Lifshitz Force Research Articles

The normal Casimir–Lifshitz force for laterally moving graphene

We consider the system of two parallel sheets of graphene which are moving with relative parallel velocity v⃗ and calculate the Casimir energy by using the scattering approach. We analyze in detail the normal (perpendicular to the planes) Casimir force for two systems—graphene/graphene and ideal metal/graphene. In the non-relativistic case v ≪ v F, the relative correction to the Casimir energy (Ev−E0)/E0 is proportional to the (v/c)2 (the maximum value is 0.0033 for the gapeless case and v = v F) for the first system, and it is zero up to the Fermi velocity v = v F for system ideal metal/graphene.

Casimir–Lifshitz Frictional Heating in a System of Parallel Metallic Plates

The Casimir–Lifshitz force of friction between neutral bodies in relative motion, along with the drag effect, causes their heating. This paper considers this frictional heating in a system of two metal plates within the framework of fluctuation electromagnetic theory. Analytical expressions for the friction force in the limiting cases of low (zero) temperature and low and high speeds, as well as general expressions describing the kinetics of heating, have been obtained. It is shown that the combination of low temperatures (T < 10 K) and velocities of 10–103 m/s provides the most favorable conditions when measuring the Casimir–Lifshitz friction force from heat measurements. In particular, the friction force of two coaxial disks of gold 10 cm in diameter and 500 nm in thickness, one of which rotates at a frequency of 10–103 rps (revolutions per second), can be measured using the heating effect of 1–2 K in less than 1 min. A possible experimental layout is discussed.

Confinement-induced nonlocality and casimir force in transdimensional systems.

We study within the framework of the Lifshitz theory the long-range Casimir force for in-plane isotropic and anisotropic free-standing transdimensional material slabs. In the former case, we show that the confinement-induced nonlocality not only weakens the attraction of ultrathin slabs but also changes the distance dependence of the material-dependent correction to the Casimir force to go as contrary to the ∼1/l dependence of that of the local Lifshitz force. In the latter case, we use closely packed array of parallel aligned single-wall carbon nanotubes in a dielectric layer of finite thickness to demonstrate strong orientational anisotropy and crossover behavior for the inter-slab attractive force in addition to its reduction with decreasing slab thickness. We give physical insight as to why such a pair of ultrathin slabs prefers to stick together in the perpendicularly oriented manner, rather than in the parallel relative orientation as one would customarily expect.

Fluctuational electrodynamics in and out of equilibrium

Dispersion forces between neutral material bodies are due to fluctuations of the polarization of the bodies. For bodies in equilibrium these forces are often referred to as Casimir–Lifshitz forces. For bodies in relative motion, in addition to the Casimir–Lifshitz force, a lateral frictional force (“quantum friction”, in the zero temperature limit) comes into play. The widely accepted theory of the fluctuation-induced forces is based on the “fluctuational electrodynamics”, when the Maxwell equations are supplemented by random current sources responsible for the fluctuations of the medium polarization. The first part of our paper touches on some conceptual issues of the theory, such as the dissipation-less limit and the link between Rytov’s approach and quantum electrodynamics. We point out the problems with the dissipation-less plasma model (with its unphysical double pole at zero frequency) which still appears in the literature. The second part of the paper is devoted to “quantum friction”, in a broad sense, and it contains some novel material. In particular, it is pointed out that in weakly dissipative systems the friction force may not be a stationary process. It is shown, using an “exact” (nonperturbative) quantum treatment, that under appropriate conditions, an instability can occur when the kinetic energy (due to the relative motion between the bodies) is transformed into coherent radiation, exponentially growing in intensity (the instability gets eventually limited by nonlinear effects). We also discuss a setup when the two bodies are at rest but a constant electric current is flowing in one of the bodies. One may say that only the electron component of one body is dragged with respect to the other body, unlike the usual setup when the two bodies are in relative motion. Clearly, there are differences in the frictional forces between the two setups.

Effect of Spatial Inhomogeneity on Quantum Trapping

An object that is immersed in a fluid and approaching a substrate may find a potential energy minimum at a certain distance due to the balance between attractive and repulsive Casimir–Lifshitz forces, a phenomenon referred to as quantum trapping. This equilibrium depends on the relative values of the dielectric functions of the materials involved. Herein, we study quantum trapping effects in planar nanocomposite materials and demonstrate that they are strongly dependent on the characteristics of the spatial inhomogeneity. As a model case, we consider spherical particles embedded in an otherwise homogeneous material. We propose an effective medium approximation that accounts for the effect of inclusions and find that an unprecedented and counterintuitive intense repulsive Casimir–Lifshitz force arises as a result of the strong optical scattering and absorption size-dependent resonances caused by their presence. Our results imply that the proper analysis of quantum trapping effects requires comprehensive knowledge and a detailed description of the potential inhomogeneity (caused by imperfections, pores, inclusions, and density variations) present in the materials involved.

