically most favorable magnetization orientation is given by the competition between polar, longitudinal and transverse contributions to the magneto-optical Kerr effect…
We extend the Lifshitz theory of the Casimir force to the case of two parallel magnetic metal plates possessing a spatially nonlocal dielectric response. By solving Maxwell equations in the configuration of an electromagnetic wave incident on the boundary plane of a magnetic metal semispace, the exact surface impedances are expressed in terms of its magnetic permeability and longitudinal and transverse dielectric functions. This allows application of the Lifshitz theory with reflection coefficients written via the surface impedances for calculation of the Casimir pressure between magnetic meta…
We investigate the Casimir pressure between two parallel plates made of magnetic materials at nonzero temperature. It is shown that for real magnetodielectric materials only the magnetic properties of ferromagnets can influence the Casimir pressure. This influence is accomplished through the contribution of the zero-frequency term of the Lifshitz formula. The possibility of the Casimir repulsion through the vacuum gap is analyzed depending on the model used for the description of the dielectric properties of the metal plates.
We show that in order to account for the repulsive Casimir effect in the parallel plate geometry in terms of the quantum version of the Lorentz force, virtual surface densities of magnetic charges and currents must be introduced. The quantum version of the Lorentz force expressed in terms of the correlators of the electric and magnetic fields for planar geometries yields then correctly the Casimir pressure.
We present a theoretical calculation of the pull-in control in capacitive micro switches actuated by Casimir forces, using external magnetic fields. The external magnetic fields induces an optical anisotropy due to the excitation of magneto plasmons, that reduces the Casimir force. The calculations are performed in the Voigt configuration, and the results show that as the magnetic field increases the system becomes more stable. The detachment length for a cantilever is also calculated for a cantilever, showing that it increases with increasing magnetic field. At the pull-in separation, the sti…
We investigate the magnetic dipole coupling between a metallic surface and an atom in a thermal state, ground state and excited hyperine state. This interaction results in a repulsive correction and - unlike the electrical dipole contribution - depends sensitively on the Ohmic dissipation in the material.
We investigate the dispersive Casimir-Polder interaction between a Rubidium atom and a suspended graphene sheet subjected to an external magnetic field B. We demonstrate that this concrete physical system allows for an unprecedented control of dispersive interactions at micro and nanoscales. Indeed, we show that the application of an external magnetic field can induce a 80% reduction of the Casimir-Polder energy relative to its value without the field. We also show that sharp discontinuities emerge in the Casimir-Polder interaction energy for certain values of the applied magnetic field at low…
We reply to the "Comment on 'The Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic mirrors'" [arXiv:1604.06432]. We believe the comment misrepresents our papers, and fails to provide a plausible resolution to the conflict between theory and experiment.
We study the quantum and thermal fluctuations of eddy (Foucault) currents in thick metallic plates. A Casimir interaction between two plates arises from the coupling via quasi-static magnetic fields. As a function of distance, the relevant eddy current modes cross over from a quantum to a thermal regime. These modes alone reproduce previously discussed thermal anomalies of the electromagnetic Casimir interaction between good conductors. In particular, they provide a physical picture for the Casimir entropy whose nonzero value at zero temperature arises from a correlated, glassy state.
In this paper we review the role of magneto plasmon polaritons in the Casimir force calculations. By applying an external constant magnetic field a strong optical anisotropy is induced on two parallel slabs reducing the reflectivity and thus the Casimir force. As the external magnetic field increases, the Casimir force decreases. Thus, with an an external magnetic field the Casimir force can be controlled.The calculations are done in the Voigt configuration where the magnetic field is parallel to the slabs. In this configuration the reflection coefficients for TE and TM modes do not show mode …
We measured the gradient of the Casimir force between an Au sphere and a plate made of ferromagnetic metal (Ni). It is demonstrated that the magnetic properties influence the force magnitude. This opens prospective opportunities for the control of the Casimir force in nanotechnology and for obtaining Casimir repulsion by using ferromagnetic dielectrics.
We examine the conditions of validity for the Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic plane mirrors. As in the previously studied case of non-magnetic materials (Guerout et al, Phys. Rev. E 90 042125), we recover the usual expression for the lossy model of optical response, but not for the lossless plasma model. We also show that the modes associated with the Foucault currents play a crucial role in the limit of vanishing losses, in contrast to expectations.
