Search Results (16)

We review and as well obtain some new results on the temperature dependence of spatially nonlocal response functions of graphene and their applications to the calculation of both the equilibrium and nonequilibrium Casimir and Casimir–Polder forces. After a brief summary of the properties of the polarization tensor of graphene obtained within the Dirac model in the framework of quantum field theory, we derive the expressions for the longitudinal and transverse dielectric functions. The behavior of these functions at different temperatures is investigated in the regions below and above the threshold. Special attention is paid to the double pole at zero frequency, which is present in the transverse response function of graphene. An application of the response functions of graphene to the calculation of the equilibrium Casimir force between two graphene sheets and the Casimir–Polder forces between an atom (nanoparticle) and a graphene sheet is considered with due attention to the role of a nonzero energy gap, chemical potential and a material substrate underlying the graphene sheet. The same subject is discussed for out-of-thermal-equilibrium Casimir and Casimir–Polder forces. The role of the obtained and presented results for fundamental science and nanotechnology is outlined. Full article

We consider a multilevel atom, such as a hydrogen atom, interacting with the quantum electromagnetic field in the dressed ground state of the interacting system. Using perturbation theory within the dipole approximation, we evaluate the dressed ground state and investigate the effect of atomic self-dressing on several field and atomic observables. Specifically, we obtain general expressions of the renormalized electric and magnetic field fluctuations and energy densities around the atom, and analyze their scaling with the distance from the atom, obtaining approximated expressions in the so-called near and far zones. We also investigate nonlocal spatial field correlations around the atom. We stress how the quantities we evaluate can be probed through two- and three-body nonadditive Casimir–Polder dispersion interactions. We also investigate the effect of self-dressing—namely, the virtual transitions occurring in the dressed ground state—on atomic observables, such as the average potential energy of the electron in the nuclear field. This also allows us to obtain a more fundamental quantum basis for the Welton interpretation of the Lamb shift of a ground-state hydrogen atom, in terms of the atomic self-dressing processes. Full article

We investigate the quantum forces occurring between the defects and/or boundaries of a conformal field theory (CFT). We propose to model imperfect defects and boundaries as localized relevant double-trace operators that deform the CFT. Our focus is on pointlike and codimension-one planar defects. In the case of two parallel membranes, we point out that the CFT 2-point function tends to get confined and develops a tower of resonances with a constant decay rate when the operator dimension approaches the free field dimension. Using a functional formalism, we compute the quantum forces induced by the CFT between a variety of configurations of pointlike defects, infinite plates and membranes. Consistency arguments imply that these quantum forces are attractive at any distance. Forces of the Casimir–Polder type appear in the UV (ultraviolet), while forces of the Casimir type appear in the IR (infrared), in which case the CFT gets repelled from the defects. Most of the forces behave as a non-integer power of the separation, controlled by the dimension of the double-trace deformation. In the Casimir regime of the membrane–membrane configuration, the quantum pressure behaves universally as $1/{\ell }^d$; however, information about the double-trace nature of the defects still remains encoded in the strength of the pressure. Full article

The Casimir–Polder force between spherical nanoparticles and a graphene-coated silica plate is investigated in situations out of thermal equilibrium, i.e., with broken time-reversal symmetry. The response of the graphene coating to the electromagnetic field is described on the basis of first principles of quantum electrodynamics at nonzero temperature using the formalism of the polarization tensor in the framework of the Dirac model. The nonequilibrium Casimir–Polder force is calculated as a function of the mass-gap parameter, the chemical potential of graphene, and the temperature of the graphene-coated plate, which can be both higher or lower than that of the environment. It is shown that the force value increases with the increasing chemical potential, and this increase is more pronounced when the temperature of a graphene-coated plate is lower than that of the environment. The nonequilibrium force also increases with increasing temperature of the graphene-coated plate. This increase is larger when the plate is hotter than the environment. The effect is revealed that the combined impact of the chemical potential, $\mu$, and mass gap, $\Delta$, of the graphene coating depends on the relationship between $\Delta$ and 2$\mu$. If $2\mu >\Delta$, the magnitude of the nonequilibrium force between nanoparticles and a cooled graphene-coated plate becomes much larger than for a graphene coating with $\mu =0$. The physical reasons explaining this effect are elucidated. Possible applications of the obtained results are discussed. Full article

We review the derivative expansion (DE) method in Casimir physics, an approach which extends the proximity force approximation (PFA). After introducing and motivating the DE in contexts other than the Casimir effect, we present different examples which correspond to that realm. We focus on different particular geometries, boundary conditions, types of fields, and quantum and thermal fluctuations. Besides providing various examples where the method can be applied, we discuss a concrete example for which the DE cannot be applied; namely, the case of perfect Neumann conditions in $2+1$ dimensions. By the same example, we show how a more realistic type of boundary condition circumvents the problem. We also comment on the application of the DE to the Casimir–Polder interaction which provides a broader perspective on particle–surface interactions. Full article

