Two silica nanospheres trapped ~9 μm apart in a bichromatic optical tweezer and coupled through their residual surface charges have reached the classical strong-coupling regime (2g>γ2g>\gamma, gZ/2π=1323±38g_Z/2\pi=1323\pm38 Hz at 1.5 mbar gas pressure, evidenced by an avoided crossing of the axial normal modes), but only at room temperature and only for the axial modes. The open problem is to bring this Coulomb-coupled pair into the quantum regime: operate at pressures where mechanical decoherence falls below the coupling rate, cool the axial motion of both particles simultaneously to the motional ground state, demonstrate quantum-coherent exchange (or stationary entanglement) between the two center-of-mass modes, and enable individual addressing of each nanosphere by wavelength modulation of the chromatic-aberration-separated trap centers. As of mid-2026 this remains open: the same group's 2025 follow-up achieved cavity-mediated strong coupling of transverse modes and dark modes but stayed classical, and all two-particle ground-state-cooling and entanglement schemes in the literature are theoretical proposals.

Background

Levitated optomechanics studies the center-of-mass (CoM) motion of dielectric nanoparticles trapped by optical tweezers (tightly focused laser beams creating a conservative dipole potential) in vacuum; each trapped particle behaves as a mechanical harmonic oscillator with kHz-range frequencies whose damping rate γ\gamma is set mainly by residual gas collisions and can be reduced by lowering the pressure. A central goal of the field is to observe quantum mechanics in massive objects by cooling this motion to the motional ground state (mean occupation nˉ<1\bar{n}<1), which was achieved for a single particle by feedback cooling (continuous measurement of the particle position plus a calibrated force that extracts energy) and by cavity coherent-scattering cooling (the tweezer light scattered by the particle into a high-finesse optical cavity both detects and cools the motion). Two such oscillators that are coupled to each other at a rate gg form a paradigmatic interacting many-body system. When 2g>γ2g>\gamma the system is in the strong-coupling regime: its two normal modes are spectrally resolved, and the characteristic avoided crossing of the mode frequencies as the bare trap frequencies are tuned through degeneracy directly measures gg. The dielectric nanospheres used in experiments carry residual surface charges (tens to hundreds of elementary charges), so two nearby particles experience a Coulomb force that couples their CoM motions with a strength that scales as q1q2/r123q_1 q_2/r_{12}^3 for separation r12r_{12}. Deplano, Pontin, Ranfagni, Marino, and Marin (Optica 11, 1773 (2024)) demonstrated exactly this: two nanospheres individually trapped in a bichromatic optical tweezer — two copropagating trapping lasers at 1064 nm and 976 nm whose chromatic aberration (the wavelength dependence of the focal length of the focusing optics) creates two traps about 9 μm apart along one axis. The Coulomb coupling of the axial (ZZ) CoM modes, gZ/2π=1323±38g_Z/2\pi = 1323\pm38 Hz, exceeded the linewidth γ≈1.5\gamma\approx1.5 kHz at the working pressure of 1.5 mbar, giving a resolvable avoided crossing, while the transverse couplings (gX/2π≈−114g_X/2\pi\approx-114 Hz, gY/2π≈−127g_Y/2\pi\approx-127 Hz) remained far below γ\gamma; optical binding (the light-induced dipole–dipole interaction in which each particle is acted on by the tweezer light Rayleigh-scattered by the other) was calculated in their supplement to be more than two orders of magnitude weaker than the Coulomb interaction at these parameters. Several neighboring two-particle platforms exist — light-induced dipole–dipole (optical-binding) coupling of two levitated nanoparticles (Rieser et al., Science 2022), programmable long-range cavity-mediated coupling (Vijayan et al., Nature Physics 2024), and sympathetic cooling of a Coulomb-coupled pair in a Paul trap (an electrodynamic ion-trap-like device; Penny et al., Phys. Rev. Research 2023) — but all operate in the classical, room-temperature regime. The quantum regime of any coupled pair of levitated particles, and of this Coulomb-coupled tweezer pair in particular, has not been reached: single-particle quantum control (Tebbenjohanns et al., Nature 2021) has not been extended to a coupled pair, and a quantum theory of optical binding between nanoparticles exists (Rudolph et al., Phys. Rev. A 110, 063507 (2024)) but no coupled pair has been cooled or entangled.

Problem Statement

Bring the pair of Coulomb-coupled nanospheres in a bichromatic optical tweezer from the demonstrated room-temperature classical strong-coupling regime into the quantum regime, with individual control of each particle. The common objective is a quantum-coherent, individually addressable two-oscillator system; the following components jointly support it and are all required. (1) Low-pressure coherent operation: operate the chromatic-aberration-separated double tweezer at gas pressures low enough that the decoherence rate of both axial CoM modes falls below their Coulomb coupling rate (about 1.3 kHz), replacing the 1.5 mbar damping used for stability, while retaining particle stability and the detection efficiency needed to monitor both particles (e.g. via free-space rather than fibered collection). (2) Quantum ground state of both oscillators: cool the axial CoM motion of both nanospheres simultaneously to mean occupation below 1, by feedback cooling, cavity coherent-scattering cooling, or an equivalent method, extending to the coupled pair what has been shown for a single levitated particle. (3) Quantum coherent exchange: demonstrate quantum-coherent dynamics of the coupled pair at the single-quantum level — coherent exchange of excitations between the two axial modes at a rate exceeding the total decoherence rate, or preparation and verification of a stationary entangled (e.g. two-mode-squeezed or Einstein–Podolsky–Rosen-type) state of the two CoM modes. (4) Individual addressing: enable selective preparation and readout of the state of each nanosphere — for instance through the proposed wavelength-modulation scheme, which displaces the chromatic trap centers by modulating the tweezer laser wavelength with the sub-picometer depth (≈0.2 pm, the scale of the zero-point motion — the residual position uncertainty of a harmonic oscillator in its ground state, per the source's estimate) and low noise needed for such individual control.

References

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