Electromagnetic vacuum fluctuations have observable consequences, like the Casimir force between mirrors in vacuum. This force is now measured with good accuracy and agreement with theory when the effect of imperfect reflection of mirrors is properly taken into account. We discuss the simple case of bulk metallic mirrors described by a plasma model and show that simple scaling laws are obtained at the limits of long and short distances. The crossover between the short and long-distance laws is quite similar to the crossover between Van der Waals and Casimir-Polder forces for two atoms in vacuum. The result obtained at short distances can be understood as the London interaction between plasmon excitations at the surface of each bulk mirror.
We investigate the thermal Casimir-Polder (CP) potential of \textsuperscript{87}Rb atoms in Rydberg $n$S-states near single- and double-layer graphene. The dependence of the CP potential on parameters such as atom-surface distance, temperature, principal quantum number $n$ and graphene Fermi energy are explored. Through large scale numerical simulations, we show that, in the non-retarded regime, the CP potential is dominated by the non-resonant and evanescent-wave terms which are monotonic, and that, in the retarded regime, the CP potential exhibits spatial oscillations. We identify that the m…
We review modern achievements and problems in physics of the van der Waals and Casimir forces which arise due to zero-point and thermal fluctuations of the electromagnetic field between closely spaced material surfaces. This subject attracted great experimental and theoretical attention during the last few years because the fluctuation-induced forces find a lot of applications in both fundamental physics and nanotechnology. After a short introduction to the subject, we describe main experimental and theoretical results obtained in the field during the last fifteen years. In the following prese…
Interactions induced by electromagnetic fluctuations, such as van der Waals and Casimir forces, are of universal nature present at any length scale between any types of systems with finite dimensions. Such interactions are important not only for the fundamental science of materials behavior, but also for the design and improvement of micro- and nano-structured devices. In the past decade, many new materials have become available, which has stimulated the need of understanding their dispersive interactions. The field of van der Waals and Casimir forces has experienced an impetus in terms of dev…
We consider a perfectly conducting infinite cylinder with radius $R$, and investigate the Casimir-Polder (CP) and van der Waals (vdW) interactions with a neutral polarizable particle constrained to move in a plane distant $x_0>R$ from the axis of the cylinder. We show that when the relative curvature $x_0/R \lesssim 6.44$, this particle, under the action of the lateral CP force (which is the projection of the CP force onto the mentioned plane), is attracted to the point on the plane which is closest to the cylinder surface. On the other hand, when $x_0/R \gtrsim 6.44$, we also show that, for c…
Lifshitz-type formulas for graphene and single-wall carbon nanotubes: van der Waals and Casimir interations
得到了石墨烯与平板、石墨烯与原子或分子、单壁碳纳米管与平板之间的van der Waals和Casimir相互作用的Lifshitz型公式。石墨烯上电磁振荡的反射特性由施加在无限薄的带正电的等离子体片上的特定边界条件决定，该等离子体片携带具有一定质量和电荷密度的连续流体。将所得公式应用于石墨烯与Au和Si板的相互作用、氢原子和分子与石墨烯的相互作用以及单壁碳纳米管与Au和Si板的相互作用。更复杂的碳纳米结构的推广进行了讨论。
It is demonstrated that the general theory of Casimir and van der Waals forces describes the interaction-induced equilibrium thermodynamic potentials of the damped harmonic oscillator bilinearly coupled to the environment. An extended model for a damped oscillator is suggested along the lines of the general theory of Casimir and van der Waals forces, and the corresponding thermodynamic quantities obtained. While the original model involves a heat bath consisting of a large number of free oscillators having infinitesimal damping functions, the extended model allows any generally admissible freq…
我们建立了色散力之间的一般关系。首先，基于因果介质中的QED，采用首阶微扰理论，用原子极化率和体助电磁场的格林张量来表示单原子Casimir-Polder势和双原子van der Waals势。在这个几何无关的框架下，我们采用格林张量的玻恩展开和Clausius-Mosotti关系，证明了在介电体存在下，原子的宏观Casimir-Polder势是由其微观多原子与组成介电体的原子之间的范德华相互作用的无穷和所引起的.这个定理适用于非均匀的，分散的，和吸收机构的任意形状和任意原子组成的任意背景下的附加磁介电体。
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 discuss the van der Waals (Casimir) free energies and pressures of thin metallic films, consisting from one to fifteen atomic layers, with regard to the anisotropy in their dielectric properties. Both free-standing films and films deposited on a dielectric substrate are considered. The computations are performed for a Au film and a sapphire substrate. According to our results, for free-standing Au films consisting of one and three atomic layers the respective relative error arising from the use of an isotropic (bulk) dielectric permittivity is equal to 73% and 37% for the van der Waals ener…
We present a formula for the body-assisted van der Waals interaction potential between two atoms, one or both being prepared in an excited energy eigenstate. The presence of arbitrary arrangement for material environment is taken into account via the Green function. The resulting formula supports one of two conflicting findings recorded. The consistency of our formula is investigated by applying it for the case of two atoms in free space and comparing the resulting expression with the one found from the limiting Casimir-Polder potential between an excited atom and a small dielectric sphere.
