Foundations of quantum mechanics · Experiment
Observation of strong electric dipole-dipole interactions between two atoms
arXiv:2611.13665v1 ↗PDF ↗Submitted 10 November 2026
- Question
- Two atoms closer than the reduced optical wavelength \(\bar\lambda=\lambda/2\pi\) should interact through light much more strongly than they decay: the near-field dipole-dipole coupling grows as \(\hbar\Gamma/(r/\bar\lambda)^{3}\). Seeing this needs densities above \(10^{15}\,\mathrm{cm^{-3}}\), where inelastic collisions usually destroy the gas, so light-induced dipolar effects in cold atoms had been seen only in the weak far-field regime, summed over many atoms.
- Result
- With exactly two dysprosium atoms per site of a deep optical lattice, squeezed to an rms size of about 20 nm (peak density \(2\times10^{16}\,\mathrm{cm^{-3}}\), \(n\bar\lambda^{3}>10\)), the authors observe: single-photon emission giving median momentum transfers near \(8\hbar k\), with about 30% of atoms above \(10\hbar k\); a coherent force between laser-dressed dipoles of about 1 debye; and a "two-body Lamb shift" of the resonance, \(8.6\pm2.5\) MHz or \(0.27(8)\Gamma\), when the pair wavefunction is flattened. Simulations without free parameters reproduce the momentum data.
The paper in detail
A single atom coupled to the vacuum gets a Lamb shift and a decay rate \(\Gamma\). Two atoms sharing the vacuum exchange virtual photons, giving a dipole-dipole interaction with a coherent part and a dissipative part. Far apart (\(kr\gg1\)) the interaction is weak and has been seen only as a sum over many atoms, in shifts of dense clouds and in the lensing of a condensate. Close together (\(kr\ll1\)) the coherent part dominates and scales as \(1/(kr)^{3}\).
The question is what two atoms do in that strong near-field regime, where a single excitation shared between them feels a force much larger than a photon recoil.
The authors load a dysprosium condensate into a deep 3D lattice, forming a core of doubly occupied sites in the lowest spin state, where two-body and three-body losses are absent. Exciting both atoms with a fast pulse on the narrow 626 nm line and letting one photon escape leaves the pair in a symmetric single-excitation state, which pushes the atoms apart before the second decay: momenta reach several photon recoils, shrinking as the wavepackets are expanded. Driving off resonance on the 421 nm line dresses each atom with an oscillating dipole of about 1 debye; the pair then exerts a coherent force with little photon scattering. In the fluorescence spectrum, the dipolar shift averages almost to zero for a spherical pair, but flattening the pair so the atoms sit side by side gives a measurable red shift.
Open points are the blue shift for the opposite aspect ratio, the low and asymmetric photoassociation losses, and driven many-body systems with strong coherent dipolar coupling, now accessible at these densities.
Transferable methods
Densities in units of the optical wavelength
Whether the near field dominates is set by the dimensionless density \(n\bar\lambda^{3}\), not by the density alone. Converting the paper's numbers checks that two atoms in a 20 nm wavepacket are deep in the regime where coherent coupling beats spontaneous emission.
For two atoms with Gaussian wavepackets of rms size \(\sigma\), the peak density seen by one atom is about \(2/((2\pi)^{3/2}\sigma^{3})\). At \(\sigma=20\) nm this is \(1.6\times10^{16}\,\mathrm{cm^{-3}}\), the stated \(2\times10^{16}\). With \(\bar\lambda=\lambda/2\pi\), \[n\bar\lambda^{3}\approx6\ (421\ \mathrm{nm}),\qquad n\bar\lambda^{3}\approx20\ (626\ \mathrm{nm}),\] so the paper's \(n\bar\lambda^{3}>10\) refers to the 626 nm line (editorial check).
The coherent coupling exceeds \(\Gamma\) when \(r<\bar\lambda\approx100\) nm, a density of \(1/(100\ \mathrm{nm})^{3}=10^{15}\,\mathrm{cm^{-3}}\), the threshold quoted. The near-field shift scale \(\Gamma/(k\sqrt2\sigma)^{3}\) at \(\sigma=22\) nm and 421 nm is \(10\Gamma\), as stated, so the much smaller measured shift reflects angular cancellation, not weak coupling.
How to reuse it
For any light-matter platform, express separations in units of \(\bar\lambda\) and couplings in units of \(\Gamma\) before comparing regimes; the same atoms can be in the weak collective regime on one transition and the strong pairwise regime on another.
Shaping the pair to reveal an averaged-out shift
The dipolar interaction is anisotropic, so in a spherical pair it averages to almost nothing even though it is ten linewidths strong locally. Changing the aspect ratio of the pair wavefunction, without changing the cloud as a whole, exposes the shift and separates it from collective effects of the dense cloud.
The near-field interaction is \(V_{\mathrm{dd}}\propto(3\cos^{2}\theta-1)/r^{3}\), with \(\theta\) the angle between the quantisation axis and the interatomic axis. Over a sphere \[\tfrac12\int_0^{\pi}(3\cos^{2}\theta-1)\sin\theta\,d\theta=0,\] so only the convolution with the Lorentzian line leaves a small shift. Squeezing the pair vertically makes side-by-side configurations (\(\theta\approx\pi/2\), attractive) more likely and shifts the line to the red.
Measured: no shift for \((\sigma_h,\sigma_z)=(22,26)\) nm and \(8.6\pm2.5\) MHz for \((22,16)\) nm; with \(\Gamma_{421}=2\pi\times32\) MHz this is \(0.27\Gamma\) (editorial ratio). Lattice light shifts, optical-density effects and detuning-dependent losses were each ruled out by separate tests, since the cloud's overall shape was unchanged.
How to reuse it
When an interaction cancels under isotropic averaging, measure a differential signal while deforming only the relative wavefunction; this isolates pairwise physics from bulk effects of the same sample.
Context & limitations
Why it matters. The authors report the first observation of strong light-induced dipolar interaction between two atoms in well-defined states, the minimal system for near-field optical dipole physics, which earlier experiments saw only as a collective, essentially classical effect of thousands of atoms. It opens driven two-body systems with coherent dipolar coupling to study, and sheds light on photoassociation.
Limitations. The shift was observed only for one aspect ratio: lattice power did not allow the opposite shape, which should give a blue shift. The measured shift agrees with the model semi-quantitatively (prediction \(0.38\Gamma\) for the doublon-singlon mixture). Some observations, such as the absent extra incoherent scattering and asymmetric losses, are explained by motional dynamics or left as possibilities. Doublon signals are obtained by subtracting a singlon-only measurement. No AI-use statement was found.