Coherent manipulation of single electron spins with Landau-Zener sweeps

We propose a method to manipulate the state of a single electron spin in a semiconductor quantum dot (QD). The manipulation is achieved by tunnel coupling a QD, labeled $L$, and occupied with an electron to an adjacent QD, labeled $R$, which is not occupied by an electron but having an energy linearly varying in time. We identify a parameter regime in which a complete population transfer between the spin eigenstates $|L\uparrow \rangle$ and $|L\downarrow \rangle$ is achieved without occupying the adjacent QD. This method is convenient due to the fact that manipulation can be done electrically, without precise knowledge of the spin resonance condition, and is robust against Zeeman level broadening caused by nuclear spins.

Figure 1

The energy diagram. We initialize the electron in the $|L\uparrow \rangle$ state, with the $R$ quantum dot being higher in energy. We ramp the energies of the states in $R$ quantum dot with a Landau-Zener velocity $\beta$. In the figure, $\beta <0$. The goal of our scheme is to find a parameter regime in which the adiabatic evolution path is followed (red dashed arrow). The Zeeman splittings of the $L$ and $R$ quantum dots are marked as $\mathrm{\Delta }{E}_L$ and $\mathrm{\Delta }{E}_R$, respectively.

Figure 2

The comparison between the numerically computed probabilities [obtained from evolving the state using the Hamiltonian of Eq. (1)] ($\text{Num}$) and analytic adiabatic three-level probabilities Eq. (2) ($\text{An}$). The parameters of the plot are the Landau-Zener velocity $\beta =5\times {10}^3\mathrm{eV}/\mathrm{s}$, the tunnel coupling $\tau =6.5\mu \mathrm{eV}$, corresponding to an interdot separation of $l=179\text{nm}$ (for more information, see the Supplemental Material [47]), the non-spin-conserving tunnel coupling ${\tau }_{\mathrm{\Delta }}=0.25\tau$, the external magnetic field Zeeman splitting in the left QD $\mathrm{\Delta }{E}_L=1\mu \mathrm{eV}$, and Zeeman splitting in the right quantum dot $\mathrm{\Delta }{E}_R=200\mathrm{\Delta }{E}_L$. The inset represents the magnification of the occupation probabilities of the states in the $R$ quantum dot.

Figure 3

Comparison between the numerically computed probabilities [obtained from evolving the state using the Hamiltonian of Eq. (1)] ($\text{Num}$) and analytic adiabatic four-level probabilities Eq. (3) ($\text{An}$). The inset represents the magnification of the probability to occupy the $R$ quantum dot. The parameters of the plot are the Landau-Zener velocity $\beta =4\times {10}^6\mathrm{eV}/\mathrm{s}$, the tunnel hopping $\tau =50\mu \mathrm{eV}$, corresponding to interdot distance of $l=280\text{nm}$ for $m^{*}=0.023m_e$ (for more information, see the Supplemental Material [47]), the Zeeman energies $\mathrm{\Delta }{E}_L=\mathrm{\Delta }{E}_R=17\mu \mathrm{eV}$.

Figure 4

Spin manipulation in the presence of nuclear spins. The parameters of the plot are the Landau-Zener velocity $\beta =5\times {10}^3\mathrm{eV}/\mathrm{s}$, the tunnel coupling $\tau =6.5\mu \mathrm{eV}$, corresponding to an interdot separation of $l=179\text{nm}$ (for more information, see the Supplemental Material [47]), the non-spin-conserving tunnel coupling ${\tau }_{\mathrm{\Delta }}=0.25\tau$, the Zeeman energy in the left quantum dot $\mathrm{\Delta }{E}_L=1\mu \mathrm{eV}$, the standard deviation in the right quantum dot $\chi =0$, and the $g$ factor in the left quantum dot $g_L=1.2\times {10}^{-3}$. The inset represents occupation of the states in the $R$ quantum dot.

Figure 5

Spin manipulation in the presence of nuclear spins. The parameters of the plot are the Landau-Zener velocity $\beta =5\times {10}^3\mathrm{eV}/\mathrm{s}$, the tunnel coupling $\tau =6.5\mu \mathrm{eV}$, corresponding to an interdot separation of $l=179\text{nm}$ (for more information, see the Supplemental Material [47]), the non-spin-conserving tunnel coupling ${\tau }_{\mathrm{\Delta }}=0.25\tau$, the Zeeman splitting in the left quantum dot $\mathrm{\Delta }{E}_L=1\mu \mathrm{eV}$, the $g$ factor in the left quantum dot $g_L=1.2\times {10}^{-3}$, and the $g$ factor in the right quantum dot $g_R=200g_L$. The inset represents occupation of the states in the $R$ quantum dot.