We study the Casimir force between a nanoparticle and a substrate. We consider the interaction of metal nanoparticles with different substrates within the dipolar approximation. We study the force as a function of the distance for gold and potassium spheres, which are over a substrate of titanium dioxide, sapphire and a perfect conductor. We show that Casimir force is important in systems at the nanometer scale. We study the force as a function of the material properties, radii of the spheres, and the distance between the sphere and the substrate.
We present experiments in which the interaction of a single gold nanoparticle with glass substrates or with another gold particle can be tuned by in-situ control of their separations using scanning probe technology. We record the plasmon resonances of the coupled systems as a function of the polarization of the incident field and the particle position. The distinct spectral changes of the scattered light from the particle pair are in good agreement with the outcome of finite difference time-domain (FDTD) calculations. We believe our experimental technique holds promise for the investigation of…
We calculate the Casimir force in the non-retarded limit between a spherical nanoparticle and a substrate, and we found that high-multipolar contributions are very important when the sphere is very close to the substrate. We show that the highly inhomegenous electromagnetic field induced by the presence of the substrate, can enhance the Casimir force by orders of magnitude, compared with the classical dipolar approximation.
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…
We derive the analytical expressions for the thermal Casimir-Polder energy and force between a spheroidal nanoparticle above a semi-infinite material and a graphene covered interface. We analyze in detail the Casimir-Polder force between a gold nanoparticle and a single sheet of pristine graphene focusing on the impact of anisotropy. We show that the effect of anisotropy, i.e. the shape and orientation of the spheroidal nanoparticle, has a much larger influence on the force than the tunability of graphene. The effect of tuning and anisotropy both add up such that we observe a force which is be…
This letter proposes a scheme for transporting nanoparticles immersed in a fluid, relying on quantum vacuum fluctuations. The mechanism lies in the inhomogeneity-induced lateral Casimir force between a nanoparticle and a gradient metasurface, and the relaxation of the conventional Dzyaloshinskiǐ-Lifshitz-Pitaevskiǐ constraint, which allows quantum levitation for a broader class of material configurations. The velocity for a nanosphere levitated above a grating is calculated and can be up to a few microns per minute. The Born approximation gives general expressions for the Casimir energy which …
The Casimir--Polder interaction between an anisotropic particle and a surface is orientation dependent. We study novel orientational effects that arise due to curvature of the surface for distances much smaller than the radii of curvature by employing a derivative expansion. For nanoparticles we derive a general short distance expansion of the interaction potential in terms of their dipolar polarizabilities. Explicit results are presented for nano-spheroids made of SiO$_2$ and gold, both at zero and at finite temperatures. The preferred orientation of the particle is strongly dependent on curv…
It has been increasingly becoming clear that Casimir and Casimir-Polder entropies may be negative in certain regions of temperature and separation. In fact, the occurrence of negative entropy seems to be a nearly ubiquitous phenomenon. This is most highlighted in the quantum vacuum interaction of a nanoparticle with a conducting plate or between two nanoparticles. It has been argued that this phenomenon does not violate physical intuition, since the total entropy, including the self-entropies of the plate and the nanoparticle, should be positive. New calculations, in fact, seem to bear this ou…
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…
We calculate exactly the Casimir force or dispersive force, in the non-retarded limit, between a spherical nanoparticle and a substrate beyond the London's or dipolar approximation. We find that the force is a non-monotonic function of the distance between the sphere and the substrate, such that, it is enhanced by several orders of magnitude as the sphere approaches the substrate. Our results do not agree with previous predictions like the Proximity theorem approach.