We address the long-standing controversy regarding the correct description of the electromagnetic energy-momentum tensor in media and its consequences for the Casimir force. The latter being due to the zero-point momentum of the electromagnetic field, competing approaches based on the Abraham or Maxwell stress tensor lead to different predictions. We consider the test scenario of two colloidal spherical particles submerged in a dielectric medium and use three criteria to distinguish the two approaches: we show that the Abraham stress tensor, and not the Maxwell stress tensor, leads to a Casimi…
Casimir-Lifshitz interaction between ZnO and SiO2 nanorods in bromobenzene: retardation effects turn the interaction repulsive at intermediate separations
We consider the the van der Waals force involving excited atoms in general environments, constituted by magnetodielectric bodies. We develop a dynamical approach studying the dynamics of the atoms and the field, mutually coupled. When only one atom is excited, our dynamical theory suggests that for large distances the van der Waals force acting on the ground-state atom is monotonic, while the force acting in the excited atom is spatially oscillating. We show how this latter force can be related to the known oscillating Casimir--Polder force on an excited atom near a (ground-state) body. Our fo…
In this article, we rigorously analyze the effects of the dispersion forces (Casimir and van der Waals forces) on a nano-optomechanical device based on a silicon waveguide and a silicon dioxide substrate, surrounded by air and driven by optical forces. The dispersion forces are calculated using a modified Lifshitz theory, in order to take into account the device thickness and material s dielectric permittivities, which are obtained from experimental optical data and validated by means of a rigorous 3D FDTD simulation. We also take into account the mechanical nonlinearity of the waveguide, whic…
The Casimir-Polder interaction an atom with spherical shell
在流体力学方法的框架下研究了原子与有限电导率的无限薄球的Casimir Polder和van der Waals相互作用能。我们把球放入无限介质中的球腔中，然后用zeta函数方法计算真空涨落的能量。单个原子的能量是通过稀薄介质得到的。在无限球半径的极限下恢复了原子和平板的Casimir-Polder表达式。假设球的半径有限，原子与球的相互作用能随原子与球距离的三次方单调下降，随原子与球距离的七次方单调下降。
Van der Waals forces between atoms and molecules are universally assumed to act along the line separating them. Inspired by recent works on effects which can propel atoms parallel to a macroscopic surface via the Casimir--Polder force, we predict a lateral van der Waals force between two atoms, one of which is in an excited state with non-zero angular momentum and the other is isotropic and in its ground state. The resulting force acts in the same way as a planetary gear, in contrast to the rack-and-pinion motion predicted in works on the lateral Casimir--Polder force in the analogous case, fo…
Thermal quantum field theory and the Casimir interaction between dielectrics
基于热量子场论的松原公式，重新考虑了两块不同厚度介质板之间的Casimir和van der Waals相互作用。我们简要地回顾了在热量子场论的框架下，不使用涨落耗散定理的Lifshitz公式的两个主要推导。一组特殊的条件下，这些推导仍然有效的耗散的存在下，制定。低温行为的Casimir和范德华力之间的相互作用不同的介电常数被发现分析从Lifshitz理论的理想化模型的稀介电常数和真正的介电常数与有限的静态介电常数。在低温下卡西米尔和范德华相互作用的自由能、压力和熵证明了与以前发现的理想金属相同的对温度的普遍依赖性。熵在温度为零时消失，证明了能斯特热定理的正确性。这解决了长期存在的问题的一致性的利弗希茨理论与热力学的情况下，电介质板。得到的渐近表达式进行比较，数值计算的不同和类似的真正的时间和发现是非常好的协议。在介质板的情况下，零频率项的松原和的作用进行了研究。它表明，包括电导率的介电响应模型导致违反能斯特热定理。讨论了这一结果在非接触原子摩擦和实际金属间Casimir相互作用等热点问题中的应用。
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 qu…
Dependences of the Casimir-Polder interaction between an atom and a cavity wall on atomic and material properties
研究了在原子的动态极化率、腔壁材料的实际电导率和腔壁温度不为零等实际条件影响下原子与腔壁的Casimir-Polder和van der Waals相互作用.考虑了金属和电介质壁附近不同原子的情况。结果表明，要获得准确的结果，在短的分离，原子壁相互作用，应该使用完整的列表光学数据的复杂的折射率的壁材料和准确的动态极化率的原子。在金属壁的情况下，在相对大的分离处，可以使用等离子体模型介电函数来描述壁材料的介电性质。所得结果对量子反射和玻色-爱因斯坦凝聚实验的理论解释具有重要意义。
One of the most intriguing manifestations of quantum zero-point fluctuations are the van der Waals and Casimir forces, often associated with vacuum fluctuations of the electromagnetic field. Here we study generalized fluctuation potentials acting on internal degrees of freedom of components in electrical circuits. These electronic Casimir-like potentials are induced by the zero-point current fluctuations of any general conductive circuit. For realistic examples of an electromechanical capacitor and a superconducting qubit, our results reveal the possibility of tunable forces between the capaci…
