When two atoms interact more strongly than they radiate

How close must two atoms be before their mutual interaction dominates the spontaneous emission of light? In a new preprint, Yu-Kun Lu, Jiahao Lyu and Wolfgang Ketterle report experiments reaching that regime with ultracold dysprosium. They observe strong mechanical forces and a change in the light frequency at which the atoms respond.

The interaction involves electric dipoles: oscillating distributions of positive and negative charge associated with an optical transition. At short distances, the interaction energy grows approximately as the inverse cube of separation. It can therefore become strong enough to drive substantial motion before an excited atom emits a photon.

Preparing pairs, not a dense free gas

The researchers loaded dysprosium-162 into a three-dimensional optical lattice, a pattern of light that confines atoms in individual wells. Their sample contained a central region with two atoms per site and an outer region with one.

Tight confinement localized the atomic wavepackets to a root-mean-square size of about 20 nanometres, producing peak densities around 20 quadrillion atoms per cubic centimetre. That size describes the spread of each wavepacket, not a fixed separation between two stationary particles.

Preparing only pairs in the lowest spin state avoided the two-body and three-body losses that would otherwise obstruct such high densities. For several measurements, the team isolated the pairs’ contribution by comparing samples with and without the doubly occupied sites.

A large push before a photon leaves

In one experiment, a brief resonant laser pulse excited both atoms. The first spontaneous emission left the pair sharing a single excitation. During this intermediate state, the strong dipolar interaction accelerated the atoms before a second emission returned them to the ground state.

Images taken after free expansion revealed a broad momentum distribution, rather than the narrower distribution seen with more loosely confined pairs. Simulations matching these measurements gave a median momentum of about eight single-photon recoils per atom for the tightest confinement. The researchers report that roughly 30% of atoms acquired more than ten recoils and moved beyond the detection region.

This does not mean the escaping photon itself carried an unusually large momentum. The atoms exerted strong forces on one another while the pair was excited. Their individual momenta could therefore become much larger than an ordinary emission recoil.

Forces without waiting for emission

A second experiment used laser light away from the atomic resonance. Such illumination gives each atom an oscillating electric dipole moment—about one Debye under the reported conditions—and produces a force between the laser-dressed atoms.

During a 100-nanosecond pulse, each atom scattered only about 0.25 photons, yet the momentum distribution broadened substantially. Numerical calculations reproduced the measured redistribution without freely adjusted parameters. Away from local resonance, the authors’ analysis identifies the dominant force as coherent and conservative, rather than arising from random photon-scattering events.

The light scattering also exposed a surprise. Certain separations should bring the interacting pair into resonance with the laser, enhancing incoherent scattering. The expected enhancement was absent. The authors attribute this to rapid motion emptying those resonant portions of the pair’s wavefunction. That is their interpretation of the observations, not a direct image of the depletion.

Changing the shape changes the resonance

Dipolar forces depend on orientation as well as distance. With a nearly spherical wavepacket, attractive and repulsive contributions largely cancel in the resonance shift. Squeezing the confinement vertically changes their balance.

Comparing two confinement shapes, the team measured a shift toward lower frequency of 8.6 ± 2.5 megahertz. They call this a “two-body Lamb shift”: a resonance shift associated with the interaction within each pair, rather than the familiar single-atom Lamb shift.

Measurements with singly occupied sites, expanded clouds and calculations of interactions between lattice sites supported that attribution. The agreement with the pair model was semi-quantitative. Limited lattice laser power prevented a corresponding measurement of a substantial shift toward higher frequency.

An unresolved loss puzzle

The researchers also measured light-assisted atom loss associated with photoassociation, in which light couples an atom pair to an excited molecular state. Loss coefficients were five to forty times below a standard static model’s predictions. Simulations including atomic motion came closer, but an additional asymmetry between red- and blue-detuned illumination remains incompletely explained.

The preprint establishes an experimental setting for examining how two atoms move, scatter light and reshape their joint quantum state under strong optical dipolar interactions. It does not demonstrate a quantum-computing device or an engineered gravity-like force; those remain motivations for future work.