Direct and mediated dipole-dipole interactions in a reconfigurable array of optical traps

TL;DR

The paper tackles the challenge of achieving site-resolved, point-to-point tunability in arrays of optically trapped nanoparticles by introducing an ancillary coupler that sits between two target particles. A linearized three-body model reveals how phase- and geometry-dependent couplings $K$ and $K'$ mediate both direct and ancilla-facilitated interactions, while an experimental setup with polarization-engineered traps demonstrates wide-range control of direct couplings via the ancilla’s phase and position. Spectral measurements show tunable direct interactions and, when the ancilla approaches both targets, signatures of mediated coupling in the form of mode mixing and multiple normal modes, with quantitative mediation awaiting stronger coupling or cavity enhancement. Overall, the work provides a practical route to site-resolved control in optical-trap arrays, enabling programmable oscillator networks for macroscopic quantum mechanics and precision sensing, and sets the stage for scalable, multi-trap architectures.

Abstract

Optically levitated nanoparticles in vacuum experience both electrostatic and light-induced dipole-dipole interactions, offering a versatile platform to explore mesoscopic entanglement and many-body dynamics. A significant challenge in optical trap arrays is to achieve site-resolved, point-to-point tunability: adjusting the laser parameters of a single trap typically induces global cross-talk to neighboring sites, hindering independent control. Inspired by tunable couplers in superconducting circuits, we implement an ancillary nanoparticle that functions as a coupler between two target nanoparticles. Within a reconfigurable three-particle array, we demonstrate broad tunability of the direct dipole-dipole interaction by controlling the phase and position of the traps. In addition, we observe spectral signatures consistent with mediated interactions between the target particles via the ancillary one, manifested as mode participation beyond the uncoupled response. Our results establish a practical route to tailored, site-resolved control in multi-particle optical trap arrays, expanding the optical-binding toolbox and opening opportunities for programmable oscillator networks relevant to macroscopic quantum mechanics and precision sensing.

Figures (5)

• Figure 1: (a) Schematic of an ancillary nanoparticle used as a tunable coupler between two target nanoparticles in an optical trap array. Blue spheres denote the target array, and the orange sphere denotes the ancillary coupler. Red arrows indicate light-induced dipole–dipole interactions. (b) Focal-plane arrangement: particles 1, 2, and 3 are trapped in traps 1, 2, and 3, respectively. Particles 1 and 3 are targets; particle 2 is the ancillary coupler. The traps form an isosceles triangle with base angles $\theta$ and base length $d$. The laser polarization of traps 1 and 3 is along $x$, whereas trap 2 is mainly polarized along $y$. Characteristic far-field dipole-radiation patterns under these conditions are also illustrated. (c) Camera image of the three nanoparticles trapped under 532 nm illumination ($\theta \approx 45^{\circ}$, $d \approx 4.77\ \mu\mathrm{m}$).
• Figure 2: Schematic of the experimental setup. A 1064 nm trapping beam is expanded by a beam expander (BE), then passes through a polarizing beam splitter (PBS1) and a half-wave plate (HWP) to yield a linearly polarized beam with controllable P- and S-polarized components. The beam is incident on a spatial light modulator (SLM), using phase modulation to generate three optical traps. The forward-scattered light from each of the three traps is separated and then detected by quadrant photodiodes (QPD1–QPD3) for simultaneous motion readout. A high-voltage DC supply (HV) connected to bare wires inside the vacuum chamber is used to neutralize particle charge via a corona discharge, while a pair of steel electrodes (SE) applies an electric drive (ED) for charge monitoring. The setup also includes a multi-particle microscopic imaging system with 532 nm laser illumination, omitted from the schematic for clarity. L, lens; MO, microscope objective; AsL, aspheric lens; M, mirror; VI, variable iris.
• Figure 3: (a) Numerically simulated map of the eigenfrequency splitting $(\omega_1-\omega_3)/2\pi$ as a function of interparticle distance $d$ and phase difference $\Delta\phi$ at $\theta\approx 45^{\circ}$ and $\eta\approx-0.4$. (b) Experimentally measured eigenfrequency splitting under the same conditions, showing periodic modulation with $d$ and $\Delta\phi$, in good agreement with simulation. (c) Eigenfrequency splitting versus $d$ at near-zero phase difference $\Delta\phi\approx 0$. Blue dots: experimental data; red curve: simulation. Both show an oscillatory decay with period $\sim\sqrt{2}\lambda$. (d) Eigenfrequency splitting versus phase difference $\Delta\phi$ at fixed $d=3.77$$\mu\mathrm{m}$. Purple dots: experimental data; green curve: simulation. The modulation follows the interference phase.
• Figure 4: (a) Camera image of three particles arranged in an isosceles triangle ($d\approx3.77$$\mu\mathrm{m}$, $\theta\approx45.0^{\circ}$). (b) Same distance $d$ but larger angle ($\theta\approx60.4^{\circ}$). (c) Eigenfrequency splitting $(\omega_1-\omega_3)/2\pi$ versus $\theta$ for $d\approx3.77$$\mu\mathrm{m}$, $\eta\approx-0.4$, and $\Delta\phi=0$. Magenta dots: experiment; gray curve: simulation. As $\theta$ increases, the splitting oscillates with gradually decreasing amplitude and period.
• Figure 5: (a–c) Camera images of three nanoparticles in different geometric configurations defined by $d$ and $\theta$. (d–f) Corresponding power spectral densities (PSDs) of $z$-axis motion at $\eta\approx-0.4$ and $\Delta\phi=0$. For large separations (a,b), the PSDs (d,e) show distinct peaks at the intrinsic mechanical frequencies of each particle, indicating negligible coupling. When the particles are brought into close proximity (c), the ancillary particle interacts with the targets to form a coupled mechanical system. The PSDs (f) reveal three normal modes with eigenfrequencies $\omega_1$, $\omega_2$, and $\omega_3$, with the targets exhibiting participation at multiple mode frequencies.