We study the energy shift and the Casimir-Polder force of an atom out of thermal equilibrium near the surface of a dielectric substrate. We first generalize, adopting the local source hypothesis, the formalism proposed by Dalibard, Dupont-Roc and Cohen-Tannoudji, which separates the contributions of thermal fluctuations and radiation reaction to the energy shift and allows a distinct treatment to atoms in the ground and excited states, to the case out of thermal equilibrium, and then use the generalized formalism to calculate the energy shift and the Casimir-Polder force of an isotropically po…
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 consider the Casimir-Polder interaction energy between a metallic nanoparticle and a metallic plate, as well as the Casimir interaction energy between two macroscopic metal plates, in terms of the many-body dispersion interactions between their constituents. Expressions for two- and three-body dispersion interactions between the microscopic parts of a real metal are first obtained, both in the retarded and non-retarded limits. These expressions are then used to evaluate, a compare each other, the overall two- and three-body contributions to the macroscopic Casimir-Polder and Casimir force, …
We develop a spectral representation formalism to calculate the Casimir force in the non-retarded limit, between a spherical particle and a substrate, both with arbitrary local dielectric properties. This spectral formalism allows one to do a systematic study of the force as a function of the geometrical variables separately from the dielectric properties. We found that the force does not follow a simple power-law as a function of the separation between the sphere and substrate. As a consequence, the non-retarded Casimir force is enhanced by several orders of magnitude as the sphere approaches…
The Casimir free energy of peptide films on a silicon substrate: Impact of dielectric-to-metal transition in silicon and nanoparticles in peptide
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）
Negative entropy has been known in Casimir systems for some time. For example, it can occur between parallel metallic plates modeled by a realistic Drude permittivity. Less well known is that negative entropy can occur purely geometrically, say between a perfectly conducting sphere and a conducting plate. The latter effect is most pronounced in the dipole approximation, which is reliable when the size of the sphere is small compared to the separation between the sphere and the plate. Therefore, here we examine cases where negative entropy can occur between two electrically and magnetically pol…
We present a scheme for obtaining stable Casimir suspension of dielectric nontouching objects immersed in a fluid, validated here in various geometries consisting of ethanol-separated dielectric spheres and semi-infinite slabs. Stability is induced by the dispersion properties of real dielectric (monolithic) materials. A consequence of this effect is the possibility of stable configurations (clusters) of compact objects, which we illustrate via a "molecular" two-sphere dicluster geometry consiting of two bound spheres levitated above a gold slab. Our calculations also reveal a strong interplay…
We introduce an efficient technique for computing Casimir energies and forces between objects of arbitrarily complex 3D geometries. In contrast to other recently developed methods, our technique easily handles non-spheroidal, non-axisymmetric objects and objects with sharp corners. Using our new technique, we obtain the first predictions of Casimir interactions in a number of experimentally relevant geometries, including crossed cylinders and tetrahedral nanoparticles.
The gradient of the Casimir force between a Si-SiO${}_2$-graphene substrate and an Au-coated sphere is measured by means of a dynamic atomic force microscope operated in the frequency shift technique. It is shown that the presence of graphene leads to up to 9% increase in the force gradient at the shortest separation considered. This is in qualitative agreement with the predictions of an additive theory using the Dirac model of graphene.
Using the recently proposed theory, we calculate thermal effect in the Casimir interaction from graphene-coated metallic and dielectric substrates. The cases when only one or both of the two parallel plates are coated with graphene are considered. It is shown that the graphene coating does not influence the Casimir interaction between metals, but produces large impact for dielectrics. This impact increases with decreasing static dielectric permittivity of the plate material. The thermal correction to the gradient of the Casimir force between an Au sphere and graphene coated fused silica plate …
The rigorous finite-temperature QED formalism of the polarization tensor is used to study the combined effect of nonzero mass gap $m$ and chemical potential $μ$ on the Casimir force and its thermal correction in the experimentally relevant configuration of a Au sphere interacting with a real graphene sheet or with graphene-coated dielectric substrates made of different materials. It is shown that for both a free-standing graphene sheet and for graphene-coated substrates the magnitude of the Casimir force decreases as $m$ is increased, while it increases as $μ$ is increased, indicating that the…