The Casimir Effect in Topological Matter

We give an overview of the work done during the past ten years on the Casimir interaction in electronic topological materials, our focus being solids, which possess surface or bulk electronic band structures with nontrivial topologies, which can be evinced through optical properties that are characterizable in terms of nonzero topological invariants. The examples we review are three-dimensional magnetic topological insulators, two-dimensional Chern insulators, graphene monolayers exhibiting the relativistic quantum Hall effect, and time reversal symmetry-broken Weyl semimetals, which are fascinating systems in the context of Casimir physics. Firstly, this is for the reason that they possess electromagnetic properties characterizable by axial vectors (because of time reversal symmetry breaking), and, depending on the mutual orientation of a pair of such axial vectors, two systems can experience a repulsive Casimir–Lifshitz force, even though they may be dielectrically identical. Secondly, the repulsion thus generated is potentially robust against weak disorder, as such repulsion is associated with the Hall conductivity that is topologically protected in the zero-frequency limit. Finally, the far-field low-temperature behavior of the Casimir force of such systems can provide signatures of topological quantization.

Casimir-Lifshitz Force Based Optical Resonators.

We theoretically investigate the building of optical resonators based on the levitation properties of thin films subjected to strong repulsive Casimir-Lifshitz forces when immersed in an adequate medium and confronted with a planar substrate. We propose a design in which cavities supporting high Q-factor optical modes at visible frequencies can be achieved by means of combining commonly found materials, such as silicon oxide, polystyrene or gold, with glycerol as a mediating medium. We use the balance between flotation and repulsive Casimir-Lifshitz forces in the system to accurately tune the optical cavity thickness and hence its modes. The effects of other forces, such as electrostatic, that may come into play are also considered. Our results constitute a proof of concept that may open the route to the design of photonic architectures in environments in which dispersion forces play a substantial role and could be of particular relevance for devising novel microfluidic optical resonators.

Diamond polishing of crystalline materials for optoelectronics

A study of the mechanism of mechanical polishing of optoelectronic components made of crystalline materials has demonstrated that the removal rate in polishing decreases with increasing workpiece material’s bond energy and energy of transfer and grows with increasing thermal conductivity coefficient of the workpiece material, sliding distance of a workpiece surface element against the polishing pad surface, and Lifshitz force. The ratio between the volumetric wear coefficient and thermal diffusivity of the workpiece material is shown to depend on specific heat capacity and energy of transfer.

Lifshitz interaction can promote ice growth at water-silica interfaces

At air-water interfaces, the Lifshitz interaction by itself does not promote ice growth. On the contrary, we find that the Lifshitz force promotes the growth of an ice film, up to 1--8 nm thickness, near silica-water interfaces at the triple point of water. This is achieved in a system where the combined effect of the retardation and the zero frequency mode influences the short-range interactions at low temperatures, contrary to common understanding. Cancellation between the positive and negative contributions in the Lifshitz spectral function is reversed in silica with high porosity. Our results provide a model for how water freezes on glass and other surfaces.

A theory of dielectric fluid films between nanostructures

In this paper a theory of dielectric fluid films between nanostructures is developed by using the theory of nonlocal electromagnetic fluids so that the nonlocal hydrodynamic force, the Lifshitz force and solvation forces can be treated systematically within the realm of continuum mechanics. In order for a continuum model to account for these surface forces of molecular origin without ad hoc assumptions, it should be endowed with a theoretical framework in which not only to represent the inner structures of fluids but to inherently possess a rational basis to merge with the Lifshitz theory without losing its rigor and also to accommodate other types of surface forces. The proposed nonlocal continuum model is formulated as such and can be adapted to all separations for which the Lifshitz theory is valid. It is applied, as an example problem, to the case of a plane-sphere configuration in the non-retarded van der Waals limit where solvation forces manifest themselves.

Intensifying the Casimir force between two silicon substrates within three different layers of materials

We investigate the Casimir force for a system composed of two thick slabs as substrates within three different homogeneous layers. We use the scattering approach along with the Matsubara formalism in order to calculate the Casimir force at finite temperature. First, we focus on constructing the reflection matrices and then we calculate the Casimir force for a water–lipid system. According to the conventional use of silicon as a substrate, we apply the formalism to calculate the Casimir force for layers of Au, VO2, mica, KCl and foam rubber on the thick slabs of silicon. Afterwards, introducing an increasing factor, we compare our results with Lifshitz force in the vacuum between two semispaces of silicon in order to illustrate the influence of the layers on intensifying the Casimir force. We also calculate the Casimir force between two slabs of the forementioned materials with finite thicknesses to indicate the substrate's role in increasing the obtained Casimir force. Our simple calculation is interesting since one can extend it along with the Rigorous Coupled Wave Analysis to systems containing inhomogeneous layers as good candidates for designing nanomechanical devices.

