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arXiv:2103.08322 · Physical Review A

Position measurement of a dipolar scatterer via self-homodyne detection

G. Cerchiari, Lorenzo Dania, Dmitry S. Bykov, R. Blatt, Tracy E. Northup

Published Nov 19, 2021• 0 citations
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Abstract

We describe a technique to measure the position of a dipolar scatterer based on self-homodyne detection of the scattered light. The method can theoretically reach the Heisenberg limit, at which information gained about the position is constrained only by the back action of the scattered light. The technique has applications in the fields of levitated optomechanics and trapped ions and is generally applicable to the position determination of confined light scatterers.

DOI
10.1103/physreva.104.053523

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We describe a technique to measure the position of a dipolar scatterer based on self-homodyne detection of the scattered light. The method can theoretically reach the Heisenberg limit, at which information gained about the position is constrained only by the back action of the scattered light. The technique has applications in the fields of levitated optomechanics and trapped ions and is generally applicable to the position determination of confined light scatterers.
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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.
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 report a heterodyne detection scheme for position readout of an optomechanical system, in particular an optically levitated particle, implemented via digital In-phase and Quadrature demodulation on a field-programmable gate array. Compared to the standard homodyne approach, the proposed method offers three key advantages: it remains robust in the presence of strong parasitic back-reflected fields that would otherwise prevent stable phase locking; it produces a signal linearly proportional to the particle displacement, eliminating phase-wrapping distortion; and its calibration factor is intrinsically immune to drifts in the optical power of the local oscillator or scattered field. We experimentally demonstrate and quantify all three advantages through simultaneous homodyne and heterodyne measurements on the same trapped particle. The proposed method can be used in any optomechanical system based on phase readout.