How an electron’s quantum connection passes from an ion to light

A quantum connection changes partners

An electron knocked out of an atom can remain entangled with the ion left behind. Entanglement means their joint quantum state cannot be described by assigning each an independent state. If the ion subsequently emits light, what happens to that connection?

In a theoretical preprint, Axel Stenquist and Jan Marcus Dahlström of Lund University calculate how entanglement moves through an electron–ion–radiation system. Their central finding is that the change is not simply a handover between two isolated pairs. The system passes through an interval of genuine three-part entanglement before approaching an entangled electron–photon state, with the ion no longer participating.

The work analyzes a model rather than reporting a new experimental observation.

Following the atom after ionization

The modeled process starts with a short, intense laser pulse. It removes an electron and strongly couples two internal states of the remaining ion. The pulse durations considered extend up to 44 femtoseconds. Spontaneous emission occurs on a longer timescale: the excited ionic state decays and produces a photon.

The researchers retain the outgoing electron’s range of possible energies, both ionic states, and radiation states containing either no photon or one photon. The radiation subsystem therefore includes the vacuum; it is not an already-emitted photon throughout the calculation.

They select the ionized portion of the wave function, excluding atoms that remain neutral, and normalize that selected state. Within this ensemble, they do not further select a particular ionic state, electron energy or photon number.

That choice matters. Selecting only events with a detected photon, for example, would define a different quantum state and could give different entanglement results.

Establishing three-part entanglement

The authors first examine three divisions: electron versus ion and radiation together; ion versus electron and radiation; and radiation versus electron and ion.

For their pure, conditioned state, the von Neumann entropy measures entanglement across each division. It is calculated from the state remaining when the other subsystems are mathematically ignored. If every division is entangled, the pure state has genuine three-part entanglement: no subsystem can be separated from the rest.

Initially, the electron and ion become approximately maximally entangled within an effective two-state description, while the radiation remains close to an independent vacuum state. During spontaneous emission, the ion’s entanglement with the rest decreases as the radiation’s increases. In between, all three divisions have nonzero entanglement.

After decay, the ion approaches its lower state and separates from the electron–photon quantum state. The electron and photon retain approximately one bit of entanglement.

These entropy values are not separate shares that can be added into a conserved total. Each division describes overlapping information about the same joint state.

Looking at the pairs separately

Three-part entanglement does not, by itself, establish which individual pairs remain entangled when the third subsystem is ignored. Those pair states are generally mixed, so their entropy measures mixedness rather than entanglement alone.

The researchers instead use logarithmic negativity to examine each pair. It shows electron–ion entanglement decreasing while electron–photon entanglement grows. It also reveals temporary direct entanglement between the ion and radiation. Once decay is complete, the ion’s pairwise entanglement with either partner vanishes.

Logarithmic negativity also detects structure beyond a simple two-state picture. Electron and photon energies span continua, allowing additional, weakly populated components in the entangled state. These contribute more strongly to logarithmic negativity than to von Neumann entropy. Consequently, one measure rises visibly above the two-state value while the other shows only a very small excess. The authors associate these additional components with dynamics during the laser interaction.

What the approximation leaves out

After the pulse, the electron evolves independently of the combined ion–radiation subsystem. In a complete description, subsequent interactions within that combined subsystem cannot change its entanglement with the electron. They can redistribute it between ion and radiation.

The calculation uses an effective treatment of irreversible emission and neglects sectors containing two or more photons, justified by their small probability under the assumed timing. The authors attribute a slight later decrease in the calculated electron-versus-rest logarithmic negativity to decay into the omitted two-photon sector.

The result is therefore a model-based account with explicit selection and photon-number limits. Within those limits, it explains how an apparently fading electron–ion connection can survive in light, through an intermediate state involving all three subsystems.