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Conference on Lasers and Electro-Optics

Sympathetic Cooling of Nanoparticles Levitated in a Paul Trap

Dmitry S. Bykov, Lorenzo Dania, Florian Goschin, Tracy E. Northup

Published Jan 1, 2022• 0 citations
Publisher

Abstract

We demonstrate three-dimensional sympathetic cooling of the center-of-mass motion of a silica nanoparticle. The nanoparticle is coupled to a feedback-cooled particle in an ion trap. We investigate limits of the process and discuss optimum strategies.
DOI
10.1364/cleo_qels.2022.ftu1a.2

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We develop the theory describing the quantum coupled dynamics of the center-of-mass motion of a nanoparticle and an ensemble of ions co-trapped in a dual-frequency linear Paul trap. We first derive analytical expressions for the motional frequencies and classical trajectories of both nanoparticle and ions. We then derive a quantum master equation for the ion-nanoparticle system and quantify the sympathetic cooling of the nanoparticle motion enabled by its Coulomb coupling to a continuously Doppler-cooled ion. We predict that motional cooling down to sub-kelvin temperatures is achievable in state-of-the-art experiments even in the absence of motional feedback and in the presence of micromotion. We then extend our analysis to an ensemble of NNN ions, predicting a linear increase of the cooling rate as a function of NNN and motional cooling of the nanoparticle down to tenths of millikelvin in current experimental platforms. Our work establishes the theoretical toolbox needed to explore the ion-assisted preparation of non-Gaussian motional states of levitated nanoparticles.
Cooling the center-of-mass motion of levitated nanoparticles provides a route to quantum experiments at mesoscopic scales. Here we demonstrate three-dimensional sympathetic cooling and detection of the center-of-mass motion of a levitated silica nanoparticle. The nanoparticle is electrostatically coupled to a feedback-cooled particle while both particles are trapped in the same Paul trap. We identify two regimes, based on the strength of the cooling: in the first regime, the sympathetically cooled particle thermalizes with the directly cooled one, while in the second regime, the sympathetically cooled particle reaches a minimum temperature. This result provides a route to efficiently cool and detect particles that cannot be illuminated with strong laser light, such as absorptive particles, and paves the way for controlling the motion of arrays of several trapped nanoparticles.
We demonstrate optical levitation and feedback cooling of a silica nanoparticle (radius = 78~nm) trapped within a radial vector beam (RVB) in high vacuum. Radial vector beams, when focused by a high-NA lens, produce a smaller focal spot than conventional Gaussian beams, yielding tighter optical potentials and potentially reduced photon-recoil heating rates. A vortex wave plate was used to generate the RVB using an aspheric lens (NA = 0.77) to form the trap. Cold-damping feedback was used to cool the center of mass motion in the radial and axial trap directions to temperatures in the mK range. At higher temperatures and pressures, additional trap frequencies arising from the nonlinear RVB optical potential are observed. This demonstration is a step toward exploiting structured light for levitated quantum optomechanics where these traps can be used to suppress bulk and motional heating.
A proposal for cooling the translational motion of optically levitated magnetic nanoparticles is presented. The theoretical cooling scheme involves the sympathetic cooling of a ferromagnetic YIG nanosphere with a spin-polarized atomic gas. The particle–atom cloud coupling is mediated through the magnetic dipole–dipole interaction. When the particle and atom oscillations are small compared to their separation, the interaction potential becomes dominantly linear, which allows the particle to exchange energy with the N atoms. While the atoms are continuously Doppler cooled, energy is able to be removed from the nanoparticle’s motion as it exchanges energy with the atoms. The rate at which energy is removed from the nanoparticle’s motion was studied for three species of atoms (Dy, Cr, Rb) by simulating the full N + 1 equations of motion and was found to depend on system parameters with scalings that are consistent with a simplified model. The nanoparticle’s damping rate due to sympathetic cooling is competitive with and has the potential to exceed commonly employed cooling methods.