We find that the Casimir pressure in peptide films deposited on metallic substrates is always repulsive which makes these films less stable. It is shown that by adding a graphene sheet on top of peptide film one can change the sign of the Casimir pressure by making it attractive. For this purpose, the formalism of the Lifshitz theory is extended to the case when the film and substrate materials are described by the frequency-dependent dielectric permittivities, whereas the response of graphene to the electromagnetic field is governed by the polarization tensor in (2+1)-dimensional space-time f…
We propose a theory of the thermal Casimir interaction for multilayered test bodies coated with a graphene sheet. The reflection coefficients on such structures are expressed in terms of the components of the polarization tensor and the dielectric permittivities of material layers. The developed theory is applied to calculate the gradient of the Casimir force between an Au-coated sphere and a graphene sheet deposited on a SiO${}_2$ film covering a Si plate, which is the configuration of a recent experiment performed by means of a dynamic atomic force microscope. The theoretical results are fou…
We demonstrate that the Casimir-Polder force for a molecule near the surface of a real dielectric substrate out of thermal equilibrium displays distinctive behaviors as compared to that at thermal equilibrium. In particular, when the molecule-substrate separation is much less than the molecular transition wave-length, the CP force in the high temperature limit can be dramatically manipulated by varying the relative magnitude of the temperatures of the substrate and the environment so that the attractive-to-repulsive transition can occur beyond certain a threshold temperature of either the subs…
Motivated by recent experiments with confined binary liquid mixtures near their continous demixing phase transition we study the critical behavior of a system, which belongs to the Ising universality class, for the film geometry with one planar wall chemically structured such that there is a laterally alternating adsorption preference for the species of the binary liquid mixture. By means of Monte Carlo simulations and finite-size scaling analysis we determine the critical Casimir force and the corresponding universal scaling function.
By using silicon oxide based aerogels we show numerically that the Casimir force can be reduced several orders of magnitude, making its effect negligible in nanodevices. This decrease in the Casimir force is also present even when the aerogels are deposited on metallic substrates. To calculate the Casimir force we model the dielectric function of silicon oxide aerogels using an effective medium dielectric function such as the Clausius-Mossotti approximation. The results show that both the porosity of the aerogel and its thickness can be use as control parameters to reduce the magnitude of the …
We report on the first measurement of a temperature dependence of the Casimir-Polder force. This measurement was obtained by positioning a nearly pure 87-Rb Bose-Einstein condensate a few microns from a dielectric substrate and exciting its dipole oscillation. Changes in the collective oscillation frequency of the magnetically trapped atoms result from spatial variations in the surface-atom force. In our experiment, the dielectric substrate is heated up to 605 K, while the surrounding environment is kept near room temperature (310 K). The effect of the Casimir-Polder force is measured to be ne…
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…
We study the geometrical corrections to the simple Proximity Force Approximation for the non-retarded Casimir force. We present analytical results for the force between objects of various shapes and substrates, and between pairs of objects. We compare the results to those from more exact numerical calculations. We treat spheres, spheroids, cylinders, cubes, cones, and wings; the analytical PFA results together with the geometrical correction factors are summarized in a table.
Using a template-stripping method, macroscopic gold surfaces with root-mean-square (rms) roughness less than 0.4 nm have been prepared, making them useful for studies of surface interactions in the nanometer range. The utility of such substrates is demonstrated by measurements of the Casimir force at surface separations between 20 and 100 nm, resulting in good agreement with theory. The significance and quantification of this agreement is addressed, as well as some methodological aspects regarding the measurement of the Casimir force with high accuracy.
We have calculated dynamical Casimir-Polder interaction force between a moving ground state atom and a flat polarizable surface. The velocity of an atom can be close to the velocity of light. The material properties are taken into account using a single oscillator model of the atomic dynamic polarizability and the Drude dielectric function of a metal substrate. The limit cases of nonrelativistic velocities and an ideal metal substrate are also considered. We have found specific dependence of the calculated forces on the velocity (energy), distance and material properties.