Zero-point energy is generally known to be unphysical. Casimir effect, however, is often presented as a counterexample, giving rise to a conceptual confusion. To resolve the confusion we study foundational aspects of Casimir effect at a qualitative level, but also at a quantitative level within a simple toy model with only 3 degrees of freedom. In particular, we point out that Casimir vacuum is not a state without photons, and not a ground state for a Hamiltonian that can describe Casimir force. Instead, Casimir vacuum can be related to the photon vacuum by a non-trivial Bogoliubov transformat…
We derive a general procedure for finding the electromagnetic normal modes in layered structures. We apply this procedure to planar, spherical and cylindrical structures. These normal modes are important in a variety of applications. They are the only input needed in calculations of Casimir interactions. We present explicit expression for the condition for modes and Casimir energy for a large number of specific geometries. The layers are allowed to be two-dimensional so graphene and graphene-like sheets as well as two-dimensional electron gases can be handled within the formalism. Also forces …
The Casimir-Polder interaction between an atom and a multilayered system composed of infinitely thin planes is considered using the zeta-function regularization approach with summation of the zero-point energies. As a prototype material, each plane is represented by a graphene sheet whose optical response is described by a constant conductivity or Drude-Lorentz model conductivity. Asymptotic expressions for various separations are derived and compared to numerical calculations. We distinguish between large atom/plane limit, where retardation effects are prominent, and small atom/plane limit, w…
A quantum electrodynamic calculation of the interaction of an excited-state atom with a ground-state atom is performed. For an excited reference state and a lower-lying virtual state, the contribution to the interaction energy naturally splits into a pole term, and a Wick-rotated term. The pole term is shown to dominate in the long-range limit, altering the functional form of the interaction from the retarded 1/R^7 Casimir-Polder form to a long-range tail-provided by the Wick-rotated term-proportional to cos[2 (E_m-E_n) R/(hbar c)]/R^2, where E_m < E_n is the energy of a virtual state, lower t…
我们制定了一个对称性原则的基础上的对偶性的电场和磁场，并将其应用到色散力。在宏观量子电动力学的背景下，我们严格建立对偶不变性的自由电磁场的存在因果磁电。色散力的电磁场和原子的响应函数的格林张量。在讨论了格林张量在对偶变换下的行为之后，我们能够证明自由空间中物体上的Casimir力以及局域场校正的Casimir-Polder力和van der Waals力是对偶不变的。
It has always been conventionally understood that, in the dilute limit, the Casimir energy of interaction between bodies or the Casimir self-energy of a dielectric body could be identified with the sum of the van der Waals or Casimir-Polder energies of the constituents of the bodies. Recently, this proposition for self-energies has been challenged by Avni and Leonhardt [Ann.\ Phys.\ {\bf 395}, 326 (2018)], who find that the energy or self-stress of a homogeneous dielectric ball with permittivity $\varepsilon$ begins with a term of order $\varepsilon-1$. Here we demonstrate that this cannot be …
We investigate the thermal Casimir force between two parallel plates made of different isotropic materials which are separated by a uniaxial anisotropic film. Numerical computations of the Casimir pressure at T=300K are performed using the complete Lifshitz formula adapted for an anisotropic intervening layer and in the nonrelativistic limit. It is shown that the standard (nonrelativistic) theory of the van der Waals force is not applicable in this case, because the effects of retardation contribute significantly even for film thicknesses of a few nanometers. We have also obtained simple analy…
