Levitated dipolar scatterers exhibit exceptional performance as optomechanical systems for observing quantum mechanics at the mesoscopic and atomic scales. These systems scatter photons in almost every direction, and, with generally limited light collection efficiency, only partial information about the state of the system can be extracted. In this article, we present a setup to enhance information extraction of optomechanical measurements by constraining light scattering to a specific spatial direction. The setup consists of a hollow hemispherical mirror that controls the light scattered by a dipolar scatterer at high scattering angles outside the hole's region. Control of light scattering at high angles can be used to suppress the corresponding optomechanical backaction, which results in focusing of the measurement information at low angles. This mirror is compatible with existing setups commonly employed in levitated optomechanics, including confocal lenses and optical resonators.
Levitated dipolar scatterers exhibit exceptional performance as optomechanical systems for observing quantum mechanics at the mesoscopic and atomic scales. These systems scatter photons in almost every direction, and, with generally limited light collection efficiency, only partial information about the state of the system can be extracted. In this article, we present a setup to enhance information extraction of optomechanical measurements by constraining light scattering to a specific spatial direction. The setup consists of a hollow hemispherical mirror that controls the light scattered by a dipolar scatterer at high scattering angles outside the hole's region. Control of light scattering at high angles can be used to suppress the corresponding optomechanical backaction, which results in focusing of the measurement information at low angles. This mirror is compatible with existing setups commonly employed in levitated optomechanics, including confocal lenses and optical resonators.
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.
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.
In active imaging protocols, information about an object is encoded into the spatial mode of a scattered photon. Recently the quantum limits of active imaging have been explored with levitated nanoparticles, which experience a multimode radiation pressure backaction (the photon recoil force) due to radiative scattering of the probe field. Here we extend the analysis of multimode backaction to compliant surfaces, accessing a broad class of mechanical resonators and fruitful analogies to quantum imaging. As an example, we consider imaging of the flexural modes of a membrane by sorting the spatial modes of a laser reflected from its surface. We show that backaction in this setting can be understood to arise from spatiotemporal photon shot noise, an effect that cannot be observed in single-mode optomechanics. We also derive the imprecision-backaction product in the limit of purely spatial (intermodal) coupling, revealing it to be equivalent to the standard quantum limit for single-mode optomechanical coupling. Finally, we show that optomechanical correlations due to spatiotemporal backaction can give rise to two-mode entangled light, providing a mechanism for entangling desired pairs of spatial modes. In conjunction with high-Q nanomechanics, our findings point to new opportunities at the interface of quantum imaging and optomechanics, including sensors and networks enhanced by spatial mode entanglement.
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.