Lateral Casimir Force on a Rotating Particle near a Planar Surface

Alejandro Manjavacas, Francisco J. Rodríguez-Fortuño, F. Javier García de Abajo, and Anatoly V. Zayats

Phys. Rev. Lett. 118, 133605 – Published 31 March 2017

Abstract

We study the lateral Casimir force experienced by a particle that rotates near a planar surface. The origin of this force lies in the symmetry breaking induced by the particle rotation in the vacuum and thermal fluctuations of its dipole moment, and therefore, in contrast to lateral Casimir forces previously described in the literature for corrugated surfaces, it exists despite the translational invariance of the planar surface. Working within the framework of fluctuational electrodynamics, we derive analytical expressions for the lateral force and analyze its dependence on the geometrical and material properties of the system. In particular, we show that the direction of the force can be controlled by adjusting the particle-surface distance, which may be exploited as a new mechanism to manipulate nanoscale objects.

Received 8 December 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.133605

Physics Subject Headings (PhySH)

Angular momentum of light Casimir effect Casimir effect & related phenomena

Nanoparticles

Atomic, Molecular & Optical

Authors & Affiliations

Alejandro Manjavacas^1,*, Francisco J. Rodríguez-Fortuño^2,†, F. Javier García de Abajo^3,4, and Anatoly V. Zayats²

¹Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
²Department of Physics, King’s College London, London WC2R 2LS, United Kingdom
³ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
⁴ICREA—Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluís Companys 23, 08010 Barcelona, Spain

^*manjavacas@unm.edu
^†francisco.rodriguez_fortuno@kcl.ac.uk

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 118, Iss. 13 — 31 March 2017

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Sketch of the system under study. A spherical nanoparticle of radius $R$ is rotating with angular frequency $Ω$ at a center-to-surface distance $d$ above a planar surface. Because of the rotation, the particle experiences a lateral force $F_{y}$ .
Reuse & Permissions
Figure 2
(a) Imaginary part of the polarizability of SiC nanoparticles (left scale) with radius $R = 50 nm$ (red curve) and $R = 500 nm$ (blue curve) and imaginary part of the reflection coefficient of a SiC surface (right scale) calculated for $Q = 0$ (gray dashed curve) and for $Q ≫ k$ (gray solid curve). (b) Frequency integrand of the lateral force [Eq. (1)] corresponding to the two nanoparticles of (a) when they are placed at a distance $d$ from a SiC surface. The curves for $d / R = 27$ are multiplied by a factor of 200 to improve visibility. Moreover, we choose a rotation frequency $Ω / 2 π = 1 kHz$ and surface and particle temperatures $T_{0} = T_{1} = 300 K$ .
Reuse & Permissions
Figure 3
(a),(b) Lateral Casimir force experienced by a SiC nanoparticle with $R = 50 nm$ (a) and $R = 500 nm$ (b) rotating near a SiC surface, plotted as a function of the particle-surface distance $d$ for two different rotation frequencies: $Ω / 2 π = 1 kHz$ (red curves) and $Ω / 2 π = 100 kHz$ (blue curves). Shaded areas indicate the distances for which the lateral force is positive. (c) Lateral Casimir force for the same nanoparticles as in (a) and (b) plotted as a function of the rotation frequency $Ω$ for particle-surface distances as indicated in the legends, which correspond to the dashed vertical lines in (a) and (b). The surface and particle temperatures are $T_{0} = T_{1} = 300 K$ .
Reuse & Permissions
Figure 4
Lateral force experienced by a nanoparticle of radius $R = 50 nm$ plotted as a function of the transversal phonon polariton energy of the particle $ℏ ω_{T, p}$ and the surface $ℏ ω_{T, s}$ . Other parameters of the particle and surface dielectric function are taken as those of SiC (see main text), the particle-surface distance is $d = 3 R$ , the rotation frequency is $Ω / 2 π = 1 kHz$ , and the temperatures are $T_{0} = T_{1} = 300 K$ . The dashed lines correspond to $ℏ ω_{T} = 98.3 eV$ as in SiC.
Reuse & Permissions
Figure 5
Lateral force experienced by a graphite nanoparticle of radius $R = 10 nm$ plotted as a function of the particle and surface temperatures, which are taken to be equal ( $T_{0} = T_{1} = T$ ), for two different rotation frequencies. Dashed curves correspond to calculations using the full theory, while solid curves indicate the results obtained with the analytical model described in the text. The inset shows the lateral force as a function of rotation frequency for two different temperatures calculated using the analytical model. In all cases, the particle-surface distance is $d = 3 R$ .
Reuse & Permissions

Physical Review Letters