Control of spin blockade by ac magnetic fields in triple quantum dots

We analyze coherent spin phenomena in triple quantum dots in triangular configuration under crossed dc and ac magnetic fields. In particular, we discuss the interplay between Aharonov-Bohm current oscillations, coherent electron trapping and spin blockade under two-electron-spin-resonance configurations. We demonstrate an unexpected antiresonant behavior in the current, allowing for both removal and restoration of maximally entangled spin-blockaded states by tuning the ac field frequency. Our theoretical predictions indicate how to manipulate spin qubits in a triangular quantum dot array.

Figure 1

(Color online) Coherent processes in a triangular TQD, with one electron confined in the dot connected to the drain. ${\Delta }_1={\Delta }_2\ne {\Delta }_3$, where ${\Delta }_i$ is the Zeeman splitting in dot $i$. Transport through the system depends on the magnetic flux $\Phi$ penetrating the system and on the frequency $\omega$ of the time-dependent magnetic field $B_{\text{ac}}$. The shaded areas (blue and red) indicate the existence of a dark state.

Figure 2

(Color online) (a) ${\rho }_{ii}$ for $\Phi /{\Phi }_0=0.25$, $B_{\text{ac}}=0$. $I$ is blocked due to SB, once the parallel spin states (dashed and dotted red lines) are occupied. (b) ${\rho }_{ii}$ for $\Phi /{\Phi }_0=0.5$, $B_{\text{ac}}=0$. Due to SB, there is a finite occupation of parallel spin states $|{\chi }_{l\sigma \sigma }⟩$ (dashed and dotted red lines), while electrons with antiparallel spin form dark states as in (2) (solid and dashed-dotted blue lines), all of them contributing to quench the current. (c) $I\text{−}\Phi$: for $B_{\text{ac}}=0$, $I=0$ due to SB (dashed blue line); $B_{\text{ac}}\ne 0$: for $\hslash {\omega }_{\text{ac}}={\Delta }_{1,2}$, SB is removed and the current shows A-B-like oscillations (solid purple line). Rabi frequency: ${\Omega }_{\tau }=2\tau$. $\tau =0.0026$, $\Gamma =0.01$ in meV, ${\Delta }_3=0.77{\Delta }_1$, ${\Delta }_1={\Delta }_2$.

Figure 3

(Color online) 2ESR in a TQD by tuning $\omega$, for $\Phi /{\Phi }_0=0.25$, is manifested in the current as an antiresonance at $\hslash {\omega }_0=\left({\Delta }_1+{\Delta }_3\right)/2$. (a) For different $B_{\text{ac}}$ and fixed ${\tau }_{ij}=\tau$: The width of the antiresonance depends on the Rabi frequencies associated with $\tau$ and $B_{\text{ac}}$. (b) For different ${\tau }_{ij}$ and fixed $B_{\text{ac}}=\tau /2$. The antiresonance appears for any configuration of the ${\tau }_{ij}$. (c) For different $\Gamma$ and ${\tau }_{ij}=\tau$. (d) $I\text{−}\Phi$ for fixed $\omega$ while tuning $B_{\text{dc}}$, so both $\Phi$ and ${\Delta }_i$ are modified. A-B oscillations are suppressed by SB except when the Zeeman splittings are close to resonance with $\omega$. At $\Phi /{\Phi }_0=0.25$, $\omega ={\omega }_0$ and current vanishes. Parameters: $\tau =0.005$, $\Gamma ={\Gamma }^{\ast }=0.01$.

Figure 4

$I\text{−}\omega$ in a TQD for ${\Delta }_1\ne {\Delta }_2$. For $\tau ⪢{\Delta }_1-{\Delta }_2$, $I$ shows an antiresonance with a pronounced minimum at $\hslash {\omega }_1\approx \frac{1}{2}\left(\frac{{\Delta }_1+{\Delta }_2}{2}+{\Delta }_3\right)$. Dashed-dotted line: ${\Delta }_2-{\Delta }_1=0.0013$; dashed line: ${\Delta }_1-{\Delta }_2=0.0013$; solid line: ${\Delta }_1={\Delta }_2$. Parameters: $\tau =\Gamma =0.01$.

Figure 5

(Color online) ${\rho }_{ii}$ in a TQD excited by a bichromatic $B_{\text{ac}}$, where ${\omega }_1={\Delta }_{1,2}$ and ${\omega }_2={\Delta }_3$. In the stationary limit, parallel spin states decouple from $B_{\text{ac}}$ and form coherent superpositions as in Eq. (5) thereby blocking the current.