The impact of agglomeration of magnetic nanoparticles on the Casimir pressure is investigated in the configuration of two material plates and a layer of ferrofluid confined between them. Both cases of similar and dissimilar plates are considered in the framework of the Lifshitz theory of dispersion forces. It is shown that for two dielectric (SiO_2) plates, as well as for one dielectric (SiO_2) and another one metallic (Au) plates, an agglomeration of magnetite nanoparticles results in only quantitative differences in the values of the Casimir pressure if the optical data for Au are extrapolat…
The zero-point quantum fluctuations of the electromagnetic field in vacuum are known to give rise to a long-range attractive force between metal plates (Casimir effect). For ferromagnetic layers separated by vacuum, it is shown that the interplay of the Casimir effect and of the magneto-optical Kerr effect gives rise to a long-range magnetic interaction. The Casimir magnetic force is found to decay as $D^{-1}$ in the limit of short distances, and as $D^{-5}$ in the limit of long distances. Explicit expressions for realistic systems are given in the large and small distance limits. An experimen…
Advanced Science Research Center, Japan Atomic Energy Agency (JAEA)（日本原子力机构先进科学研究中心）；Research Center for Nuclear Physics, Osaka University（大阪大学核物理研究中心）；RIKEN Center for Computational Science（理化学研究所计算科学中心）
In a classical description, a neutral, polarizable object acquires a kinetic momentum when exposed to crossed electric and magnetic fields. In the presence of only a magnetic field no such momentum exists classically, although it is symmetry-allowed for an object lacking mirror symmetry. We perform a full QED calculation to show that the quantum vacuum coupled to a chiral molecule provides a kinetic "Casimir" momentum directed along the magnetic field, proportional to its rotatory power and the fine structure constant.
The Casimir pressure is investigated in three-layer systems where the intervening stratum possesses magnetic properties. This subject is gaining in importance in connection with ferrofluids and their use in various microelectromechanical devices. We present general formalism of the Lifshitz theory adapted to the case of ferrofluid sandwiched between two dielectric walls. The Casimir pressure is computed for the cases of kerosene- and water-based ferrofluids containing a 5% fraction of magnetite nanoparticles with different diameters between silica glass walls. For this purpose, we have found t…
We examine the Casimir free energy and pressure of magnetic metal films, which are free-standing in vacuum, sandwiched between two dielectric plates, and deposited on either nonmagnetic or magnetic metallic plates. All calculations are performed using both the Drude and plasma model approaches to the Lifshitz theory. According to our results, the Casimir free energies and pressures calculated using both theoretical approaches are significantly different in the magnitude and sign even for thin films of several tens of nanometers thickness. Thus, for the Ni film of 47\,nm thickness deposited on …
Recently Guerout et al. [Phys. Rev. E, v.93, 022108 (2016)] advocated that the lossless plasma model has to be redefined as the limit of the Drude model when the relaxation parameter goes to zero. It was claimed that the previously used plasma model cannot correctly describe the Casimir pressure between two plates made of both nonmagnetic and magnetic metals and has to be replaced with the redefined one. We show that the suggested redefinition does not satisfy necessary physical requirements imposed on the dielectric permittivity. We also present a plausible explanation to the fact that the lo…
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 mode…
The Casimir Force, a quantum mechanical effect, has been observed in several microelectromechanical systems (MEMS) platforms. Due to its extreme sensitivity to the separation of two objects, the Casimir Force has been proposed as an excellent avenue for quantum metrology. Practical application, however, is challenging due to attractive forces leading to stiction and failure of the device, called Casimir pull-in. In this work, we design and simulate a Casimir-driven metrology platform, where a time-delay based parametric amplification technique is developed to achieve a steady state and avoid p…
Based on a generalization of the Lifshiftz theory we calculate Casimir forces involving magnetodielectric and possibly anisotropic metamaterials, focusing on the possibility of repulsive forces. It is found that Casimir repulsion decreases with magnetic dissipation, and even a small Drude background in metallic-based metamaterials acts to make attractive a Casimir force that would otherwise be predicted to be repulsive. The sign of the force also depends sensitively on the degree of optical anisotropy of the metamaterial, and on the form of the frequency-dependency of the magnetic response.