We study the behavior of the critical Casimir force and its interplay with the van der Waals force acting between two parallel slabs separated at a distance $L$ from each other confining a non-polar simple fluid or a binary liquid mixture. The surfaces of the slabs are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture. The slabs influence the fluid by long-range competing dispersion potentials. Under such conditions one usually expects {\it attractive} Casimir force governed by universal scaling function to which the disp…
We use the extended Lifshitz theory to study the behaviors of the Casimir forces between finite-thickness effective medium slabs. We first study the interaction between a semi-infinite Drude metal and a finite-thickness magnetic slab with or without substrate. For no substrate, the large distance $d$ dependence of the force is repulsive and goes as $1/d^5$; for the Drude metal substrate, a stable equilibrium point appears at an intermediate distance which can be tuned by the thickness of the slab. We then study the interaction between two identical chiral metamaterial slabs with and without su…
Thermal effects contributing to the Casimir interaction between objects are usually small at room temperature and they are difficult to separate from quantum mechanical contributions at higher temperatures. We propose that the thermal Casimir force effect can be observed for a graphene flake suspended in a fluid between substrates at the room temperature regime. The properly chosen materials for the substrates and fluid induce a Casimir repulsion. The balance with the other forces, such as gravity and buoyancy, results in a stable temperature dependent equilibrium separation. The suspended gra…
We study the optomechanical coupling of a oscillating effective mirror with a Rydberg atomic gas, mediated by the dynamical atom-mirror Casimir-Polder force. This coupling may produce a near-field resonant atomic excitation whose probability scales as $\propto (d^2\;a\;n^4\;t)^2/z_0^8$, where $z_0$ is the average atom-surface distance, $d$ the atomic dipole moment, $a$ the mirror's effective oscillation amplitude, $n$ the initial principal quantum number, and $t$ the time. We propose an experimental configuration to realize this system with a cold atom gas trapped at a distance $\sim 2\cdot10 …
The attractive Casimir force acting on a micrometer-sphere suspended in a spherical dip, close to the wall, is discussed. This setup is in principle directly accessible to experiment. The sphere and the substrate are assumed to be made of the same perfectly conducting material.
We show that an isotropic dipolar particle in the vicinity of a substrate made of nonreciprocal plasmonic materials can experience a lateral Casimir force and torque when the particle's temperature differs from that of the slab and the environment. We connect the existence of the lateral force to the asymmetric dispersion of nonreciprocal surface polaritons and the existence of the lateral torque to the spin-momentum locking of such surface waves. Using the formalism of fluctuational electrodynamics, we show that the features of lateral force and torque should be experimentally observable usin…
We present calculations of the zero-temperature Casimir interaction between two freestanding graphene sheets as well as between a graphene sheet and a substrate. Results are given for undoped graphene and for a set of doping levels covering the range of experimentally accessible values. We describe different approaches that can be used to derive the interaction. We point out both the predicted power law for the interaction and the actual distance dependence.
One of the most important tools in modern science is the analysis of electromagnetic properties via spectroscopy. The various types of spectroscopy can be classified by the underlying type of interactions between energy and material. In this paper we demonstrate a new class of spectroscopy based on Casimir interactions between a solid investigated object and a reference surface embedded in an environmental liquid medium. Our main example is based on the measurement of Hamaker constants upon changing the concentration of an intervening two-component liquid, where we demonstrate a possible recon…
Casimir forces on suspended thin dielectric membranes covered with graphene
The Hong Kong University of Science and Technology（香港科技大学）；Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier（夏尔·库隆实验室（L2C），CNRS-蒙彼利埃大学联合研究单位5221）
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 …
The thermal Casimir-Lifshitz force among two bodies held at different temperatures displays striking features that are absent in systems in thermal equilibrium. The manifestation of this force has been observed so far only in Bose-Einstein condensates close to a heated substrate, but never between two macroscopic bodies. Observation of the thermal Casimir-Lifhitz force out of thermal equilibrium with conventional Casimir setups is very difficult, because for experimentally accessible separations the thermal force is small compared to the zero-temperature quantum Casimir force, unless prohibiti…
In this paper we theoretically demonstrate the tunability of the Casimir force both in sign and magnitude between parallel plates coated with dispersive materials. We show that this force, existing between uncharged plates, can be tuned by carefully choosing the value of the plasma frequency (i.e., the epsilon-near-zero frequency) of the coating in the neighborhood of the resonance frequency of the cavity. The coating layer enables a continuous variation of the force between four limiting values when a coating is placed on each plate. We explore the consequences of such variation when pairs of…