Giant non-equilibrium vacuum friction: role of singular evanescent wave resonances in moving media

We recently reported on the existence of a singular resonance in moving media which arises due to perfect amplitude and phase balance of evanescent waves. We show here that the nonequilibrium vacuum friction (lateral Casimir–Lifshitz force) between moving plates separated by a finite gap is fundamentally dominated by this resonance. Our result is robust to losses and dispersion as well as polarization mixing which occurs in the relativistic limit.

Casimir energy, dispersion, and the Lifshitz formula

Despite suggestions to the contrary, we show in this paper that the usual dispersive form of the electromagnetic energy must be used to derive the Lifshitz force between parallel dielectric media. This conclusion follows from the general form of the quantum vacuum energy, which is the basis of the multiple-scattering formalism. As an illustration, we explicitly derive the Lifshitz formula for the interaction between parallel dielectric semispaces, including dispersion, starting from the expression for the total energy of the system. The issues of constancy of the energy between parallel plates and of the observability of electrostrictive forces are briefly addressed.

Comment on “Thermal Lifshitz Force between an Atom and a Conductor with a Small Density of Carriers”

We demonstrate that the generalization of the Lifshitz theory proposed by L. P. Pitaevskii arXiv:0801.0656 [Phys. Rev. Lett. v.101, 163202 (2008)] violates the Nernst heat theorem for many dielectric materials and is experimentally inconsistent.

Contribution of Drifting Carriers to the Casimir-Lifshitz and Casimir-Polder Interactions With Semiconductor Materials

We develop a theory for Casimir-Lifshitz and Casimir-Polder interactions with semiconductor or insulator surfaces that takes into account charge drift in the bulk material through use of the classical Boltzmann equation. We derive frequency-dependent dispersion relations that give the usual Lifshitz results for dielectrics as a limiting case and, in the quasistatic limit, coincide with those recently computed to account for Debye screening in the thermal Lifshitz force with conducting surfaces with small density of carriers.

Thermal Lifshitz Force between an Atom and a Conductor with a Small Density of Carriers

A new theory describing the interaction between atoms and a conductor with small densities of current carriers is presented. The theory takes into account the penetration of the static component of the thermally fluctuating field in the conductor and generalizes the Lifshitz theory in the presence of a spatial dispersion. The equation obtained for the force describes the continuous crossover between the Lifshitz results for dielectrics and metals.

Quantum fluctuations in the presence of thin metallic films and anisotropic materials

We present our most recent results seeking to understand the dependence of quantum fluctuations of the electromagnetic field on the dielectric properties of two boundary surfaces. In the first section, we provide a detailed description of our measurement of the skin-depth effect of the Casimir–Lifshitz force. The second section is devoted to the torque induced by quantum fluctuations on two birefringent plates.

Retarded Casimir interaction in the asymptotic domain of an electron and a dielectric wall.

A number of different approaches have been used to determine the interactions between a variety of pairs of polarizable systems asymptotically far apart; these are examples of retardation or Casimir interactions. The pairs include two dielectric walls, and an atom and a dielectric wall, but not an electron and a dielectric wall. (The asymptotic value of the interaction between an electron and an ideal conducting wall has been evaluated.) We here apply a method not previously used in the evaluation of retardation potentials, quantized Fresnel modes, to determine the interaction in the asymptotic domain of a polarizable system and a dielectric wall. We thereby reproduce the known result for an atom and a dielectric wall and obtain a previously unobtained result, that for an electron and a dielectric wall. The result simplifies greatly for an ideal metallic wall and for a wall made from a material such as liquid helium for which the dielectric constant is very close to unity. We also discuss the question of a connection between the electron--dielectric-wall interaction and Lifshitz's force per unit area between two dielectric walls. The determination of the amplitudes of the Fresnel modes, by quantization, is the only nonclassical element in the calculation.

Retarded dispersion forces in dielectrics at finite temperatures

The long-range dispersion forces in a non-uniform dielectric at finite temperature are deduced from the frequency-dependent susceptibility of the electric field and the dielectric constant at imaginary frequency by a method which gives the main results of Lifshitz’s treatment and does not use quantum field theory. The fluctuation-dissipation theorem allows one to express the dispersion free energy of an atom in terms of its electric polarizability, and to derive the image force on an atom near a metal surface, or the dispersion force between two atoms in vacuo at any temperature. By considering the relation between the force on an atom outside a dielectric and the state of the field inside the dielectric we derive an expression for the long-range dispersion part of the free energy of the medium , and find the force between two dissolved atom s in a dielectric fluid. The forces are equivalent to a system of Maxwell stresses which can be calculated from the field susceptibilities. A simple classical treatment of the susceptibility then gives the Lifshitz force between two parallel plates of dielectric at close distances.