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Tailoring the van der Waals interaction with rotation

H. S. G. Amaral, P. P. Abrantes, F. Impens, P. A. Maia Neto, R. de Melo e Souza

TL;DR

The work addresses tuning van der Waals forces between levitated nanoparticles by driving them into fast rotation. It develops a nonequilibrium quantum framework for rotating dipoles, deriving rotation-induced Doppler sidebands in the polarizability and introducing rotating-frame Hadamard functions that include off-diagonal terms, thus reshaping the vdW interaction. By computing the interaction energy for several geometric configurations and applying a Lorentz model and BST GHz polaritonic resonance, it demonstrates that rotation can strongly enhance, suppress, or even reverse vdW forces, with resonant features controlled by relative and total angular velocities. The findings suggest a practical route to tailor nanoscale forces in levitated optomechanics and highlight the necessity of a nonequilibrium fluctuation-dissipation treatment in rotating systems, with potential implications for quantum optomechanics and rotationally quantized molecules.

Abstract

We report a systematic procedure to engineer the van der Waals force between levitated nanoparticles in high vacuum by setting them into a fast rotation. By tuning the rotation frequency close to a polaritonic resonance, we can significantly enhance the van der Waals attraction. In addition, for frequencies slightly beyond resonance, rotation can change the nature of the interaction from attraction to repulsion. Rotational Doppler shifts effectively modify the frequency-dependent polarizability of the nanoparticles, thereby reshaping their mutual interaction. As a concrete and realistic example, we consider spinning barium strontium titanate nanoparticles at state-of-the-art rotation frequencies and demonstrate a modification of the force within the sensitivity of current experimental techniques.

Tailoring the van der Waals interaction with rotation

TL;DR

The work addresses tuning van der Waals forces between levitated nanoparticles by driving them into fast rotation. It develops a nonequilibrium quantum framework for rotating dipoles, deriving rotation-induced Doppler sidebands in the polarizability and introducing rotating-frame Hadamard functions that include off-diagonal terms, thus reshaping the vdW interaction. By computing the interaction energy for several geometric configurations and applying a Lorentz model and BST GHz polaritonic resonance, it demonstrates that rotation can strongly enhance, suppress, or even reverse vdW forces, with resonant features controlled by relative and total angular velocities. The findings suggest a practical route to tailor nanoscale forces in levitated optomechanics and highlight the necessity of a nonequilibrium fluctuation-dissipation treatment in rotating systems, with potential implications for quantum optomechanics and rotationally quantized molecules.

Abstract

We report a systematic procedure to engineer the van der Waals force between levitated nanoparticles in high vacuum by setting them into a fast rotation. By tuning the rotation frequency close to a polaritonic resonance, we can significantly enhance the van der Waals attraction. In addition, for frequencies slightly beyond resonance, rotation can change the nature of the interaction from attraction to repulsion. Rotational Doppler shifts effectively modify the frequency-dependent polarizability of the nanoparticles, thereby reshaping their mutual interaction. As a concrete and realistic example, we consider spinning barium strontium titanate nanoparticles at state-of-the-art rotation frequencies and demonstrate a modification of the force within the sensitivity of current experimental techniques.
Paper Structure (8 sections, 45 equations, 3 figures)

This paper contains 8 sections, 45 equations, 3 figures.

Table of Contents

  1. Dipole response functions in a rotating frame
  2. Interaction energy between rotating nanospheres for different geometric arrangements
  3. Spheres spinning parallel to each other and parallel to the line joining them $(\rightarrow\rightarrow)$
  4. Spheres spinning parallel to each other and perpendicular to the line joining them $(\uparrow\uparrow)$
  5. Spheres spinning perpendicular to each other with one of them parallel to the line joining them $(\uparrow\rightarrow)$
  6. Spheres spinning perpendicular to each other with both perpendicular to the line joining them $\uparrow\odot$
  7. Estimate of the total vdW force between nanospheres
  8. Interaction energy obtained from a naive application of FDT in the rotating frame

Figures (3)

  • Figure 1: Modification of the vdW force for the $\rightarrow\rightarrow$ configuration as a function of the relative angular velocity $\Omega_{AB}=\Omega_A-\Omega_B$ (in units of the polaritonic resonance frequency $\omega_0$). Positive values indicate a repulsive contribution. The nanospheres are made of BST, with material parameters given in the main text.
  • Figure 2: Modification of the vdW force for co-rotating (red) and counter-rotating (green) BST nanospheres in the $\uparrow\uparrow$ configuration as a function of $\Omega_A$ (in units of the polaritonic resonance frequency $\omega_0$) for $|\Omega_B|/|\Omega_A|$ equal to (a) $0.5$, (b) $0.9$, and (c) $1$. We take $T=1500\,{\rm K.}$
  • Figure 3: Different geometric arrangements of the two rotation axes and relative positions of the spinning nanospheres.