Double-slit photoelectron interference in strong-field ionization of the neon dimer

This Nature Communications paper asks whether the classic “molecular double-slit” idea—interference between electron wave packets emitted coherently from two atomic centers—can survive and be directly observed in strong-field ionization, where electrons are typically thought to originate from a laser-determined tunnel exit rather than from the atomic cores, and where subsequent laser acceleration and Coulomb interactions could distort the phase fronts. The question matters because it probes the quantum coherence of electron emission and propagation in intense laser fields on ultrafast timescales, and it tests whether two-center phase information can be imprinted onto measurable electron momentum distributions.

The authors’ central significance claim is that they observe full two-center interference fringes in the molecular-frame photoelectron momentum distribution of the neon dimer (Ne2) under strong-field ionization. Earlier work suggested related effects (e.g., suppression of ionization for certain diatomics, or differences between dimer and monomer spectra), but some interpretations were contested—particularly whether observed spectral differences truly reflect two-center interference or instead arise from post-collision interaction. By contrast, this experiment reports interference patterns with the expected fringe structure and demonstrates a key control knob: by postselecting the dissociation channel (and thus the orbital symmetry from which the electron was liberated), they can switch between gerade and ungerade interference, which should correspond to phase differences of $\Delta \varphi =0$ versus $\Delta \varphi =\pi$. This provides a stringent phase-sensitive test of the double-slit mechanism in the strong-field regime.

Methodologically, the study combines (i) coincidence momentum spectroscopy with (ii) molecular-frame reconstruction and (iii) theoretical modeling using the time-dependent Schrödinger equation (TDSE) in a single-active-electron approximation.

Experimentally, Ne2 dimers are prepared in a molecular beam at 60 K using supersonic expansion and matter-wave diffraction to enhance the dimer fraction (reported as 20% relative to monomer). The dimers are ionized by a 40 fs (FWHM intensity) 780 nm laser pulse at high intensity. Two polarization regimes are used: circular polarization at $7.3\times 10^{14}W/c{\mathrm{m}}^2$ with Keldysh parameter $\gamma =0.72$, and linear polarization at $1.2\times 10^{15}W/c{\mathrm{m}}^2$ with $\gamma =0.4$. After ionization, the charged fragments are detected in coincidence with the emitted electron using COLTRIMS (cold target recoil ion momentum spectroscopy). The key experimental trick is that Ne2 dissociates rapidly after single ionization into Ne0 and Ne+, so the direction of the detected Ne+ in coincidence with the electron provides the molecular axis for each event. This enables projection of the electron momentum onto the internuclear axis, which is the observable needed to see two-center interference.

The paper focuses on the single-ionization channel that leads to breakup into a singly charged and neutral neon atom (Ne+ + Ne0). The authors analyze the molecular-frame photoelectron momentum distribution in terms of components parallel and perpendicular to the internuclear axis (denoted $k_{\parallel }$ and $k_{\perp }$ in the molecular frame). To isolate the two-center interference, they also normalize the dimer electron spectra by the corresponding monomer single-ionization spectrum measured under the same conditions. This normalization removes an intrinsic “ionization weighting” (described as a doughnut-like momentum dependence due to tunneling ionization in circular polarization) so that the remaining structure can be attributed to interference rather than to emission probability.

A crucial part of the methodology is orbital and phase selection. The neon dimer has two relevant dissociation pathways associated with different ionic potentials and initial molecular orbitals: emission from the $2p{\sigma }_g$ orbital corresponds to a low kinetic-energy release (KER) feature around $0.25\mathrm{eV}$ and is linked to direct dissociation along the $II(1/2)g$ ionic state. A higher KER feature around $1.3\mathrm{eV}$ corresponds to an indirect pathway where the system evolves along the $I(1/2)u$ potential and then absorbs one additional photon to reach the $II(1/2)g$ state at shorter internuclear distance, effectively changing the phase relation of the emitted electron waves. By selecting events in KER regions corresponding to these pathways, the authors separate gerade from ungerade emission and thereby control whether the interference behaves as $\Delta \varphi =0$ (constructive at the expected locations) or $\Delta \varphi =\pi$ (fringes converted to anti-fringes).

