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The H2 Double-Slit Experiment: Where Quantum and Classical Physics Meet Print

 

For the first time, an international research team carried out a double-slit experiment in H2, the smallest and simplest molecule. Thomas Young's original experiment in 1803 passed light through two slits cut in a solid thin plate. In the groundbreaking experiment performed at ALS Beamlines 4.0 and 11.0.1, the researchers used electrons instead of light and the nuclei of the hydrogen molecule as the slits. The experiment revealed that only one "observing" electron suffices to induce the emergence of classical properties such as loss of coherence.

Double photoionization of H2. Left: Circularly polarized light comes from the top. All angular distributions are in the plane perpendicular to the photon propagation vector: Φe–mol is the angle of the fast electron's trajectory to the molecular axis; Φe–e is the angle between both electron trajectories. Center: Photoionization by circularly polarized light launches a coherent spherical photoelectron wave at each nucleus of the molecule; the light propagates into the plane. Right: Measured electron angular distribution Φe–mol of the faster electron (E1) from double photoionization of H2 by circularly polarized light. The orientation of the molecule is horizontal. Light propagates into the plane of the figure, the molecule is fixed ±10° within the plane shown, Eϒ = 240 eV, and the energy of the slow electron E2 = 0 to 5 eV, resulting in E1 = 185 to 190 eV.

The Mysterious Relationship
of Dielectrons

Electrons can function as a dielectron, a two-electron quasiparticle whose relationship is entanglement: what one does affects the other, even if they are far apart. The double-slit experiment taught us that if light, a particle, or a quasiparticle goes through a double slit, it can interfere with itself. Thus, particles act like waves—when two wave crests meet, an interference pattern with bright fringes results; when a crest meets a trough, dark bands result—leaving a fingerprint of quantum-like behavior.

Researchers at the ALS discharged two electrons from a hydrogen molecule, which went through a microscopic double slit composed of the hydrogen's two nuclei. One was the slow electron (almost at rest), the other the fast. In most cases, the fast one zoomed away, interfering with itself at the two-proton double slit; the slow one never caught up. They then selected slow electrons with a little more energy, changing the relationship dynamic. The slow electron now acted as an active observer, becoming an environment. In the quantum world, observing a phenomenon changes it. Here, the fast electron no longer showed an interference pattern, due to loss in coherence of the quantum mechanical system coming from interaction with the environment (the observing slow electron). However, since they were still entangled, a record of the electrons' "quantum-ness" could be reconstructed in the dielectron.

Present-day single photoionization experiments demonstrate double-slit self-interference for a single particle fully isolated from the classical environment. But if quantum particles were put in contact with the classical world in a controlled manner, at what scale would quantum interference begin to diminish and particles start to behave classically? The team decided to study the double photoionization (complete fragmentation) of H2, creating two repelling protons acting as a double slit, a fast interfering electron, and a second electron behaving as an active or inactive observer.

Experiments were performed at two different photon energies: Eϒ = 240 and 160 eV, leaving about 190 and 110 eV to be shared between the two electrons, respectively. At these high photon energies, double photoionization of H2 led in most cases to one fast and one slow electron. The fast electron's energies were 185 to 190 eV; the slow electron’s were 5 eV or less (corresponding to an inactive observer). The interference pattern of the fast electron was conditioned by the presence and velocity of the other: the greater the difference in their speeds, the less their interaction and the more visible the interference patterns. Both electrons were isolated from their surroundings, and quantum coherence prevailed, revealed by the fast electron's wavelike interference pattern at the two protons.

However, at high photon-energy levels, the fast electron absorbed almost all the energy of the incident single photon, leaving the system too rapidly for interaction with the slow electron. Yet the slow electron was also ejected from the molecule through the mysterious process of electron–electron correlation. This "secret entanglement" allows two electrons to remain connected even though far apart. The researchers now had what they needed to build their classical/quantum interface.

 

Correlation between both electrons for double photoionization of H2 at Eϒ = 160 eV and 5 eV < E2 < 25 eV, corresponding to E1 ≈ 85 to 105 eV. (a) x axis: angle of fast electron to the molecular axis (Φe–mol); y axis: angle Φe–e between the two electrons. Both electrons and the molecule are selected to lie within ±30° of the polarization plane. (b) Projection of (a) onto the horizontal axis for 50° < Φe–e < 80°. (c) Polar presentation of the data shown in (b). (d) Projection analogous to (b) for –80° < Φe–e < –50°. (e) Polar presentation of data shown in (d).

They choose ionization events where the slow electron had a bit more energy (5–25 eV) allowing it act as the classical environment (an active observer). The quantum system of the fast electron now interacted with the slow electron and began to decohere, its interference pattern disappearing. However, the overall coherence was still hidden in the two electrons' entanglement.

The dielectron's wavelength was short enough to still interfere (the sum energy of the two electrons was high enough), and there was no environment to disturb the interference as the two electrons were now combined into one quasiparticle. Thus, interference between the entangled electrons could be reconstructed by graphing their correlated momenta from the angles at which they were ejected. Two waveforms appeared in the graph, either of which could be projected to show an interference pattern. Because the two waveforms were out of phase with each other, when viewed simultaneously, the interference vanished.

If the two-electron system is split into its subsystems and one is thought of as the environment of the other, it becomes evident that classical properties such as loss of coherence can emerge even when only four particles are involved. Yet because the two electrons' subsystems are entangled in a tractable way, their quantum coherence can be reconstructed. In solid-state–based quantum computing devices, such electron–electron interaction represents a key challenge as decoherence and loss of information occur on the tiny scale of a single hydrogen molecule. The good news, however, is that, in theory, the information is not completely lost.

 


 

Research conducted by D. Akoury, Th. Weber (University Frankfurt, Germany, and Berkeley Lab, U.S.); K. Kreidi, t. Jahnke, A. Staudte, M. Schöffler, N. Neumann, J. Titze, L. Ph. H. Schmidt, A. Czasch, O. Jagutzki, R. A. Costa Fraga, R. E. Grisenti, H. Schmidt-Böcking, R. Dörner (University Frankfurt, Germany); T. Osipov, H. Adaniya, M. H. Prior, A. Belkacem, (Berkeley Lab, CA, U.S.); R. Díez Muiño (Centro de Física de Materiales and Donostia International Physics Center, San Sebastian, Spain); N. A. Cherepkov, S. K. Semenov (State University of Aerospace Instrumentation, St. Petersburg, Russia); P. Ranitovic, C. L. Cocke (Kansas State University, U.S.); J. C. Thompson, A. L. Landers (Auburn University, U.S.)

Research funding: Deutsche Forschungsgemeinschaft and by the U. S. Department of Energy, Office of Basic Energy Sciences (BES). Operation of the ALS is supported by BES.

Publication about this research: D. Akoury, K. Kreidi, T. Jahnke, Th. Weber, A. Staudte, M. Schöffler, N. Neumann, J. Titze, L. Ph. H. Schmidt, A. Czasch, O. Jagutzki, R. A. Costa Fraga, R. E. Grisenti, R. Díez Muiño, N. A. Cherepkov, S. K. Semenov, P. Ranitovic, C. L. Cocke, T. Osipov, H. Adaniya, J. C. Thompson, M. H. Prior, A. Belkacem, A. L. Landers, H. Schmidt-Böcking, R. Dörner, "The simplest double slit: Interference and entanglement in double photoionization of H2," Science 318, 949 (2007).