Distribution of laser shot noise energy delivered to a levitated nanoparticle

Abstract

This paper quantifies the rate at which laser shot noise energy is delivered to a nanoparticle for the various scenarios commonly encountered in levitated optomechanics. While previous articles have the same form and dependencies, the proportionality constants often differ in the literature. This paper resolves these discrepancies. The rate at which energy is delivered to an optically trapped particle's respective degrees of freedom depends on the radiation pattern of scattered light as well as the direction of laser propagation. For a traveling plane wave with linearly polarized light, in the Rayleigh regime this leads the translational shot noise heating rate to be proportional to $1/10$ of the total rate in the laser polarization direction, $7/10$ in the laser propagation direction, and $2/10$ in the direction perpendicular to both. Analytical expressions for the shot noise heating rate are provided in the Rayleigh limit as well as numerical calculations for particles in the Mie regime for silica and diamond. For completeness, numerical calculations of the shot noise heating for silica Mie particles at the focus of a strongly focused laser beam are calculated for varying numerical aperture and common laser wavelengths. Both numerical calculations show that the Rayleigh expression generally gives an overestimate of the shot noise heating especially for larger radii, but is still a good approximation even for incident focal fields. The exception to the relative decrease is when a Mie resonance is reached which was found for diamond. Lastly, Rayleigh expressions for the rotational shot noise heating for a symmetric top-like particle for linear, elliptically, and unpolarized light are also provided.

arXiv comment11 pages, 3 figures

References in corpus (26)

• Motional Quantum Ground State of a Levitated Nanoparticle from Room Temperature
• Sub-Kelvin Parametric Feedback Cooling of a Laser-Trapped Nanoparticle
• Cavity optomechanics using an optically levitated nanosphere
• Direct Measurement of Photon Recoil from a Levitated Nanoparticle
• Cavity cooling of an optically levitated nanoparticle
• Optomechanics with Levitated Particles
• Cold Damping of an Optically Levitated Nanoparticle to micro-Kelvin Temperatures
• Cavity cooling of a levitated nanosphere by coherent scattering
• Brownian motion at short time scales
• Cavity-Based 3D Cooling of a Levitated Nanoparticle via Coherent Scattering
• Theory of Optical Tweezers
• Testing Wavefunction Collapse Models using Parametric Heating of a Trapped Nanosphere
• Levitated Nanoparticles for Microscopic Thermodynamics - A Review
• Optimal Position Detection of a Dipolar Scatterer in a Focused Field
• Theory for Cavity Cooling of Levitated Nanoparticles via Coherent Scattering: Master Equation Approach
• An ultra-narrow line width levitated nano-oscillator for testing dissipative wavefunction collapse
• Quantum Model of Cooling and Force Sensing With an Optically Trapped Nanoparticle
• Master equation approach to optomechanics with arbitrary dielectrics
• Resolved Sideband Cooling of a Levitated Nanoparticle in the Presence of Laser Phase Noise
• Spatio-Orientational Decoherence of Nanoparticles
• Levitated cavity optomechanics in high vacuum
• Decoherence of rotational degrees of freedom
• Quantum Angular Momentum Diffusion of Rigid Bodies
• Parametric Feedback Cooling of Rigid Body Nanodumbbells in Levitated Optomechanics
• Radiation Damping of a Polarizable Particle
• Shot noise dominant regime for ellipsoidal nanoparticles in a linearly polarized beam

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• Coherent scattering 2D cooling in levitated cavity optomechanics
• Suppressing Recoil Heating in Levitated Optomechanics using Squeezed Light
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• Squeezing below the ground state of motion of a continuously monitored levitating nanoparticle
• Search for Dark Matter Scattering from Optically Levitated Nanoparticles
• Backaction suppression in levitated optomechanics using reflective boundaries
• Quantum state purity versus average phonon number for characterization of mechanical oscillators in cavity optomechanics
• Roto-translational optomechanics
• Spectral Analysis of Quantum Field Fluctuations in a Strongly Coupled Optomechanical System
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