Distribution of laser shot-noise energy delivered to a levitated nanoparticle

Abstract

This paper aims to correct the expression for the rate at which laser shot noise energy is delivered to a particle in levitated optomechanics. While previous articles have the same overall form and dependencies, the proportionality constants are either incorrect or misleading. 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 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, expressions for the rotational shot noise heating for a symmetric top-like particle for linear, elliptically, and unpolarized light is also provided.

Sub-Kelvin Feedback Cooling and Heating Dynamics of an Optically Levitated Librator

“…Besides linear momentum, light also carries angular momentum [29]. While the quantization of light's linear momentum gives rise to radiation pressure shot noise, the field's spin quantization must give rise to torque fluctuations (termed radiation torque shot noise) in the interaction with a mechanical object [30][31][32]. This torque noise can be understood as the particle's dipole moment (induced by the driving field) interacting with the field's vacuum fluctuations in the orthogonal polarization direction, as illustrated in Fig.…”

“…Our second cross-check of this hypothesis is by comparison of Γ res to the theoretical expectation. In a simple model, treating the dumbbell as a lossless anisotropic dipolar scatterer, the heating rate Γ sn expected due to radiation torque shot noise is given by [20,[30][31][32]]…”

Optimal position detection of a dipolar scatterer in a focused field

“…Having determined the imprecision of our measurement scheme for the orientation angles δ and of the anisotropic scatterer, we now turn to an analysis of the measurement backaction. This backaction arises as a torque noise driving the rotational motion of the scatterer and has been derived earlier [23,27,28]. To make this article self contained, we provide a particularly simple and didactic treatment here.…”

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“…The increase in the kinetic energy of the particle due to the fluctuation in the photon number [1,24,25] is…”