Prediction of a measurable sign change in the Casimir force using a magnetic fluid

Abstract

We demonstrate quantum levitation controlled by Casimir forces acting between a polystyrene surface and a Teflon-coated metallic substrate immersed in a mixture of Toluene and magnetite particles. This system experiences repulsion-attraction transitions in the Casimir interaction for distances where the effect is measurable. This Casimir trapping can be controlled by clever choices of metallic and ferrofluid materials, which are directly linked to the emergence of the trapping effect. Thermal and quantum contributions are investigated in detail, showing how the optical and magnetic properties of the ferrofluid and other materials affect the magnitude of the trapping and its distance range of observability.

Figures (4)

• Figure 1: Schematics of the system under consideration consisting of a ferrofluid layer (denoted as $m$) with thickness $\ell$ between a polystyrene substrate ($A$) and a metallic substrate ($B$) covered by a Teflon layer $B_1$ of thickness $b_1$.
• Figure 2: Dielectric functions in the imaginary frequency range as a function of $\hbar\xi$ for the materials in the $A-m-B_1-B$ four-layer system: (a) $A$=polystyrene, $B$=gold, silver, aluminum, lithium, $B_1$=Teflon, $m$=Toluene with $\Phi=5\%$, $D=20$ nm of Magnetite spheres; (b) $A$=polystyrene, $B$=gold, $B_1$=Teflon, $m$=Toluene, with $\Phi=1\%$, $5\%$, $10\%$, and $15\%$, $D=20$ nm of Magnetite spheres; (c) $A$=polystyrene, $B$=gold, $B_1$=Teflon, $m$=Toluene, Benzene, Cyclohexane, Octane with $\Phi=5\%$, $D=20$ nm of Magnetite spheres.
• Figure 3: Casimir pressures normalized to the perfect conductor limit $P_m(\ell)=-\frac{\pi^2\hbar c}{240\ell^4}$ in the four-layer system from Figure \ref{['schematicFig']}, where the ferrofluid is Toluene with magnetite nanoparticles with average diameter $D=20$ nm and volume fractions $\Phi$=5%. For panels (a)-(d), the thickness of the Teflon layer is $b_1=10$ nm while the metallic material B varies in plasma frequency $\omega_P$ and relaxing frequency $\gamma$, such as (a) lithium ($\hbar\omega_P=6.45$ eV, $\gamma=0.13$ eV), (b) silver ($\hbar\omega_P=8.9$ eV, $\gamma=0.02$ eV), (c) gold ($\hbar\omega_P=9$ eV, $\gamma=0.03$ eV), and (d) aluminum ($\hbar\omega_P=12.04$ eV, $\gamma=0.13$ eV) zeman1987accuratemilton2004casimir. For panels (e)-(h), the metallic layer is gold while the thickness of the Teflon layer varies, such as (e) $b_1=5$ nm, (f) $b_1=10$ nm, (g) $b_1=15$ nm, (h) $b_1=20$ nm. The different contributions from TE and TM modes with zero-frequency ($n=0$) and summed frequencies ($n>0$) terms are also displayed.
• Figure 4: Casimir pressures normalized to the perfect conductor limit $P_m(\ell)=-\frac{\pi^2\hbar c}{240\ell^4}$ for the system in Figure \ref{['schematicFig']}. For sub-panels (a)-(d), the volume fraction of the magnetite particles with $D=20$ nm in the Toluene ferrofluid are (a) $\Phi$=1%, (b) $\Phi$=5%, (c) $\Phi$=10%, and (d) $\Phi$=15%. For sub-panel (e)-(h), the nanoparticles are dispersed in Toluene with a volume fraction $\Phi=5\%$ with diameters taken as (e) $D=5$ nm, (f) $D=10$ nm, (g) $D=15$ nm, and (h) $D=20$ nm. For sub-panels (i)-($l$), nanoparticles with $D=20$ nm and volume fraction $\Phi=5\%$ are dispersed in (i) Toluene, (j) Benzene, (k) Cyclohexane, and ($\ell$) Octane. In all cases, $B$=gold and the thickness of the Teflon layer is $b_1=10$ nm. The different contributions from TE and TM modes with zero-frequency (n=0) and summed non-zero frequencies ($n>0$) terms are also given with distinct line symbols and line styles.