Control of electron spin and orbital resonances in quantum dots through spin-orbit interactions

The influence of a resonant oscillating electromagnetic field on a single electron in coupled lateral quantum dots in the presence of phonon-induced relaxation and decoherence is investigated. Using symmetry arguments, it is shown that the spin and orbital resonances can be efficiently controlled by spin-orbit interactions. The control is possible due to the strong sensitivity of the Rabi frequency to the dot configuration (the orientation of the dot and the applied static magnetic field); the sensitivity is a result of the anisotropy of the spin-orbit interactions. The so-called easy passage configuration is shown to be particularly suitable for a magnetic manipulation of spin qubits, ensuring long spin relaxation times and protecting the spin qubits from electric field disturbances accompanying on-chip manipulations.

Figure 1

The orientation of the potential dot minima (denoted as the two circles) with respect to the crystallographic axes ($x=\left[100\right]$ and $y=\left[010\right]$) is defined by the angle $\delta$. The orientation of the inplane magnetic field is given by the angle $\gamma$.

Figure 2

(Color online) The lowest part of the energy spectrum of Hamiltonian $H_0$ [Eq. (2)] in zero magnetic field as a function of the tunneling energy $\left(\delta E_t\right)$ in the units of the confinement energy $E_0$. Each eigenfunction belongs to one of the four symmetry classes of $C_{2v}$, which are denoted by different color/type of the line. Spin indices are omitted.

Figure 3

Calculated matrix elements between the resonant states due to magnetic and electric oscillating fields. The two upper panels [(a) and (b)] show the matrix elements ${\Omega }_{\text{spin}}$ for the spin resonance, while the two lower panels show orbital resonance elements ${\Omega }_{\mathrm{orb}}$. On the left, in (a) and (c), the elements are functions of the static magnetic field, with a fixed tunneling energy of 20% of the confinement energy. On the right, in (b) and (d), the elements are functions of the tunneling energy at a fixed magnetic field $B=1\mathrm{T}$. The dots are oriented along [100], while the static magnetic field lies along [010].

Figure 4

Calculated matrix elements for the spin [upper two panels (a) and (b)] and the orbital [lower two panels (c) and (d)] resonance due to oscillating magnetic and electric fields as functions of $\gamma$, the orientation of the static magnetic field, $B=1\mathrm{T}$. The tunneling energy is 20% of the confinement energy. On the left, in (a) and (c), the dots are oriented along [100], that is, $\delta =0$. On the right, in (b) and (d), the dots are oriented along [110], $\delta =45°$.

Figure 5

Calculated induced rate $J$ at resonance (solid line), decoherence ${\gamma }_{ba}$ (dashed line), and the FWHM of the excited population (dot-dashed line) as functions of the ratio of the tunneling energy $\delta E_t$ and the confinement energy $E_0$ for (a) spin resonance and (b) orbital resonance. The static in-plane magnetic field is $B=1\mathrm{T}$. If the solid line is above (under) the dashed one, it means that $J_0^r>1$ $(J_0^r<1)$. The dots are oriented along [100], while the static magnetic field lies along [010].