On the theory side, the authors solve the three-dimensional TDSE numerically within a single-active-electron approximation. They propagate on a Cartesian grid (512 points per dimension, spacing 0.25 au, time step 0.02 au) up to final time $T=1500$ au, projecting outgoing wavefunction parts onto Volkov states to obtain momentum distributions. To model the dimer interference, they compute an atomic-like momentum distribution from an initial p orbital aligned along the internuclear axis (resembling one lobe of a $2p\sigma$ orbital) and then coherently superimpose two copies with phase factors $e^{\pm i\vec{k}\cdot \vec{R}/2}$, with an additional $\pm 1$ factor to represent gerade versus ungerade symmetry. They also account for orientation averaging by varying the angle between the dimer axis and the polarization plane in eight steps up to 45 degrees and projecting onto the polarization plane.

The key findings are qualitative-to-semiquantitative but strongly structured by the expected interference physics.

First, when both ionization pathways are mixed (no KER selection), the molecular-frame photoelectron distribution shows no clear interference fringes, consistent with gerade and ungerade contributions having a relative phase shift of $\pi$ that washes out the pattern. In contrast, after KER postselection, the authors observe pronounced two-center interference fringes in the molecular-frame momentum distribution. For gerade emission (from $2p{\sigma }_g$), the interference shows a minimum along the $k_{\perp }$-related direction at $k_{\parallel }=0$; for ungerade emission (from $2p{\sigma }_u$), the pattern is “swapped,” producing a maximum at $k_{\parallel }=0$. This swapped behavior is exactly what one expects when the initial phase difference between the two-center partial waves changes by $\pi$ between gerade and ungerade orbitals.

Second, the authors demonstrate that the interference is visible in the final electron momentum distribution even though the electron is accelerated in the laser field after ionization. Their interpretation is that the relevant phase information is preserved and becomes encoded in the momentum distribution acquired in the continuum.

Third, they report that the contrast of the interference fringes is finite rather than perfect. The authors attribute reduced contrast primarily to interaction of the outgoing electron with the neighboring atom in the dimer (post-emission Coulomb effects), supported by more complete theory described as reproducing the observed reduced visibility.

Fourth, in the linear polarization case, they observe interference patterns that depend on molecular alignment. By postselecting events where the dimer axis lies within $\pm 20^{\circ }$ of the laser polarization direction, they see that the two-center interference significantly reshapes the photoelectron distribution. For the direct ionization pathway, they report that the pronounced minimum appears at zero momentum, where tunneling theory would otherwise predict a maximum—again consistent with the phase-sensitive nature of the interference.

Finally, the paper connects the interference fringe spacing to the internuclear separation $|\vec{R}|$, positioning the method as a form of diffractive imaging. They show that as the effective slit separation decreases, the interference maxima move apart in momentum space, corresponding to higher ion momenta. They reproduce this trend using the expected two-center interference formula with $\Delta \varphi =\pi$ for the relevant pathway and a mapping from internuclear distance to ion kinetic energy along the $II(1/2)g$ potential. This provides an experimentally grounded route to extracting structural information (bond distance) from strong-field ionization observables.

Limitations are discussed implicitly through the experimental/theoretical choices and explicitly through the observed finite contrast. Experimentally, the molecular-frame reconstruction relies on the rapid dissociation of Ne2 and on event selection (KER windows, alignment windows for linear polarization), which can reduce statistics and may bias the sampled internuclear geometries. The molecular-frame transformation used projects electron momenta onto the polarization plane using the ion momentum projection; the authors note that this avoids nodes along the dimer axis but does not conserve $\vec{k}\cdot \vec{R}$, though they argue that contrast loss from this is negligible. Theoretically, the single-active-electron approximation and the modeling of the atomic potential via a pseudopotential (with removed singularity) may limit quantitative accuracy, and the authors’ own modeling indicates that electron–neighbor interactions are needed to explain reduced contrast.

Practical implications are broad for strong-field molecular physics and for quantum-mechanical imaging. For experimentalists, the work provides a clear protocol: use coincidence momentum spectroscopy to reconstruct molecular orientation, use KER (and alignment) postselection to isolate orbital symmetry, normalize by monomer spectra to remove tunneling weighting, and then read out two-center interference fringes in momentum space. For theorists, it offers a stringent benchmark for models of phase coherence and continuum propagation in molecules under intense fields. For the broader field, it strengthens the case that strong-field ionization can preserve and transmit two-center phase information, enabling time-resolved structural probing and deeper tests of quantum coherence in driven many-body systems.

Overall, the paper’s core contribution is the experimental observation of full two-center interference fringes in strong-field ionization of Ne2, together with the ability to switch between gerade and ungerade interference via orbital-selective postselection, and the demonstration that the resulting fringe pattern can encode internuclear distance for diffractive imaging-like applications.