We extend our previous work [Phys. Rev. Lett. {\bf 100}, 183602 (2008)] on the generalization of the Casimir-Lifshitz theory to treat anisotropic magnetodielectric media, focusing on the forces between metals and magnetodielectric metamaterials and on the possibility of inferring magnetic effects by measurements of these forces. We present results for metamaterials including structures with uniaxial and biaxial magnetodielectric anisotropies, as well as for structures with isolated metallic or dielectric properties that we describe in terms of filling factors and a Maxwell Garnett approximatio…
Magnon excitation in a spinor Bose-Einstein condensate by a driven magnetic field is shown to have a close analogy with the dynamical Casimir effect. A time-dependent external magnetic field amplifies quantum fluctuations in the magnetic ground state of the condensate, leading to magnetization of the system. The magnetization occurs in a direction perpendicular to the magnetic field breaking the rotation symmetry. This phenomenon is numerically demonstrated and the excited quantum field is shown to be squeezed.
We propose a definitive test of whether plates involved in Casimir experiments should be modeled with ballistic or diffusive electrons--a prominent controversy highlighted by a number of conflicting experiments. The unambiguous test we propose is a measurement of the Casimir force between a disordered quasi-2D metallic plate and a three-dimensional metallic system at low temperatures, in which disorder-induced weak localization effects modify the well-known Drude result in an experimentally tunable way. We calculate the weak localization correction to the Casimir force as a function of magneti…
The repulsive nature of the static Casimir force between two half-spaces, one perfectly dielectric and the other purely magnetic, has been known since Boyer's work [T. H. Boyer, Phys. Rev. A {\bf 9}, 2078 (1974)]. We here analyze the corresponding friction force in the magnetodielectric case. Our main method is that of quantum mechanical statistical mechanics. The basic model we introduce is a harmonic oscillator model: an electric dipole oscillating in the $x$ direction and a magnetic one oscillating in the $y$ direction, while their separation is in the $z$ direction. This is then extended t…
It is well known that the Casimir force between two half-spaces is dictated by their electromagnetic properties. In particular, when one of the half-spaces is mainly metallic or dielectric and the other is mainly magnetic, it is possible to show that the force is repulsive. This has attracted lots of interest towards the study of metamterials (MMs) in the context of Casimir effect, as their magnetic activity might help bring the idea of Casimir repulsion from the theoretical realm to experimental verification. In this paper we investigate the possibility of repulsion when the MM magnetic perme…
We find that thin peptide films and coatings doped with metallic nanoparticles are more stable due to the role of electromagnetic fluctuations. It is shown that for the doped freestanding in vacuum peptide film the Casimir attraction becomes larger in magnitude. For dielectric substrates coated with peptide films, the nanoparticle doping leads to a wider range of film thicknesses where the Casimir pressure is attractive and to larger pressure magnitudes at the points of extremum. The doping of peptide coatings with magnetic nanoparticles preserves all the advantages of nonmagnetic ones and sim…
A perfectly reflecting (Dirichlet) boundary condition at the edge of an impenetrable magnetic-flux-carrying tube of nonzero transverse size is imposed on the charged massive scalar matter field which is quantized outside the tube. We show that the vacuum polarization effects outside the tube give rise to a macroscopic force acting at the increase of the tube radius (if the magnetic flux is held steady). The Casimir energy and force are periodic in the value of the magnetic flux, being independent of the coupling to the space-time curvature scalar. We conclude that a topological defect of the v…
Weyl semimetals are a class of topological materials that exhibit a bulk Hall effect due to time-reversal symmetry breaking. We show that for the idealized semi-infinite case, the Casimir force between two identical Weyl semimetals is repulsive at short range and attractive at long range. Considering plates of finite thickness, we can reduce the size of the long-range attraction even making it repulsive for all distances when thin enough. In the thin-film limit, we study the appearance of an attractive Casimir force at shorter distances due to the longitudinal conductivity. Magnetic field, thi…
We study the influence of a background uniform magnetic field and boundary conditions on the vacuum of a quantized charged massive scalar matter field confined between two parallel plates; the magnetic field is directed orthogonally to the plates. The admissible set of boundary conditions at the plates is determined by the requirements that the operator of one-particle energy squared be self-adjoint and positive definite. We show that, in the case of a weak magnetic field and a small separation of the plates, the Casimir force is either attractive or repulsive, depending on the choice of a bou…
