Shuttling of spin qubits in semiconductors, valleys in silicon, and Landau-Zener transitions
Guido Burkard (University of Konstanz, Germany)
Silicon has become the leading material for semiconductor spin qubits. In order to scale up spin qubits based in semiconductor quantum dots, long-distance qubit connectivity can be provided by either circuit QED or electron shuttling. Here, we theoretically discuss spin qubit shuttling of electrons in silicon in the presence of the valley degeneracy in the Si conduction band. As a quantum dot carrying an electron spin qubit is shuttled along a disordered hetero-interface in silicon-based structures, the time-dependent valley splitting can cause inter-valley transitions. In combination with the valley-dependent g-factor and non-deterministic valley relaxation, this effect may lead to spin decoherence. While at first sight, the transition probability P seems to be governed by the Landau-Zener (LZ) model, we find the LZ model to be inadequate because both the valley splitting and the valley phase are essential. We find a generalization of the Landau-Zener (LZ) model characterized by distinct paths of the instantaneous (valley) eigenstates as the system evolves in time, describing inter-valley transitions during shuttling and determining P. This often leads to superadiabatic (SA) behavior, i.e., to a substantial reduction of P, and therefore to an improvement of the shuttling fidelity.