Hailong Pi

Optically levitated multiple nanoparticles have emerged as a platform for studying complex fundamental physics such as non‐equilibrium phenomena, quantum entanglement, and light–matter interaction, which could be applied for sensing weak forces and torques with high sensitivity and accuracy. An optical trapping landscape of increased complexity is needed to engineer the interaction between levitated particles beyond the single harmonic trap. However, existing platforms based on spatial light modulators for studying interactions between levitated particles suffered from low efficiency, instability at focal points, the complexity of optical systems, and the scalability for sensing applications. Here, we experimentally demonstrated that a metasurface which forms two diffraction‐limited focal points with a high numerical aperture (∼0.9) and high efficiency (31 %) can generate tunable optical potential wells without any intensity fluctuations. A bistable potential and double potential wells were observed in the experiment by varying the focal points’ distance, and two nanoparticles were levitated in double potential wells for hours, which could be used for investigating the levitated particles’ nonlinear dynamics, thermal dynamics and optical binding. This would pave the way for scaling the number of levitated optomechanical devices or realizing paralleled levitated sensors.

This paper presents the total angular momentum-conserving Poincaré sphere (TAM-C PS), which offers a novel framework for efficiently characterizing a wide range of vector vortex beams. Unlike other types of Poincaré spheres, the TAM-C PS achieves a better balance between generality and validity, while also providing clearer physical interpretation. By linking the poles of different spheres, the study also introduces two distinct categories of TAM-C PS braid clusters, enabling the representation of various Poincaré spheres within a unified framework. The Poincaré spheres include classical, higher-order, hybrid-order, Poincaré sphere with orbital angular momentum, and TAM-C PS. This is the first clear and unified approach to express multiple Poincaré spheres within a single framework. The TAM-C PS and its braid cluster can be employed to guide the creation of targeted vector vortex light beams, offer a geometric description of optical field evolution, and calculate the geometric phase of optical cyclic evolution.