Vacuum Torque Without Anisotropy: Switchable Casimir Torque Between Altermagnets
Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong University（上海交大李政道研究所与物理与天文学院）；Shanghai Branch, Hefei National Laboratory（合肥国家实验室上海分部）
It has been recently shown that a chiral molecule accelerates linearly along a spatially uniform magnetic field, as a result of the parity-time symmetry breaking induced in its QED self-interaction. In this work we extend this result to fundamental particles which present EW self-interaction, in which case parity is violated by the EW interaction itself. In particular, we demonstrate that, in a spatially uniform and adiabatically time-varying magnetic field, an unpolarized proton coupled to the leptonic vacuum acquires a kinetic momentum antiparallel to the magnetic field, whereas virtual lept…
We discuss repulsive Casimir forces between dielectric materials with non trivial magnetic susceptibility. It is shown that considerations based on naive pair-wise summation of Van der Waals and Casimir Polder forces may not only give an incorrect estimate of the magnitude of the total Casimir force, but even the wrong sign of the force when materials with high dielectric and magnetic response are involved. Indeed repulsive Casimir forces may be found in a large range of parameters, and we suggest that the effect may be realized in known materials. The phenomenon of repulsive Casimir forces ma…
We consider two immobile spin $1/2$ fermions in a two-dimensional magnetic system that is close to the $ O(3)$ magnetic quantum critical point (QCP) which separates magnetically ordered and disordered phases. Focusing on the disordered phase in the vicinity of the QCP, we demonstrate that the criticality results in a strong long range attraction between the fermions, with potential $V(r) \propto -1/r^ν$, $ν\approx 0.75$, where $r$ is separation between the fermions. The mechanism of the enhanced attraction is similar to Casimir effect and corresponds to multi-magnon exchange processes between …
Perfect magnetic conductor (PMC) boundary conditions are dual to the more familiar perfect electric conductor (PEC) conditions and can be viewed as the electromagnetic analog of the boundary conditions in the bag model for hadrons in QCD. Recent advances and requirements in communication technologies have attracted great interest in PMC's and Casimir experiments involving structures that approximate PMC's may be carried out in the not too distant future. In this paper, we make a study of the zero-temperature PMC Casimir piston in $d+1$ dimensions. The PMC Casimir energy is explicitly evaluated…
We study the influence of a background uniform magnetic field and boundary conditions on the vacuum of a quantized charged spinor matter field confined between two parallel neutral plates; the magnetic field is directed orthogonally to the plates. The admissible set of boundary conditions at the plates is determined by the requirement that the Dirac Hamiltonian operator be self-adjoint. It is shown that, in the case of a sufficiently strong magnetic field and a sufficiently large separation of the plates, the generalized Casimir force is repulsive, being independent of the choice of a boundary…
The electromagnetic vacuum energy is considered in the presence of a perfectly conducting plane and a ball with dielectric permittivity $\varepsilon$ and magnetic permeability $μ$, $μ\ne1$. The attention is focused on the Casimir repulsion in this system caused by magnetic permeability of the sphere. In the case of perfectly permeable sphere, $μ=\infty$, the vacuum energy is estimated numerically. The short and long distance asymptotes corresponding to the repulsive force and respective low temperature corrections and high temperature limits are found for a wide range of $μ$. The constraints o…
We investigate the Casimir effect between two-dimensional electron systems driven to the quantum Hall regime by a strong perpendicular magnetic field. In the large separation (d) limit where retardation effects are essential we find i) that the Casimir force is quantized in units of 3\hbar c α^2/(8π^2 d^4), and ii) that the force is repulsive for mirrors with same type of carrier, and attractive for mirrors with opposite types of carrier. The sign of the Casimir force is therefore electrically tunable in ambipolar materials like graphene. The Casimir force is suppressed when one mirror is a ch…
In this article we investigate the Casimir effect in the presence of a medium by quantizing the Electromagnetic (EM) field in the presence of a magnetodielectric medium by using the path integral formalism. For a given medium with definite electric and magnetic susceptibilities, explicit expressions for the Casimir force are obtained which are in agree with the original Casimir force between two conducting parallel plates immersed in the quantum electromagnetic vacuum.
