Realizing singlet-triplet qubits in multivalley Si quantum dots

Abstract

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 coupling 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

Theory of spin relaxation in two-electron laterally coupled Si/SiGe quantum dots

“…34,35,50,53,54,[56][57][58][59][60][61][62][63][64][65][66][67] Our work completes these findings by a global, quantitative understanding of two-electron lateral silicon double quantum dots. We investigate the spin-orbit and hyperfine-induced relaxation rate as a function of interdot coupling, detuning, and the magnitude and orientation of the external magnetic field for zero and finite temperatures, and for natural and isotopically purified silicon.…”

“…The double dot is charged with two electrons and not coupled to leads. Assuming the validity of the effective single-valley approximation, 50 the Hamiltonian in the two-dimensional and the envelope function approximation reads…”

“…If this is the case, the multivalley system can be reduced to an effective single-valley qubit, a potentially nuclear-spin-free analog to the well-known GaAs counterpart. 50,51 In fact, many recent experiments performed on Si/SiGe quantum dots have no evidence of valley degeneracy, [33][34][35][52][53][54] indicating that the splitting is large enough to justify a single-valley treatment. On the other hand, a recent proposal of valley-defined qubits uses the valley degree of freedom as a tool for gate operations.…”

“…This remaining degeneracy is further split if the perpendicular confinement is asymmetric, resulting in an energy difference called the ground-state gap. [42][43][44][45][46][47][48][49] As the valley degeneracy is believed to be the main obstacle for silicon-based quantum computation, 46,50,51 a large valley splitting is desired. If this is the case, the multivalley system can be reduced to an effective single-valley qubit, a potentially nuclear-spin-free analog to the well-known GaAs counterpart.…”

Two-electron dephasing in single Si and GaAs quantum dots

“…A further complicating factor in silicon-based quantum dot devices is the presence of two nearly degenerate, low-lying valley states. [26][27][28][29][30][31][32][33] These levels are split near a sharp interface by an amount that is typically comparable to the orbital energy spacing. Hence, single-electron first excited states have two characteristic types: orbital, where the electron occupies the same valley state but the P-like first excited state of the lateral confinement potential, and valley, where the electron is in the orbital ground state and a higher valley state.…”