Optimal geometry of lateral GaAs and Si/SiGe quantum dots for electrical control of spin qubits

Abstract

We investigate the effects of the orientation of the magnetic field and the orientation of a quantum dot, with respect to crystallographic coordinates, on the quality of an electrically controlled qubit realized in a gated semiconductor quantum dot. We find that, due to the anisotropy of the spin-orbit interactions, by varying the two orientations it is possible to tune the qubit in the sense of optimizing the ratio of its couplings to phonons and to a control electric field. We find conditions under which such optimal setup can be reached by solely reorienting the magnetic field, and when a specific positioning of the dot is required. We also find that the knowledge of the relative sign of the spin-orbit interaction strengths allows to choose a robust optimal dot geometry, with the dot main axis along [110], or [110], where the qubit can be always optimized by reorienting the magnetic field.

Control of a spin qubit in a lateral GaAs quantum dot based on symmetry of gating potential

“…is again consistent with Ref. [22]. In the case of the C 1v symmetry, using a similar analysis as in the previous case, we obtain the expression for the dipole moment…”

“…Since it is known that the standard perturbation technique badly incorporates the spin-orbitinduced corrections [34,35], we follow the procedure explained in Ref. [22]: the Hamiltonian H is transformed using the unitary operator U = exp(in so · s), defined with the help of the position-dependent spin-orbit vector n so = l −1 so (r 1 sin ν + r 2 cos ν, −r 1 cos ν − r 2 sin ν, 0):…”

Electrical control of a spin qubit in InSb nanowire quantum dots: Strongly suppressed spin relaxation in high magnetic field

“…The role of |T yz | 2 in the spin relaxation rate depends on the regime in which spin qubit operates. At low magnetic fields, when |q|z 0 ≪ 1 and |q|y 0 ≪ 1, dipole approximation, e iq·r ≈ 1 + iq · r, is valid [18] and |T yz | 2 can be replaced with (1 + |q| 2 z 2 0 cos 2 θ) ≈ 1, implying that onedimensional approximation of the gating potential is justified. However, at higher magnetic fields, dipole approximation is not valid and confinement in the yz-direction can play a significant role.…”

Depletion-mode quantum dots in intrinsic silicon

“…These results show that we can form a robust hole-QD using a straightforward process and simple design. Further reduction of the lithographical dimensions of this design, which is already optimized for spin-qubit performance 39 , may allow reaching the few-hole regime.…”