This thesis focuses on the study of quantum decoherence, inter-channel tunneling, and dissipation in the integer and fractional quantum Hall states, using the platform of two-dimensional gases—notably formed at the interface of the n-doped GaAs/AlGaAs heterostructure used here. Quantum decoherence refers to the loss of quantum behavior of a studied system, which can be induced by coupling to the external environment. Quantum computing relies on the principle of quantum coherence, and understanding the mechanisms leading to decoherence would enhance our grasp of quantum computing theory, and quantum mechanics in general. During this thesis, the initial focus was on understanding the mechanisms by which decoherence occurs in two different situations : in the integer quantum Hall
effect and in the fractional quantum Hall effect (2/3). Then, in the final part, the research was dedicated to the fabrication of a single-electron detector, the last missing link in the chain needed to perform operations with flying electronic qubits — qubits not defined by a two-level energy system, but by a system with two spatial positions.
Firstly, in the case of the integer quantum Hall effect, the edge channels all propagate in the same direction, determined in this case by the direction of the magnetic field applied perpendicularly to the sample, and can have opposite spins, which does not favor inter-channel tunneling. However, the n-doped GaAs/AlGaAs heterostructure, due to symmetry breaking in the direction perpendicular to the 2D gas, possesses spin-orbit coupling via the Bychkov-Rashba effect. Thus, the spin can be flipped, which is conducive to elastic inter-channel tunneling. Furthermore, the presence of gates in the middle of the sample, such as the quantum point contact—which is associated with an electric field locally depleting the 2D gas beneath its surface—causes a sudden change in direction for the electrons, potentially leading to tunneling at the point of spatial curvature change. The presence of tunneling is then highlighted here by modeling the partition noise produced by a tunneling point and its measurement.
Secondly, in the case of the fractional quantum Hall effect at 2/3, the edge channels are counter-propagating, favoring inter-channel tunneling, which occurs frequently, inelastically, and randomly. A very simple model of this effect can be reproduced by introducing “black boxes”, the Landauer reservoirs—or equivalently, energy-preserving reservoirs—where inelastic tunneling is allowed within. The model converges to the historical KFP model when enough reservoirs are introduced. When a quantum point contact is introduced, a conductance plateau at 0.5e^2/his predicted and measured during the experiments conducted in this thesis. Additionally, the presence of dissipation is shown and validated. However, Hong-Ou-Mandel type interferometry experiments reveal a non-zero visibility, indicating that the dissipation mechanism does not cause a total loss of coherence.
Finally, in addition to the previous experiments, a single-electron detector was conceived to preserve quantum coherence when measuring a flying qubit, allowing it to be reused for subsequent operations, thus paving the way for quantum computing in two-dimensional electron gases under the quantum Hall effect regime. While the detector has been realized and can detect up to several hundred electrons, the technical optimizations needed to detect a single electron could not be completed before the end of the allotted time for this thesis.