Optimal displacement detection of arbitrarily-shaped levitated dielectric objects using optical radiation

TL;DR

The paper develops a general Fisher-information framework to compute Information Radiation Patterns (IRP) for arbitrarily shaped levitated dielectric objects, enabling optimal displacement detection from scattered light via $\mathcal{I}_{\mu}$ and its integrated form $\mathcal{I}^\text{Fisher}_{\mu}$. It validates the method against Lorentz–Mie results for spheres and extends to non-spherical geometries such as hexagonal disks and nanorods, covering translational and librational degrees of freedom. Numerically, it implements the framework with SCUFF-EM, pyGDM, and COMSOL, and demonstrates IRPs in realistic trap configurations, including comparisons to interferometric detection using practical reference fields and a discussion of detection efficiencies. The work provides a geometry-agnostic tool to maximize displacement sensitivity in levitated optomechanics, with implications for torque sensing, high-frequency gravitational wave detection, and quantum control, and makes simulation data and code openly available.

Abstract

Optically-levitated dielectric objects are promising for precision force, acceleration, torque, and rotation sensing due to their extreme environmental decoupling. While many levitated opto-mechanics experiments employ spherical objects, for some applications non-spherical geometries offer advantages. For example, rod-shaped or dumbbell shaped particles have been demonstrated for torque and rotation sensing and high aspect ratio plate-like particles can exhibit reduced photon recoil heating and may be useful for high-frequency gravitational wave detection or as high bandwidth accelerometers. To achieve optimal sensitivity, cooling, and quantum control in these systems, it is beneficial to achieve optimal displacement detection using scattered light. We describe and numerically implement a method based on Fisher information that is applicable to suspended particles of arbitrary geometry. We demonstrate the agreement between our method and prior methods employed for spherical particles, both in the Rayleigh and Lorentz-Mie regimes. As practical examples we analyze the optical detection limits of an optically-levitated high-aspect-ratio disc-like dielectric object and a rod-shaped object for configurations recently realized in experimental work.

Figures (7)

• Figure 1: (upper) A hexagonal plate levitated in a standing wave optical trap and labeled coordinates corresponding to the displayed information radiation patterns. Laser fields are linearly polarized along the $x-$ direction and propagating along the $z-$ direction. Angles $\theta_x,\theta_y,\theta_z$ represent librations about the $x-,y-$ and $z-$ axes, respectively. (lower) IRPs from the SCUFF-EM implementation for each degree of freedom $\mu$ of a hexagonal disk trapped in a standing wave trap made up of two counter-propagating beams with wavelength $\lambda = 1550 ~\text{nm}$ and a beam waist of $w_0 = 12~\mu\text{m}$. Each plate has dimensions given in Table \ref{['Table:Hex Sizes']}. We also show the detection efficiencies for the left and right focusing lenses each with a numerical aperture of $\text{NA} = 0.082$.
• Figure 2: (upper) A rod levitated in a standing wave optical trap. Angles $\theta_x,\theta_y,\theta_z$ represent librations about the $x-,y-$ and $z-$ axes, respectively. (lower) IRPs from the SCUFF-EM implementation for each degree of freedom $\mu$ of a rod trapped in a standing wave trap made up of two counter-propagating beams with wavelength $\lambda = 1550 ~\text{nm}$ and a beam waist of $w_0 = 12~\mu\text{m}$. The rods have the dimensions given in Table \ref{['Table:Rod Sizes']}. We also show the detection efficiencies for the left and right focusing lenses each with a numerical aperture of $\text{NA} = 0.082$.
• Figure 3: Information patterns for varying radii of spherical particles in a Gaussian beam traveling in the positive $z$ direction. The beam is focused by a lens to the left with a numerical aperture of $\text{NA}=0.1$. a) Shows the analytical results reproduced from maurer2022quantum and b) are the numerical results from SCUFF-EM. The numbers in the bottom corners of each panel refer to the detection efficiencies $\eta_\mu$ for a lens to the left and to the right. The left collection lens is the same as the focusing lens, while the right collection lens has a numerical aperture of $\text{NA} = 0.75$.
• Figure 4: Information patterns for varying radii of spherical particles in a Gaussian beam traveling in the positive $z$ direction. The beam is focused by a lens to the left with a numerical aperture of $\text{NA}=0.75$ which is also used as the left collection lens for the detection efficiencies. The right collection lens also has a numerical aperture of $\text{NA}= 0.75$. a) shows the results reported from maurer2022quantum and b) are the numerical results from SCUFF-EM.
• Figure 5: The information pattern for a H1 hexagonal plate illuminated by a single Gaussian beam with wavelength $\lambda = 1550 ~\text{nm}$ and a beam waist of $w_0 = 12 ~\mu\text{m}$. The left set of panels are the IRPs created using the Fisher information approach discussed in the main text. The panels on the right use a reference field to extract the information. This reference field is taken to be a Gaussian beam traveling in both the positive and negative $z$ directions. For improved numerical precision, the reference beam has the same parameters as the trapping beam with a $10^5$ increase in magnitude and a $\pi/2$ phase shift used to maximize the amount of information that can be obtained from the phase of the scattered light. These IRPs are generated by interfering the scattered field with the reference and using Eq. \ref{['EQ:Scuff-Laser-Ref']}