|Researchers from SPEC (in collaboration with the C2N and the University of Genoa) have observed the fading and partial reappearance of an electron injected at a finite energy into chiral one dimensional electronic channels propagating along the edges of a two dimensional electron system. These results will help elucidating to which extent these electrons can be used to implement the electronic analogues of quantum information experiments done with photons.
The quantum Hall effect is a peculiar state of condensed matter arising at low temperature: when a strong perpendicular magnetic field is applied to a gas of electrons confined in two dimensions, the bulk of the electron gas becomes insulating, while the electric current is only carried along the edges of the sample, along an integer number of one-dimensional edge channels. These edge channels form ideal quantum wires, being dissipationless and chiral (the latter corresponding to the fact that their propagation direction is fixed by the direction of the magnetic field). Since electrons cannot jump from one edge channel to the next, the edge channels are commonly thought as being independent. These textbook-like features have led to decades-long efforts to use edge channels as “fiber optics” for electrons, to implement the electrical analogue of quantum optics experiments. In these so-called electron quantum optics experiments, one aims to manipulate, in a quantum coherent way, single charges emitted in an edge channel.
Left: in a perfect two-dimensional conductor the conduction electrons move freely according to their wave vector. Middle: In a classical vision, the application of a magnetic field deflects the electrons from their trajectory, which becomes circular when the field is very intense. The conductor then becomes an insulator. If the trajectory of an electron encounters one of the edges of the sample, it is reflected, then continues its circular trajectory and thus propagates along the edge. On the right, quantum computation shows that electronic edge channels form at the sample edge, where the current can only flow in one direction imposed by the orientation of the field.
However, recent experiments have shown that the edge channels are not fully independent, but actually coupled through electrostatic interactions: charges travelling in one edge channel are sensitive to the presence of charges in the next edge channel. As a consequence, the elementary states naturally describing the system do not correspond to a single charge propagating along one edge channel, but rather to collective excitations distributed between the co-propagating edge channels. In electron quantum optics experiments, these interactions manifest themselves through decoherence and energy relaxation. The former corresponds to a loss of the phase coherence of a quantum state (for instance, a single electron) emitted in one edge channel as it decomposes onto the collective excitations shared with the other channels. The latter corresponds to losses of the energy of the initial state, which is redistributed among all edge channels. A classic and straightforward way to picture energy relaxation is the following: if one emits an electron at a well-defined energy above the Fermi energy (defined as the energy below which all electronic levels in the edge channel are occupied), its energy will gradually decrease as the electron propagates, while low-energy charge neutral excitations are created in all edge channels.
Surprisingly, despite the many recent experiments involving single charges emitted at a well-defined energy, their relaxation was never directly observed, and the above picture never validated.
Researchers from the Nanoelectronics group of SPEC, in collaboration with the C2N (Palaiseau) and the University of Genoa, have recently performed a series of experiments directly probing this picture. By using quantum dots (regions of the electron gas where electrons are strongly confined in all directions by a set of electrostatic gates) as electronic energy filters, they have performed a fully energy-resolved injection and spectroscopy depicted in Figure 1. A stream of single charges is emitted at a well-defined energy in an edge channel, and left to propagate in presence of a second nearby edge channel. After a few hundreds of nanometers of propagation (from 480 nm, up to 3.4 microns), a spectroscopy of the edge channel is performed, allowing to check whether the injected charges have remained at their original energy, or if they have collapsed into a sea of low-energy excitations.
The results of these experiments, illustrated in Fig. 2, present the first experimental observation of charges remaining at their initial energy after propagation in an edge channel. They appear as a distinct peak in the measured energy distribution function, as shown in Fig. 2a. The peak strongly decreases with increasing injection energy and propagation length, indicating an important effect of relaxation. Remarkably, at some point, the peak reappears (see inset of Fig. 2b), indicating that the collective excitations shared between the edge channels interfere constructively to partially rebuild the initial excitation.
By comparing the experimental data with a theoretical model developed at the University of Genoa, an additional loss of energy has been put into light. Along with the energy relaxation caused by the presence of the nearby edge channel, charges propagating in the edge channel are also subjected to a strong dissipation, that is, energy losses towards external degrees of freedom that are not encompassed by the system formed by the two edge channels. The mechanisms responsible for this dissipation remain to be investigated. If left unmitigated, this strong dissipation can critically hamper future applications of electron quantum optics, in particular quantum information processing. Our results thus not only validate the conceptual framework in which such applications have been proposed, but also identify their next big challenge.
Relaxation and revival of quasiparticles injected in an interacting quantum Hall liquid, R. H. Rodriguez, F. D. Parmentier, D. Ferraro, P. Roulleau, U. Gennser, A. Cavanna, M. Sassetti, F. Portier, D. Mailly, P. Roche, Nature Communications 11, 2426 (2020)