Coherent scattering 2D cooling in levitated cavity optomechanics

Abstract

The strong light-matter optomechanical coupling offered by Coherent Scattering (CS) set-ups have allowed the experimental realisation of quantum ground state cavity cooling of the axial motion of a levitated nanoparticle [U. Delić et al., Science 367, 892 (2020)]. An appealing milestone is now quantum 2D cooling of the full in-plane motion, in any direction in the transverse plane. By a simple adjustment of the trap polarisation, one obtains two nearly equivalent modes, with similar frequencies ${\omega }_x\sim {\omega }_y$ and optomechanical couplings $g_x\simeq g_y$ -- in this experimental configuration we identify an optimal trap ellipticity, nanosphere size and cavity linewidth which allows for efficient 2D cooling. Moreover, we find that 2D cooling to occupancies $n_x+n_y\lesssim 1$ at moderate vacuum ($10^{-6}$ mbar) is possible in a "Goldilocks" zone bounded by $\sqrt{\kappa \Gamma /4}\lesssim g_x,g_y\lesssim |{\omega }_x-{\omega }_y|\lesssim \kappa$, where one balances the need to suppress dark modes whilst avoiding far-detuning of either mode or low cooperativities, and $\kappa$ ($\Gamma$) is the cavity decay rate (motional heating rate). With strong-coupling regimes $g_x,g_y\gtrsim \kappa$ in view one must consider the genuine three-way hybridisation between $x$, $y$ and the cavity light mode resulting in hybridized bright/dark modes. Finally, we show that bright/dark modes in the levitated set-up have a simple geometrical interpretation, related by rotations in the transverse plane, with implications for directional sensing.

17 pages; 6 figures

References in corpus (31)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Cavity Optomechanics
• Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion
• Observation of strong coupling between a micromechanical resonator and an optical cavity field
• Motional Quantum Ground State of a Levitated Nanoparticle from Room Temperature
• Cavity optomechanics using an optically levitated nanosphere
• Preparation of Nonclassical States in Cavities with a Moving Mirror
• Toward Quantum Superposition of Living Organisms
• Direct Measurement of Photon Recoil from a Levitated Nanoparticle
• Cavity cooling of an optically levitated nanoparticle
• Cavity cooling a single charged nanoparticle
• Optomechanics with Levitated Particles
• Optically Mediated Hybridization Between Two Mechanical Modes
• Cavity cooling of an optically trapped nanoparticle
• Cavity cooling of a levitated nanosphere by coherent scattering
• Nonlinear dynamics and millikelvin cavity-cooling of levitated nanoparticles
• Sensing of Static Forces with Free-Falling Nanoparticles
• Motional Sideband Asymmetry of a Nanoparticle Optically Levitated in Free Space
• Cavity cooling of free silicon nanoparticles in high-vacuum
• Cavity-Based 3D Cooling of a Levitated Nanoparticle via Coherent Scattering
• Cavity sideband cooling of a single trapped ion
• Terrestrial Gravity Fluctuations
• Long distance manipulation of a levitated nanoparticle in high vacuum
• Strong Optomechanical Coupling at Room Temperature by Coherent Scattering
• Dynamics of levitated nanospheres: towards the strong coupling regime
• Near-field coupling of a levitated nanoparticle to a photonic crystal cavity
• Optomechanical cooling of levitated spheres with doubly-resonant fields
• Distribution of laser shot noise energy delivered to a levitated nanoparticle
• Quantum displacement sensing and cooling in 3D levitated cavity optomechanics
• Cavity cooling of many atoms
• Static force characterization with Fano anti-resonance in levitated optomechanics

Cited by in corpus (15)

• Simultaneous ground-state cooling of two mechanical modes of a levitated nanoparticle
• Two-dimensional quantum motion of a levitated nanosphere
• Simultaneous cooling of all six degrees of freedom of an optically levitated nanoparticle by elliptic coherent scattering
• Quantum theory of light interaction with a Lorenz-Mie particle: Optical detection and three-dimensional ground-state cooling
• Dark Matter Searches with Levitated Sensors
• Sensing microscopic directional noise baths with an optically cooled and levitated nanoparticle
• Squeezing lights via a levitated cavity optomechanics
• Quantum Electrodynamics with a Nonmoving Dielectric Sphere: Quantizing Lorenz-Mie Scattering
• Coulomb coupling between two nanospheres trapped in a bichromatic optical tweezer
• Quantum state purity versus average phonon number for characterization of mechanical oscillators in cavity optomechanics
• Coherent Scattering-mediated correlations between levitated nanospheres
• Roto-translational optomechanics
• Spectral Analysis of Quantum Field Fluctuations in a Strongly Coupled Optomechanical System
• Steady motional entanglement between two distant levitated nanoparticles
• Vectorial polaritons in the quantum motion of a levitated nanosphere