Fluctuation-induced forces are a hallmark of the interplay between fluctuations and geometry. We recently proved the existence of a multi-parametric family of exact representations of Casimir and Casimir–Polder interactions between bodies of arbitrary shape and material composition, admitting a multiple scattering expansion (MSE) as a sequence of inter-body and intra-body multiple wave scatterings. The approach requires no knowledge of the scattering amplitude (T-matrix) of the bodies. In this paper, we investigate the convergence properties of the MSE for the Casimir–Polder interaction of a polarizable particle with a macroscopic body. We consider representative materials from different classes, such as insulators, conductors, and semiconductors. Using a sphere and a cylinder as benchmarks, we demonstrate that the MSE can be used to efficiently and accurately compute the Casimir–Polder interaction for bodies with smooth surfaces. Full article

The design of a photonic system for the trapping and waveguiding of ultracold atoms far above a dielectric surface is proposed and analyzed. The system consists of an optical rib waveguide deposited on a planar one-dimensional photonic crystal, which sustains two wavelengths of photonic crystal surface modes tuned in the red and blue sides relative to the atomic transition of the neutral atom. The addition of a third blue-tuned wavelength to the system allows the neutral atoms to be stabilized in the lateral dimension above the rib waveguide. Trapping atoms at relatively large distances, more than 600 nm above the dielectric surface, allows to reduce the influence of Casimir–Polder forces in this system. The detailed design methodology and specifications of the photonic system are provided. The presented design can be employed in atomic chips and quantum sensors. Full article

The Casimir–Polder force between atoms or nanoparticles and graphene-coated dielectric substrates is investigated in the region of large separations. Graphene coating with any value of the energy gap and chemical potential is described in the framework of the Dirac model using the formalism of the polarization tensor. It is shown that the Casimir–Polder force from a graphene-coated substrate reaches the limit of large separations at approximately 5.6 $\mathsf{\mu }$m distance between an atom or a nanoparticle and graphene coating independently of the values of the energy gap and chemical potential. According to our results, however, the classical limit, where the Casimir–Polder force no longer depends on the Planck constant and the speed of light, may be attained at much larger separations depending on the values of the energy gap and chemical potential. In addition, we have found a simple analytic expression for the Casimir–Polder force from a graphene-coated substrate at large separations and determined the region of its applicability. It is demonstrated that the asymptotic results for the large-separation Casimir–Polder force from a graphene-coated substrate are in better agreement with the results of numerical computations for the graphene sheets with larger chemical potential and smaller energy gap. Possible applications of the obtained results in nanotechnology and bioelectronics are discussed. Full article

The out-of-thermal-equilibrium Casimir–Polder force between nanoparticles and dielectric substrates coated with gapped graphene is considered in the framework of the Dirac model using the formalism of the polarization tensor. This is an example of physical phenomena violating the time-reversal symmetry. After presenting the main points of the used formalism, we calculate two contributions to the Casimir–Polder force acting on a nanoparticle on the source side of a fused silica glass substrate coated with gapped graphene, which is either cooler or hotter than the environment. The total nonequilibrium force magnitudes are computed as a function of separation for different values of the energy gap and compared with those from an uncoated plate and with the equilibrium force in the presence of graphene coating. According to our results, the presence of a substrate increases the magnitude of the nonequlibrium force. The force magnitude becomes larger with higher and smaller with lower temperature of the graphene-coated substrate as compared to the equilibrium force at the environmental temperature. It is shown that, with increasing energy gap, the magnitude of the nonequilibrium force becomes smaller, and the graphene coating makes a lesser impact on the force acting on a nanoparticle from the uncoated substrate. Possible applications of the obtained results are discussed. Full article

The Casimir–Polder force acting on atoms and nanoparticles spaced at large separations from real graphene sheets possessing some energy gaps and chemical potentials is investigated in the framework of the Lifshitz theory. The reflection coefficients expressed via the polarization tensor of graphene, found based on the first principles of thermal quantum field theory, are used. It is shown that for graphene the separation distances, starting from which the zero-frequency term of the Lifshitz formula contributes more than 99% of the total Casimir–Polder force, are less than the standard thermal length. According to our results, however, the classical limit for graphene, where the force becomes independent of the Planck constant, may be reached at much larger separations than the limit of the large separations determined by the zero-frequency term of the Lifshitz formula, depending on the values of the energy gap and chemical potential. The analytic asymptotic expressions for the zero-frequency term of the Lifshitz formula at large separations are derived. These asymptotic expressions agree up to 1% with the results of numerical computations starting from some separation distances that increase with increasing energy gaps and decrease with increasing chemical potentials. The possible applications of the obtained results are discussed. Full article

