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

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.

💡 Research Summary

The paper presents a comprehensive framework for achieving optimal displacement detection of arbitrarily‑shaped levitated dielectric particles by exploiting the Fisher information carried by scattered light. Recognizing that most levitated optomechanics experiments have focused on spherical particles, the authors address the growing interest in non‑spherical geometries—such as high‑aspect‑ratio disks, rods, and dumbbells—that offer distinct advantages for torque sensing, reduced photon‑recoil heating, and high‑frequency gravitational‑wave detection.

The theoretical core is the definition of a Fisher information flux, (S_{\text{FI}}(\theta,\phi){\mu}=2\hbar\omega\Re{\partial{\mu}\mathbf{E}^{*}(\theta,\phi)\times\partial_{\mu}\mathbf{H}(\theta,\phi)}), where (\mathbf{E}) and (\mathbf{H}) are the scattered electric and magnetic fields in the far‑field, (\omega) is the optical frequency, and (\mu) denotes the parameter of interest (Cartesian displacement or angular libration). This expression quantifies, per unit solid angle, how much information about a small change in the particle’s position or orientation is encoded in the scattered field. By integrating the flux over a measurement sphere and normalizing by the total scattered information, the authors obtain a dimensionless “information radiation pattern” (IRP) that directly maps to the achievable signal‑to‑noise ratio for any given detector geometry.

Because analytical solutions for the scattered fields exist only for simple shapes (Rayleigh dipoles, Mie spheres), the authors implement three independent numerical solvers to compute (\mathbf{E}) and (\mathbf{H}) for arbitrary geometries:

1. SCUFF‑EM – a surface‑integral‑equation / boundary‑element method that discretizes only the particle surface. It scales with surface area and is especially efficient for large, high‑aspect‑ratio objects.
2. pyGDM – a volume‑discretized Green‑Dyadic Method (GDM) that solves the Lippmann‑Schwinger equation for the full interior of the object. It provides full near‑field information but scales with the cube of the particle volume.
3. COMSOL Multiphysics – a finite‑element method with adaptive meshing and a built‑in perfectly‑matched‑layer for open‑boundary conditions. It offers flexibility for complex material environments but requires careful solver selection to ensure convergence.

The authors validate their pipeline by reproducing known IRPs for spheres in both the Rayleigh and Mie regimes, confirming agreement with earlier works (Refs.