Pseudorotation and N-body Forces in an Optical Matter System

Isomerization in molecular systems almost invariably occurs through 3-dimensional motion due to the nature of chemical bonding. Pseudorotation is an unusual type of isomerization that occurs in some high symmetry systems that gives the appearance of rigid-body rotation yet only involves atom rearrangements. This paper demonstrates that pseudorotation occurs in 2-dimensions in an optical matter (OM) system of metal nanoparticle constituents. The difference in dimensionality of the dynamics arises from the electrodynamic field-interference nature of optical binding vs. quantum mechanical bonding in polyatomic molecules. The 8-nanoparticle OM “kite” structure we study in experiments and simulations has D2 (D2h) symmetry and a D4 symmetric transition state. The mechanism for pseudorotation involves correlated motion of all 8 nanoparticles with smooth (continuous) evolution of their interactions and without particles jumping in or out of the OM array. While the OM kite structure only occurs with 10% probability vs. other OM isomers, its rate of pseudorotation is rapid relative to transitions to other structural isomers (e.g., “teardrop”). The other isomers have structures that lie on a trigonal lattice with inter-particle separations at distances that enhance field interference and induced polarizations. Even though the kite isomer has inter-particle separations that would manifest destructive interference on a particle pair (i.e., 2-body) basis, the kite structure is the slowest to rearrange into any other isomer. We show that the unusual structure and dynamics of the kite optical matter system result from N-body interactions and forces demonstrating that N-body effects are important in this class of active matter and presumably more generally.

💡 Research Summary

This paper presents a groundbreaking experimental and computational study demonstrating and analyzing the phenomenon of pseudorotation within a two-dimensional optical matter (OM) system. Unlike traditional molecular isomerization, which occurs in three dimensions due to chemical bonding constraints, this work shows that pseudorotation—where a structure appears to rotate rigidly through internal rearrangements of its constituents—can occur in a 2D plane. The system under investigation is an OM array composed of eight silver nanoparticles, self-assembled via optical binding forces within a loosely focused, circularly polarized laser trap.

The research meticulously characterizes the various structural isomers (e.g., “teardrop,” “boat mast,” “kite,” “spaceport”) that the 8-particle system can adopt, analyzing their relative probabilities and stability as a function of ionic strength, which modulates electrostatic double-layer repulsion between particles. Among these, the “kite” isomer, characterized by a distinctive central quartet of particles, is of primary interest. Although it occurs with only ~10% probability under optimized conditions, it exhibits unique dynamics.

The core discovery is the pseudorotation of the kite isomer. The mechanism involves the correlated, continuous motion of all eight nanoparticles, tracked using the difference between two orthogonal distances (d1-d2) within the central four-particle group. This coordinate oscillates over time, making the structure appear to rotate by 90 degrees without any particle entering or leaving the array. Both dark-field microscopy experiments and ElectroDynamics-Langevin Dynamics (EDLD) simulations confirm this smooth, intra-state transition. The kite isomer has a D2 symmetry in its stable states and passes through a D4 symmetric transition state during pseudorotation.

A pivotal finding is the role of N-body interactions. Analysis of pair distribution functions reveals that the inter-particle distances in the kite structure would lead to destructive optical interference on a simple pair-wise (2-body) basis. Despite this, the kite isomer is the most stable, exhibiting the slowest rate of transition to any other isomer. This paradox is resolved through EDLD simulations, which demonstrate that the unusual stability and the pseudorotation dynamics are governed by multi-particle (N-body) optical forces, not merely the sum of 2-body interactions. The high symmetry of the structure also leads to collective scattering of angular momentum, inducing a net rigid-body rotation in the transition state.

In summary, this work successfully transposes a classic chemical concept—pseudorotation—into a nanophotonic context, revealing the fundamental importance of many-body electrodynamic effects in optical matter. It establishes OM arrays as a rich platform for studying collective phenomena and non-equilibrium dynamics in soft matter, where structure and motion are dictated by complex interference patterns and N-body forces.