As for photons, the wave-particle duality shows up in a spectacular way in the electronic transport in small size conductors at very low temperatures. On the one hand, interference effects, characteristic of a wave-like description, govern the current flowing through the conductor. On the other hand, the fluctuations of the current are associated with the granularity of the electric charge.
The experiment realized at the Laboratoire Pierre Aigrain, in collaboration with researchers from the Laboratoire de Photonique et de Nanostructures and from the Ecole Normale Supérieure of Lyon, cannot be described neither by the wave-like nor by the particle-like description. The essential ingredient of this experiment is an electronic beamsplitter which comprises two input and two output arms. When a single electron is sent in one of the input arms, the other input being empty, it escapes randomly in one of the outputs. In the experiment, two electrons, generated by two identical, synchronized but otherwise independent emitters, arrive simultaneously on the two input arms of the splitter. Classical particles would have a one half probability to escape in two different outputs. The two electrons, on the contrary, have a tendency to avoid each other and emerge more often in two distinct output arms.
This effect, called electron antibunching, can only be explained by quantum mechanics. It is a two-particle quantum interference related to the indistinguishability of the emitted particles. For fermions, and in particular for electrons, it leads to the total antibunching of two perfectly indistinguishable particles. For bosons on the opposite, it leads to the bunching of particles which always emerge in the same output arm as demonstrated for photons in 1987 by Hong, Ou and Mandel.
Beyond its fundamental interest, this experiment demonstrates the possibility to generate on-demand, in condensed matter, two indistinguishable electrons using two independent emitters. It allows envisioning the coding and treatment of quantum information on the degrees of freedom of flying electrons as it is done using photons propagating in optic fibers.
The two-dimensional electron gas is pictured in green. The single electron emitters, located on the left and right sides of the figure, are made of a submicronic island of the electron gas called quantum dots. The metallic electrodes colored in gold and deposited on top of each emitter are used to trigger the emission of a single electron from the quantum dot. The electrons emitted by each source, represented by wavepackets, propagate along the edges of the sample towards an electronic beamsplitter which comprises two golden electrodes at the center of the figure. When an electron reaches the splitter (the other input of the splitter being empty), it can be randomly transmitted to one of the two outputs. The figure represents the cases of perfect synchronization between the sources ; the electrons emitted by each emitter reach the splitter simultaneously. The two-particle interference then shows up by the systematic exit of both particles in two distinct arms of the splitter.
Credits : D. Darson, Laboratoire Pierre Aigrain, Ecole Normale Supérieure, Paris.
“Coherence and Indistinguishability of Single Electrons Emitted by Independent Sources”, E. Bocquillon, V. Freulon, J.-M Berroir, P. Degiovanni, B. Plaçais, A. Cavanna, Y. Jin, G. Fève.
Science, DOI : 10.1126/science.1232572