We propose Green functions scattering method to obtain the Casimir–Polder potential between anisotropic atom and one or two planar parallel plates. Lifshitz formula for pressure between two dielectric half-spaces separated by a vacuum slit is derived within the same method. The method is also applied to known conducting systems including graphene which are overviewed. Full article

We investigate optical forces on oscillating dipoles close to a phase change vanadium dioxide (VO${}_2$) film, which exhibits a metal-insulator transition around 340 K and low thermal hysteresis. This configuration emulates the interaction between an illuminated nanosphere and an interface and we employ a classical description to capture its important aspects. We consider both electric and magnetic dipoles for two different configurations, namely with the dipole moments parallel and perpendicular to the VO${}_2$ film. By using Bruggeman theory to describe the effective optical response of the material, we show that the thermal hysteresis present in the VO${}_2$ transition clearly shows up in the behavior of optical forces. In the near-field regime, the force on both dipoles can change from attractive to repulsive just by heating (or cooling) the film for a selected frequency range. We also verified that the optical forces are comparable to the Casimir-Polder force in a similar system, revealing the possibility of modulating or even changing the sign of the resultant force on an illuminated nano-object due to the presence of a thermochromic material. We hope that this work contributes to set the grounds for alternative approaches to control light-matter interactions using phase-change materials. Full article

We consider the low-temperature expansion of the Casimir-Polder free energy for an atom and graphene by using the Poisson representation of the free energy. We extend our previous analysis on the different relations between chemical potential $\mu$ and mass gap parameter m. The key role plays the dependence of graphene conductivities on the $\mu$ and m. For simplicity, we made the manifest calculations for zero values of the Fermi velocity. For $\mu >m$, the thermal correction $\sim T^2$, and for $\mu <m$, we confirm the recent result of Klimchitskaya and Mostepanenko, that the thermal correction $\sim T^5$. In the case of exact equality $\mu =m$, the correction $\sim T$. This point is unstable, and the system falls to the regime with $\mu >m$ or $\mu <m$. The analytical calculations are illustrated by numerical evaluations for the Hydrogen atom/graphene system. Full article

We consider the out-of-thermal-equilibrium Casimir-Polder interaction between atoms of He${}^{*}$, Na, Cs, and Rb and a cavity wall made of sapphire coated with a vanadium dioxide film which undergoes the dielectric-to-metal phase transition with increasing wall temperature. Numerical computations of the Casimir-Polder force and its gradient as the functions of atom-wall separation and wall temperature are made when the latter exceeds the temperature of the environment. The obtained results are compared with those in experiment on measuring the gradient of the Casimir-Polder force between ${}^{87}$Rb atoms and a silica glass wall out of thermal equilibrium. It is shown that the use of phase-change wall material significantly increases the force magnitude and especially the force gradient, as opposed to the case of a dielectric wall. Full article

We review recent results on the low-temperature behaviors of the Casimir-Polder and Casimir free energy an entropy for a polarizable atom interacting with a graphene sheet and for two graphene sheets, respectively. These results are discussed in the wide context of problems arising in the Lifshitz theory of van der Waals and Casimir forces when it is applied to metallic and dielectric bodies. After a brief treatment of different approaches to theoretical description of the electromagnetic response of graphene, we concentrate on the derivation of response function in the framework of thermal quantum field theory in the Matsubara formulation using the polarization tensor in (2 + 1)-dimensional space—time. The asymptotic expressions for the Casimir-Polder and Casimir free energy and entropy at low temperature, obtained with the polarization tensor, are presented for a pristine graphene as well as for graphene sheets possessing some nonzero energy gap $\Delta$ and chemical potential $\mu$ under different relationships between the values of $\Delta$ and $\mu$. Along with reviewing the results obtained in the literature, we present some new findings concerning the case $\mu \ne 0$, $\Delta =0$. The conclusion is made that the Lifshitz theory of the Casimir and Casimir-Polder forces in graphene systems using the quantum field theoretical description of a pristine graphene, as well as real graphene sheets with $\Delta >2\mu$ or $\Delta <2\mu$, is consistent with the requirements of thermodynamics. The case of graphene with $\Delta =2\mu \ne 0$ leads to an entropic anomaly, but is argued to be physically unrealistic. The way to a resolution of thermodynamic problems in the Lifshitz theory based on the results obtained for graphene is discussed. Full article