Realizing singlet-triplet qubits in multivalley Si quantum dots

There has been significant progress in the implementation and manipulation of singlet-triplet qubits in GaAs quantum dots. Given the considerably longer spin coherence times measured in Si, considerable interest has been generated recently in Si quantum dots. The physics of these systems is considerably more complex than the physics of GaAs quantum dots owing to the presence of the valley degree of freedom, which constitutes the focus of this work. In this paper we investigate the physics of Si quantum dots and focus on the feasibility of quantum coherent singlet-triplet qubit experiments analogous to those performed in GaAs. This additional degree of freedom greatly increases the complexity of the ground state and gives rise to highly nontrivial and interesting physics in the processes of qubit initialization, coherent manipulation and readout. We discuss the operational definition of a qubit in Si-based quantum dots. We find that in the presence of valley degeneracy a singlet-triplet qubit cannot be constructed, whereas for large valley splitting (≫ k_B T) the experiment is similar to GaAs. We show that experiments on singlet-triplet qubits analogous to those in GaAs would provide a method for estimating the valley splitting in Si. A Zeeman field distinguishes between different initialized states for any valley splitting and provides a tool to determine the size of this splitting.