Interference and Switching of Josephson Current Carried by Nonlocal Spin-Entangled Electrons in a SQUID-Like System with Quantum Dots

The Josephson current of spin-entangled electrons through the two branches of a SQUID-like structure with two quantum dots exhibits a magnetic-flux response different from the conventional Josephson current. Because of their interference, the period of maximum Josephson current changes from $h/2e$ to $h/e$, which can be used for detecting the Cooper-pair splitting efficiency. The nonlocal spin entanglement provides a quantum mechanical functionale for switching on and off this novel Josephson current, and explicitly a switch is formulated by including a pilot junction. It is shown that the device can be used to measure the magnitude of split-tunneling Josephson current.

Figure 1

Schematic setup of a Cooper-pair splitter. Two superconductors are connected by two leads with QDs embedded. The QDs are defined by voltage gate $g_1$ and $g_2$.

Figure 2

Magnetic response of the maximum dc Josephson current. The dash–double-dotted, dashed, dash-dotted, dotted, and solid lines are for the case of splitting efficiency $\gamma =0$, 0.25, 0.5, 0.75, and 1, respectively. Each curve was normalized and shifted for clarity.

Figure 3

Schematic setup of a switch of the novel Josephson current. The Cooper-pair splitter displayed in Fig. 1 is connected in parallel with a pilot Josephson junction.

Figure 4

The maximum Josephson current of the total system in response to the critical current of the pilot junction $J$. The dashed (dash-dotted) line is for the spin-triplet (spin-singlet) state, and the solid lines are for the states realized.