Detecting Majorana modes by readout of poisoning-induced parity flips

Reading out the parity degree of freedom of Majorana bound states is key to demonstrating their non-Abelian exchange properties. Here, we present a low-energy model describing localized edge states in a two-arm device. We study parity-to-charge conversion based on coupling the superconductor bound states to a quantum dot whose charge is read out by a sensor. The dynamics of the system, including the readout device, is analyzed in full using a quantum-jump approach. We show how the resulting signal and signal-to-noise ratio differentiates between local Majorana and Andreev bound states.

Figure 1

(a) Subgap modes in two superconducting wires tunnel-coupled to a parity-to-charge converter dot [Eq. (1)] that capacitively couples to a charge sensor. (b) Sensor current $I_{\text{L}}\left(t\right)$ due to driven ${\mu }_{\text{L}}$, corresponding first harmonic $G\left(t\right)$ [Eq. (2)], and dot-subgap parity $p_{\text{d,SC}}$. (c) Sample-averaged conductances $G_{\text{e/o}}=G_{p_{\text{d,SC}}=\pm 1}$ scaled by $G_T=\mathrm{\Gamma }/\left(8T\right)$. (b) shares parameters with (c); other parameters are from Fig. 2.

Figure 2

Signal $\mathcal{S}$ and signal-to-noise ratio $\mathcal{D}$ [Eq. (3)] as a function of various parameters for $N=1$ [(a), (b)] and $N=2$ [(c), (d)] zero-energy subgap modes. All panels use ${\epsilon }_i=0, {\lambda }_i=\lambda , {\epsilon }_{\text{S}}=0, E_{\text{cap}}=2\lambda =6T=6\delta \mu =20\mathrm{\Gamma }, 2\pi /\mathrm{\Omega }=4t_{\text{b}}=2\pi \times 2400/\lambda ={10}^4\delta t=1\mu \text{s}, N_{\text{osc}}=2, N_{\text{T}}=10, M_{\text{T}}=50$.

Figure 3

Signal-to-noise ratio $\mathcal{D}$ [Eq. (3)] as a function of the subgap energies ${\epsilon }_i$ for (a) one coupled wire with $N=1,|u_1{|}^2=0.5$, and (b) one mode per wire, $N=2,|u_i{|}^2=0.5$. In (b), we set ${\epsilon }_2=2{\epsilon }_1=2{\epsilon }_{\text{sg}}>0$. Other parameters are as in Fig. 2.