Application of the Lifshitz theory to poor conductors

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 Interaction between Spheres Immersed in Electrolytes

We investigate the Casimir interaction between two dielectric spheres immersed in an electrolyte solution. Since ionized solutions typically correspond to a plasma frequency much smaller than kBT/ħ at room temperature, only the contribution of the zeroth Matsubara frequency is affected by ionic screening. We follow the electrostatic fluctuational approach and derive the zero-frequency contribution from the linear Poisson-Boltzmann (Debye-Hückel) equation for the geometry of two spherical surfaces of arbitrary radii. We show that a contribution from monopole fluctuations, which is reminiscent of the Kirkwood-Shumaker interaction, arises from the exclusion of ionic charge in the volume occupied by the spheres. Alongside the contribution from dipole fluctuations, such monopolar term provides the leading-order Casimir energy for very small spheres. Finally, we also investigate the large sphere limit and the conditions for validity of the proximity force (Derjaguin) approximation. Altogether, our results represent the first step towards a full scattering approach to the screening of the Casimir interaction between spheres that takes into account the nonlocal response of the electrolyte solution.

van der Waals interactions at the nanoscale: the effects of nonlocality

Calculated using classical electromagnetism, the van der Waals force increases without limit as two surfaces approach. In reality, the force saturates because the electrons cannot respond to fields of very short wavelength: polarization charges are always smeared out to some degree and in consequence the response is nonlocal. Nonlocality also plays an important role in the optical spectrum and distribution of the modes but introduces complexity into calculations, hindering an analytical solution for interactions at the nanometer scale. Here, taking as an example the case of two touching nanospheres, we show for the first time, to our knowledge, that nonlocality in 3D plasmonic systems can be accurately analyzed using the transformation optics approach. The effects of nonlocality are found to dramatically weaken the field enhancement between the spheres and hence the van der Waals interaction and to modify the spectral shifts of plasmon modes.

Thermally induced resonances in a three-body system including a solid surface

Dispersion energy of a system out of equilibrium containing two molecules and substrate in different thermostats is calculated taking into account nonlocal optical effects. A resonance increase of energy due to three-body interaction in a system out of equilibrium is shown. In particular, dispersion energy of a two-body subsystem of the three-body system out of equilibrium may be essentially larger than the energy of the same subsystem in equilibrium. A necessary condition of the resonance increase is a closeness of eigenfrequencies of the subsystems composing the whole system. It is shown that different nonlocal reflectivities of surface corresponding to different additional boundary conditions lead to similar results in resonance magnification of dispersion interaction of subsystems in a system out of equilibrium.

Casimir interaction from magnetically coupled eddy currents

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 quasistatic 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.