Casimir-Polder Repulsive Interaction
Keywords:
Casimir effect, Vacuum-separated metallic geometry, MEMS and NEMS, Casimir-Polder free energy, Magneto-dielectric sheet, Non trivial magnetic susceptibility, Electromagnetic impedance. P ACS: 73.22.-f, 61.48.Gh, 71.15.Mb. The mutual electromagnetic correlation between two spatially separated systems gives rise to Casimir/ Casmir-Polder effect. The corresponding forces, which are generally attractive for most vacuum-separated metallic or dielectric geometries, are due to the contribution to the ground-state [1, 2] energy of the coupled system. The repulsive Casimir forces [3] are believed to occur in four types of materials, viz. the fluid-separated dielectrics [4], the composite meta-materials [5], the systems with different geometries [6, 7], and the time-reversal symmetry (TRS) broken systems [8, 9]. It is well-known [10, 11.12] that the Weyl semimetal state−a novel topological phase of matter−must break TRS or the inversion symmetry. Therefore, the corresponding host materials are expected to yield a Casimir/Casimir-Polder (CP) repulsion tunable with carrier doping or a magnetic field [13]. Experimentally, the forces have been realized for the first time involving test bodies immersed in a liquid medium- ethanol [4]. We investigate here the Casimir-Polder free energy corresponding to interactions of an electrically and magnetically polarizable micro-particle with a magneto-dielectric sheet. Our task is to look for the repulsive Casimir-Polder forces between a micro-particle possessing non trivial ratio of the magnetic polarizability and the electric polarizability and the artificially engineered dielectric material (meta-material) sheet having non trivial magnetic permeability values, as the natural materials have a magnetic permeability roughly equal to one in the range of frequencies relevant for the Casimir effect. The natural materials, such as ferrites and garnets, are perhaps suitable to demonstrate the repulsive Casimir force as they have high permeability. We show that for non-trivial permeability values, the crossover between attractive and repulsive behavior depends on ‘polarizability ratio’ of the micro-particle, and the impedance Z = √(μ/ε) of the sheet apart from the ratio of the film thickness and the micro-particle separation (D/d) and temperature(T). The importance of CP repulsion cannot be understated. The repulsion stabilizes the operation of MEMS and NEMS, as it liberates one from the badgering problem of ‘stiction’ in such systems. We consider a micro-particle in an intervening medium characterized by the dynamic electric polarizability η e(ω) and the dynamic magnetic polarizability ηm(ω) as shown in Figure 1. The static electric and magnetic polarizabilities of the micro- particle are η e(0) and ηm(0), respec-tively. We wish to discuss first the Casimir-Polder interaction in the static limit. We define their ratio as r(0) = √ ( η m(0)/ η e(0)). The quantities ε(0)(ω) and μ(0)(ω) are the dynamic dielectric permittivity and the dynamic magnetic permeability of the intervening medium. If the medium happens to be vacuum and then each of them is equal to one. The sample in the figure consists of a thin magneto-dielectric film of thickness ‘D’ deposited on a thick substrate at temperature T. Suppose the film is characterized by the dielectric permittivity ε (1)(ω) and the magnetic permeability μ(1)(ω), and the substrate is by the permittivity ε(2)(ω) and the permeability μ(2)(ω). These Mater. Sci. Eng. Adv. Res 1(2). Page | 27 Citation: Partha Goswami (2015) Casimir-Polder Repulsive Interaction. Mater. Sci. Eng. Adv. Res 1(2): 26-35. doi: https://doi.org/10.24218/ msear.2015.10. might be made of either conducting or poorly conducting materials. Also, for the film material there exist finite limiting values ε(1)(0) ≡ 0ε (1) and μ(1)(0) ≡ μ (1). The finite limiting values of these quantities for the substrate are ε ( 2) and μ (2). These static values are the values of the Faraday-Maxwell dielectric constant and permeability. For the fields slowly varying in space and time, such limiting values of the function ε (1)(ω) and μ(1)(ω) exist. Our first aim is to investigate the interaction of the micro-particle with the magneto-dielectric sheet in this limit, ignoring the frequency dependence completely. Suppose now the particle is at a separation ‘d’ (d >> d(T) ħc/(2πk BT)) above the sample. We further assume ( k﬩max ~ d −1, where the wave vector projection on the (x, y) plane is k﬩is yields k﬩ << 2πkBT)/ ħc. One can also express the ensuing condition as T >> Tc ħc /(2π dkB). This is the high-temperature limit. Our second aim is to investigate the micro-particle-sheet interaction in the high-temperature and the moderately high-temperature limits. To elucidate ab initio the concept of the classical Casimir-Polder interaction (CPI), say, on the basis of the Lifshitz theory [1, 3, 14], we assume the interaction of the particle with the sheet to be of the classical CPI type in the first approximation. The classical case is valid under the large-separation assumption d >> d(T) ħc/(2πk BT). The quantities d(T) (and Tc )set the classical limit in the sense that the limit starts from d ≈ 5 d(T) and T ≈ 5Tc. For ordinary materials at temperature T, one may write a characteristic separation d(T) = ħc/(2πk BT) originating from the characteristic mode frequency ωl=1 = 2π k BT/ħ = c/d(T). The classical limit occurs when d>> d(T). At room temperature 300 K, d(T)~ 1μm. So, the classical limit is achieved at separations d >> 1 μm. A different way of looking at this issue is in terms of temperature. For the separation d = 10 μm, the classical limit edge is T c ≈ 20 K. Thus, at T >> Tc ≈ 20 K, at room temperature T = 300 K, the classical limit is most definitely achieved. The characteristic thermal mode frequency in this situation is 10 13 Hz. We denote the reflection coefficients of the electromagnetic fluctuations on the sheet material plus substrate, dependentAbstract
The Casimir effect is attractive in most vacuum-separated metallic or dielectric geometries. Two electrically neutral spatially separated systems interacting via Casimir force will have access to the stable separation state only when the force transitions from repulsive at small separations to attractive at large separations. Such issues are important in the future development of micro- and nano-electromechanical systems (MEMS and NEMS). We investigate here the Casimir-Polder free energy corresponding to interactions of a magnetically and electrically polarizable micro-particle with a magneto-dielectric sheet. Our theoretical study shows that such an interaction is tunable in strength and sign.The latter, particularly, is true provided we go beyond the natural materials and look for the meta-materials fabricated at scales between the micron and the nanometer. We assume that the particle and the sheet have access to non-tivial values of the polarizability ratio and the electromagnetic impedance, respectively. The crossover between attractive and repulsive behavior is found to depend on these quantities.Downloads
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2015-09-16
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