Andreev spin qubits based on the helical edge states of magnetically doped two-dimensional topological insulators

Abstract

We show that Andreev spin qubits can be realized in a Josephson junction based on the helical edge states of a two-dimensional topological insulator (quantum spin Hall system) proximized by superconducting films, in the presence of magnetic doping. We demonstrate that the electrical dipole transitions between the Andreev spin states induced by the magnetic doping can be harnessed to optically manipulate the Andreev spin qubit by microwave radiation pulses. We numerically simulate the realization of NOT and Hadamard quantum logic gates, and discuss implementations in realistic setups.

Figures (10)

• Figure 1: Scheme of realization of an ASQ based on a two-dimensional topological insulator: A helical Josephson junction realized by proximizing the helical edge states of a QSHI with $s$-wave superconducting (S) films. The presence of magnetic doping (black spots) induces electric dipole transitions between the ABSs localized in the weak link (inset), enabling optical control of the qubit via coupling with an electromagnetic radiation.
• Figure 2: The ABS energy levels as a function of the superconducting phase difference $\phi$ are shown for a helical JJ with a length parameter $\lambda=2$, in the presence of a ferromagnetic barrier, characterized by a parameter $\alpha=m_\perp L_m/\hbar v_F=1$, for chemical potential value $\mu= \Delta_0/2$. The black solid curve and the dashed red curve describe the cases of extended and localized magnetic disorder, respectively. As a comparison, the dotted blue curve depictes the ABS in the absence of any magnetic disorder.
• Figure 3: Spatial profile of the three spin density components $S_x, S_y, S_z$ (in units of $1/L$), for the two ABSs present in a weak link with length parameter $\lambda=2$. The vertical dashed lines at $x/L=\pm 1/2$ are a guide to the eye to identify the weak link region. The value of the superconducting phase difference is $\phi=\pi/2$. The solid curves refer to the case of the presence of a magnetic $\delta$-impurity located at $\xi_0=x_0/L=1/4$, while the thick dashed curves depict, for comparison, the case of a clean JJ without magnetic disorder, where $S_z$ is the only non vanishing component.
• Figure 4: The magnitude $|g_{12}|$ of the optical transition amplitude between two ABSs is shown as a function of the ratio of the spatial extension $L_m$ of the magnetic disorder to the JJ weak link length $L$, for a fixed value of the magnetic barrier parameter $\alpha=m_\perp L_m/\hbar v_F =0.5$, and for different values of the superconducting phase difference $\phi$. The magnetic disorder is distributed around the center $x_0=0$ of the weak link, which has a length parameter $\lambda=2$. The chemical potential is set to $\mu=0$.
• Figure 5: The magnitude $|g_{12}|$ of the optical transition amplitude between two ABSs is shown as a function of the transmission $T_\delta$ of a magnetic $\delta$-impurity present in the weak link, for different values of the impurity relative location $\xi_0=x_0/L$ from the weak link center. The length parameter is $\lambda=2$, and the superconducting phase difference is $\phi=\pi/2$.