We theoretically investigate the problem of position detection of an optically levitated Mie particle. The information radiation field (IRF) is proposed and defined to characterize the scattered light carrying complete information about the center-of-mass (c.m.) motion of the particle. Based on the IRF, we suggest an optimal detection scheme for the position of arbitrary particles. We calculate both the information losses of objective collection and mode-matching in levitated optomechanical experiments. Our results conclude that the backward detection scheme, using an incident Gaussian beam focused by a high numerical aperture lens, provides sufficient information to achieve the quantum ground state through cooling of the three-dimensional c.m. motion of the Mie particle.
We theoretically investigate the problem of position detection of an optically levitated Mie particle. The information radiation field (IRF) is proposed and defined to characterize the scattered light carrying complete information about the center-of-mass (c.m.) motion of the particle. Based on the IRF, we suggest an optimal detection scheme for the position of arbitrary particles. We calculate both the information losses of objective collection and mode-matching in levitated optomechanical experiments. Our results conclude that the backward detection scheme, using an incident Gaussian beam focused by a high numerical aperture lens, provides sufficient information to achieve the quantum ground state through cooling of the three-dimensional c.m. motion of the Mie particle.
We theoretically investigate the problem of position detection of an optically levitated Mie particle. The information radiation field (IRF) is proposed and defined to characterize the scattered light carrying complete information about the center-of-mass (c.m.) motion of the particle. Based on the IRF, we suggest an optimal detection scheme for the position of arbitrary particles. We calculate both the information losses of objective collection and mode-matching in levitated optomechanical experiments. Our results conclude that the backward detection scheme, using an incident Gaussian beam focused by a high numerical aperture lens, provides sufficient information to achieve the quantum ground state through cooling of the three-dimensional c.m. motion of the Mie particle.
We develop a fully vectorial, semiclassical scattering formalism for optically levitated dipolar scatterers, expressed within the angular spectrum representation and applicable to arbitrary trapping-field configurations as well as to high--numerical-aperture focusing. Within this framework, we introduce the information radiation pattern to characterize the angular distribution of position-dependent information and use a Richards--Wolf projection of the scattered field onto the local-oscillator mode to quantify the resulting mode-matching efficiency, yielding experimentally realistic forward- and backward-detection efficiencies. As a worked example, we apply the formalism to a radially polarized trapping beam and confirm that the axial recoil heating rate is reduced relative to a conventional linearly polarized Gaussian tweezer. The theoretical framework is implemented in LevitationToolbox, an open-source Python package intended to support the design and optimization of near-Heisenberg-limited levitated optomechanical experiments.
We propose and experimentally demonstrate a novel detection method that significantly improves the precision of real-time measurement of the three-dimensional displacement of a levitated dipolar scatterer. Our technique relies on spatial mode sorting of the light scattered by the levitated object, allowing us to selectively extract the position information of all translational degrees of freedom with minimal losses. To this end, we collect all the light back-scattered from a levitated nanoparticle using a parabolic mirror and couple it into a spatial mode sorter. We measure displacement sensitivities (√︁𝑆imp,𝑥,√︁𝑆imp,𝑦,√︁𝑆imp,𝑧) = (1.7, 2.4, 1.0) × 10−14 m/√Hz below the zero-point motion (𝑥zpm, 𝑦zpm, 𝑧zpm) = (2.2, 2.4, 1.6)× 10−12 m of the levitated particle considered here. In the regime where environmental decoherence is not limited by gas collision we estimate that our method can reach measurement efficiencies of (𝜂𝑥 tot , 𝜂𝑦 tot , 𝜂𝑧 tot) = (0.13, 0.18, 0.33) > 1/9, which would enable the 3D motional quantum ground state of a levitated optomechanical system.
We propose and experimentally demonstrate a novel detection method that significantly improves the precision of real-time measurement of the three-dimensional displacement of a levitated dipolar scatterer. Our technique relies on spatial mode sorting of the light scat tered by the levitated object, allowing us to selectively extract the position information of all translational degrees of freedom with minimal losses. To this end, we collect all the light back-scattered from a levitated nanoparticle using a parabolic mirror and couple it into a spatial mode sorter. We measure displacement sensitivities (√︁𝑆imp,𝑥,√︁𝑆imp,𝑦,√︁𝑆imp,𝑧) = (1.7, 2.4, 1.0) × 10−14 m/√Hz below the zero-point motion (𝑥zpm, 𝑦zpm, 𝑧zpm) = (2.2, 2.4, 1.6)× 10−12 m of the levitated particle considered here. In the regime where environmental decoherence is not limited by gas collision we estimate that our method can reach measurement efficiencies of (𝜂𝑥tot , 𝜂𝑦tot , 𝜂𝑧tot ) = (0.13, 0.18, 0.33) > 1/9, which would enable the 3D motional quantum ground state of a levitated optomechanical system.
Interferometric methods for detecting the motion of a levitated nanoparticle provide a route to the quantum ground state, but such methods are currently limited by mode mismatch between the reference beam and the dipolar field scattered by the particle. Here we demonstrate a self-interference method to detect the particle's motion that solves this problem. A Paul trap confines a charged dielectric nanoparticle in high vacuum, and a mirror retro-reflects the scattered light. We measure the particle's motion with a sensitivity of 1.7×10^{-12} m/sqrt[Hz], corresponding to a detection efficiency of 2.1%, with a numerical aperture of 0.18. As an application of this method, we cool the particle, via feedback, to temperatures below those achieved in the same setup using a standard position measurement.
We propose and experimentally demonstrate a novel detection method that significantly improves the precision of real-time measurement of the three-dimensional displacement of a levitated dipolar scatterer. Our technique relies on spatial mode sorting of the light scattered by the levitated object, allowing us to selectively extract the position information of all translational degrees of freedom with minimal losses. To this end, we collect all the light back-scattered from a levitated nanoparticle using a parabolic mirror and couple it into a spatial mode sorter. We measure displacement sensitivities (√︁𝑆imp,𝑥,√︁𝑆imp,𝑦,√︁𝑆imp,𝑧) = (1.7, 2.4, 1.0) × 10−14 m/√Hz below the zero-point motion (𝑥zpm, 𝑦zpm, 𝑧zpm) = (2.2, 2.4, 1.6)× 10−12 m of the levitated particle considered here. In the regime where environmental decoherence is not limited by gas collision we estimate that our method can reach measurement efficiencies of (𝜂𝑥 tot , 𝜂𝑦 tot , 𝜂𝑧 tot) = (0.13, 0.18, 0.33) > 1/9, which would enable the 3D motional quantum ground state of a levitated optomechanical system.