QUANTUM MECHANICS: Double-slit experiment succeeds in a single hydrogen molecule

Jan. 1, 2008

A team of researchers has performed the smallest and simplest double-slit experiment to date.

In single-molecule double-slit experiment polarized light shines down onto the hydrogen molecule (left) initially causing emission of fast and slow electrons at different angles. Equivalent slit separation is 1.4 au (the internuclear distance in the hydrogen molecule), and the light wavelength is 3.75 au, corresponding to an electron energy of 190 eV. Photoionization by circularly polarized light launches a coherent spherical photoelectron wave at each nucleus of the molecule (center). In cases in which slow electron energy is negligible (right), large horizontal side lobes in measured electron angular distribution indicate diffraction pattern due to quantum behavior.

A team of researchers has performed the smallest and simplest double-slit experiment to date. First recorded more than 200 years ago, the double-slit experiment has become “one of the most powerful ways to explore the quantum world,” according to Ali Belkacem, coleader of the international team of researchers that used high-energy illumination from the Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory (LBNL; Berkeley, CA) and a momentum spectrometer to accomplish the experiment.¹

The two slits consisted of the adjacent potential wells in twin protons of a single hydrogen molecule (separated by only 1.4 atomic units). The setup enabled them to observe the diffraction pattern caused by wavelike behavior of a single electron, which has been observed before, but also to switch the electron from wavelike to particle, or better from quantum to classical, behavior by simply introducing one other additional electron as an “observer;” a significant departure from previous experiments which have relied on much larger environmental manipulations, such as heating, to cause the shift.

The researchers passed photon beams at two different energy levels, 240 and 160 eV, through a supersonic hydrogen gas jet enabling collisions between individual photons and hydrogen molecules to cause double photoionization. “The photon hits only one electron, but because the two electrons share a quantum correlation, the electron that is hit flies off in one direction with a certain momentum, and the other electron also flies off at another angle with a different momentum,” said Thorsten Weber, another coleader of the research team (see figure).

As the electrons depart the molecule, Coulomb forces take over and cause the protons to fly apart. This small but explosive chemical reaction takes place in what Weber described as a “reaction microscope” that images the trajectories of the products of the explosion. “We use a simple spectrometer, a momentum spectrometer that makes the trajectories visible,” he said.

The spectrometer consists primarily of a static electric field (50 V/cm) that separates the different particles according to charge, and a slight magnetic field (8 G) that acts as a trap to confine the particles within the overall system. Positively charged protons are collected at one multichannel plate detector and negatively charged electrons are collected at another. “We then measure the time of flight from the reaction zone to the detectors and the position of particle impact on the detectors, which enables us to determine the vector moment of each particle,” Weber said. The experiment only took a couple of days to perform, he added, but it took more than a year to complete a computer analysis of the quantum-mechanical possibilities, and to observe the transition from quantum to classical behavior.

About 50 eV of the incident photon energy in the initial collision goes into overcoming the binding energy of the hydrogen molecule and into the momentum of the departing protons. The remaining 190 or 110 eV, for the 240 or 160 eV beams respectively, propels the escaping electrons. In most cases the double photoionization process leads to one fast electron containing just about all of the momentum energy and a slow electron with practically none.

In such cases, the fast electron launches a pair of photoelectron waves from the twin proton nucleus, creating a diffraction pattern similar to the effect seen in the original double slit experiment. In cases in which the slow electron acquires about 10% to 20% of the ionization energy, however, the diffraction pattern disappears and the system returns to classical or particle-like behavior, similar to the effect of blocking one slit in the original experiment.

The situation is not quite that simple, however. The researchers found that the interference pattern for the fast electron actually disappears due to the interaction with the environment (the active second electron), but that the coherence of the system remains. “It is now in the correlated electron pair which forms a quasi particle, a ‘dielectron’ that leaves the molecule with enough energy to show interference,” Weber said. The researchers uncovered this behavior whileanalyzing subsets of the data, restricted to angular ranges determined by the scattering angles between the two electrons.

“It is important that we can control the environment and can make the interference pattern go away, but that the coherence is still there, and that we can dig it out,” Weber said. “We have a tool, a reaction microscope, that enables us to look at all parts of the experiment-not just the static structure, as in examining a snow flake, but the motion dynamics of the electrons, which are in a correlated dance.”

The achievement of a double-slit experiment in a single hydrogen molecule is the result of a 10-year collaboration between a research team at the University of Frankfurt (Germany), led by Reinhard Doerner, and a team at the LBNL led by Belkacem and Weber, who was previously at Frankfurt. Researchers at universities in San Sebastian, Spain, St. Petersburg, Russia, Manhattan, KS, and Auburn, AL, also participated.