Solitonic Andreev spin qubits from Andreev states in Corbino Josephson junctions

TL;DR

This work proposes a solitonic Andreev spin qubit (SASQ) realized in a Corbino Josephson junction on a 2DEG with spin-orbit coupling, where a weak out-of-plane field creates a fluxoid mismatch that traps spinful, chargeless Andreev bound states around a phase soliton. The qubit is controlled holonomically by moving the soliton with a phase bias $\phi$, leveraging SOC to generate full Bloch-sphere rotations as the ABSs are shuttled around the junction; a minimal 1D model and a tight-binding extension establish the solitonic ABS spectrum and its Jackiw-Rebbi topological origin. The paper highlights robustness to disorder, analyzes non-holonomic corrections, and provides quantitative estimates of holonomic operation speeds, arguing for practical realization in micron-scale aluminum devices with modest magnetic fields. Overall, SASQ merges aspects of Andreev and geometric spin qubits, enabling fast, geometry-driven holonomic single-qubit gates with potential advantages for scalable superconducting quantum computing.

Abstract

We study a novel type of solitonic Andreev bound state (ABS) in a Corbino-geometry Josephson junction created on a 2DEG. The Josephson junction is subjected to a weak magnetic flux that induces a fluxoid mismatch between the inner disk and outer ring superconductors. The mismatch produces a Josephson vortex (phase soliton) that binds unconventional spinful but chargeless ABSs, analogous to Jackiw-Rebbi solitonic states. The position around the Josephson junction of the trapped ABSs can be controlled externally by a junction phase bias. As the solitonic ABSs are shuttled around the Josephson junction, the 2DEG spin-orbit coupling induces a geometric precession of their spin. We argue that these solitonic ABSs constitute a natural candidate for a novel type of superconducting Andreev spin qubit, dubbed solitonic Andreev spin qubit (SASQ), that combines features of Andreev spin qubits and geometric spin qubits. Holonomic single-qubit SASQ operations are induced through soliton shuttling, with the resulting SU(2) trajectories densely covering the qubit Bloch sphere. Effects of disorder, non-holonomic SASQ dynamics and other aspects of qubit operation are also analyzed.

Figures (6)

• Figure 1: The solitonic Andreev spin qubit (c) combines elements from the Andreev spin qubit (a) and the geometric spin qubit (b). It is controlled with a phase bias $\phi$ like the former and allows holonomic operations like the latter. In (c), superconducting regions (blue) form a Corbino Josephson junction on a 2DEG (white). The junction is subjected to a weak out-of-plane magnetic field to induce a fluxoid mismatch between the inner disk and the outer ring. This creates a solitonic Andreev bound states (ABSs) (yellow) that are spin-degenerate, and whose position can be tuned through $\phi$. Moving the solitonic ABS induces holonomic qubit rotations due to the spin-orbit coupling in the 2DEG.
• Figure 2: (a) Sketch of the solitonic ABSs (yellow) concentrated at radius $R$ within an angular spread $\delta\varphi$ from the minimum of the total pairing $|\Delta(\varphi)|$ (green) at $\varphi_0$. The $\Delta(\varphi)$ profile, Eq. \ref{['Delta']}, results from a different fluxoid number in the inner disk (zero) and the outer ring (one) produced by a flux $\Phi=\pi R^2B_z$ between $0.5\Phi_0$ and $1.5\Phi_0$, where $\Phi_0$ is the superconducting flux quantum. There are two spinful low-energy states of opposite energy around each $\nu=\pm 1$ Fermi point. Their analytical wavefunction [without spin-orbit coupling, Eq. \ref{['solution']}] is shown in (b) for $\Phi/\Phi_0=1$, $R = 2\mu$m and $\Delta_0=\Delta_1=0.2$meV, where $\Delta_0$ and $\Delta_1$ are the paring amplitudes from the disk and ring. Their corresponding energy versus $\Phi/\Phi_0$ and versus pairing asymmetry $\Delta_0-\Delta_1$ (at fixed $\Delta_0+\Delta_1$) is shown in red in (c) and (d), respectively, with the rest of the spectrum in gray.
• Figure 3: The two components of the inverse spin-orbit length (in-plane $\lambda_\parallel^{-1}$ in blue and out of plane $\lambda_z^{-1}$ in red), normalized to the SASQ perimeter $2\pi R$ for four different radii $R$, are shown in (a-d). Different curves correspond to growing values of normalized flux $\Phi/\Phi_0$ from 0.6 to 1.4 in steps of 0.1. The holonomic evolution of the SASQ as the solitonic ABS makes 20 turns around the junction is shown in (e) for three different values of $\alpha$ and $\Phi$ colored points in (c-d). A large fraction of the Bloch sphere, parametrized by angles $\theta_B$ and $\varphi_B$, is covered by the SASQ evolution, with full coverage (gray trajectory) achieved at the optimal point $2\pi R\lambda_z^{-1} = 1$ [dashed red line in (a-c)]. Parameters: $\Delta_0=\Delta_1=0.2$meV, $\mu = 4$meV and $N = 1000$.
• Figure 4: (a,b) Bogoliubov spectrum of a SASQ versus chemical potential $\mu$ measured from the center of a band with cosine-like dispersion, half-bandwidth $W$ and spin-orbit coupling $\alpha = 3$ meV nm. In (a), $\Delta_0=\Delta_1=0.2$ meV and $\Phi/\Phi_0\approx 0.50$. In (b) $\Delta_0=0.25$ meV, $\Delta_1=0.2$ meV and $\Phi/\Phi_0= 0.85$. Shared parameters are $W = 30$ meV, $a_0=6.3$ nm and $R = 1\mu$m. (c) The non-linear dispersion and finite $\alpha$ produce a small spin splitting $\delta\epsilon^\alpha$ of the two $\pm|\epsilon_\nu|$ solitonic level pairs [red curves in (a,b)]. Colored curves are different values of $\Phi/\Phi_0$ for $\Delta_0=\Delta_1$. At half-filling $\mu=0$ and at $\Phi/\Phi_0\approx 0.5$ for any $\mu$ (blue curve), the residual splitting is suppressed. The dashed line is the analytical expression \ref{['splitting']}. For $\Delta_0\neq \Delta_1$, the splitting behaves similarly to the orange curve, matching the analytic result (not shown).
• Figure 5: Bogoliubov spectrum and spin splitting of the solitonic ABSs analogous to Fig. \ref{['fig:mu']}, but in the presence of a single realization of Anderson disorder, shown in (d), with standard deviation $\sigma_A=0.2$meV.