We extend a recently introduced method for computing Casimir forces between arbitrarily--shaped metallic objects [M. T. H. Reid et al., Phys. Rev. Lett._103_ 040401 (2009)] to allow treatment of objects with arbitrary material properties, including imperfect conductors, dielectrics, and magnetic materials. Our original method considered electric currents on the surfaces of the interacting objects; the extended method considers both electric and magnetic surface current distributions, and obtains the Casimir energy of a configuration of objects in terms of the interactions of these effective su…
Making use of the quantum correlators associated with the Maxwell field vacuum distorted by the presence of plane parallel material surfaces we derive the Casimir-Polder interaction in the presence of plane parallel conducting walls and in the presence of a conducting wall and a magnetically permeable one.
Why the Casimir Force for Magnetic Metals Computed by the Lifshitz Theory Using the Drude Model Disagrees with the Measurement Data
Central Astronomical Observatory at Pulkovo of the Russian Academy of Sciences（俄罗斯科学院普尔科沃中央天文台）；Peter the Great Saint Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）；Moscow Center for Advanced Studies（莫斯科高等研究院）
We analyze the magnetic dipole contribution to atom-surface dispersion forces. Unlike its electrical counterpart, it involves small transition frequencies that are comparable to thermal energy scales. A significant temperature dependence is found near surfaces with a nonzero DC conductivity, leading to a strong suppression of the dispersion force at T > 0. We use thermal response theory for the surface material and discuss both normal metals and superconductors. The asymptotes of the free energy of interaction and of the entropy are calculated analytically over a large range of distances. Near…
It is well known that the Casimir force calculated at large separations using the Lifshitz theory differs by a factor of 2 for metals described by the Drude or plasma models. We argue that this difference is entirely determined by the contribution of transverse electric (s) evanescent waves. Taking into account that there is a lack of experimental information on the electromagnetic response of metals to low-frequency evanescent waves, we propose an experiment on measuring the magnetic field of an oscillating magnetic dipole spaced in vacuum above a thick metallic plate. According to our result…
The Lifshitz-type formulas for the free energy and Casimir-Polder force acting between an atom possessing a permanent magnetic moment and a wall made of different materials are derived. Simple model allowing analytic results is considered where the atomic magnetic susceptibility is frequency-independent and wall is made of ideal metal. Numerical computations of the Casimir-Polder force are performed for H atom interacting with walls made of ideal metal, nonmagnetic (Au) and ferromagnetic (Fe) metals and of ferromagnetic dielectric. It is shown that for the first three wall materials the inclus…
The vacuum expectation value (VEV) of the energy-momentum tensor for a massive fermionic field is investigated in a (2+1)-dimensional conical spacetime in the presence of a circular boundary and an infinitely thin magnetic flux located at the cone apex. The MIT bag boundary condition is assumed on the circle. At the cone apex we consider a special case of boundary conditions for irregular modes, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The presence of the magnetic flux leads to the Aharonov-Bohm-like effect on the VEV of the energy-momentu…
We predict a repulsive Casimir-Polder-type dispersion interaction between a single neutron and a metal or dielectric surface. We consider a scenario where a single neutron is subject to an external magnetic field. Due to its intrinsic magnetic moment, the neutron then forms a magnetisable two-level system which can exchange virtual photons with a nearby surface. The resulting dispersion interaction between a purely magnetic object (neutron) and a purely electric one (surface) is found to be repulsive, in contrast to the typical attractive interaction between electric objects. Its magnitude is …
We consider the energy shift for an atom close to a non-magnetic body with a magnetic moment coupled to a quantized magnetic field. The corresponding repulsive Casimir-Polder force is obtained for a perfect conductor, a metal, a dielectric medium, with dielectric properties modeled by a Drude formula, and a superconductor at zero temperature. The dielectric properties of the superconductor is obtained by making use of the Mattis-Bardeen linear response theory and we present some useful expressions for the low-frequency conductivity. The quantum dynamics with a given initial state is discussed …
We present boundary conditions for the electromagnetic fields on a δ-function plate, having both electric and magnetic properties, sandwiched between two magneto-electric semi-infinite half spaces. The optical properties for an isolated δ-function plate are shown to be independent of the longitudinal material properties of the plate. The Casimir-Polder energy between an isotropically polarizable atom and a magneto-electric δ-function plate is attractive for a purely electric δ-function plate, repulsive for a purely magnetic δ-function plate, and vanishes for the simultaneous perfect conductor …
