Figure 1

Layout of Josephson circuit with attached Andreev interferometer. (a) General view. (b) Andreev interferometer consisting of crossed silver wires, connected to the aluminum wires at $c$ and $d$. The resistance $R_A$ between $a$ and $b$ is measured using current ($I_1,I_2$) and voltage probes ($U_1,U_2$). (c) The superconducting quantum loop is interrupted by Josephson junctions at points 1, 2, 3, and 4. There is a superconducting phase difference ${\theta }_q$ between $e$ and $f$.Reuse & Permissions

Figure 2

(a) Normalized oscillating resistance, $r=\delta R_A/\gamma$, measured at 20 mK. (b) The phase shift ${\theta }_q({\Phi }_{\mathrm{eq}})$ between $e$ and $f$, as extracted from the oscillations in Fig. 2a; black dots are experimental data and the solid line is calculated using Eqs. (3, 4). (c) Hysteresis in the resistance at the degeneracy point ${\Phi }_{eq}={\Phi }_0/2$ in an interferometer attached to a “classical” Josephson circuit, taken with increasing (○) and decreasing (●) magnetic field. (d) Detail of oscillations in Fig. 2a near the degeneracy point ${\Phi }_{eq}={\Phi }_0/2$, taken with increasing (○) and decreasing (●) magnetic field. The dashed line corresponds to $\varphi =2\pi \frac{{\Phi }_{eA}}{{\Phi }_0}$. (e) Experimental temperature dependence of the amplitude of ${\theta }_q({\Phi }_{\mathrm{eq}})$ (●), compared to calculations for $\Delta =0.035E_J$ (+) and $\Delta =0.025E_J$ (×).Reuse & Permissions

Figure 3

Calculated fits to the experimental data of Figs. 2a, 2b, 2d using Eqs. (3, 4). (a) Calculated oscillations of the normalized resistance $r({\Phi }_{\mathrm{eq}})$ in the ground energy state as a function of the normalized external flux ${\Phi }_{\mathrm{eq}}/{\Phi }_0$. The insets show detail of oscillations in the ground (solid lines) and excited states (dashed lines) for $\Delta =0.04E_J$, $\Delta =0.03E_J$, and $\Delta =0.02E_J$ (curves 1, 2, and 3). (b) Calculated phase shifts ${\theta }_{-}({\Phi }_{\mathrm{eq}})$ and ${\theta }_{+}({\Phi }_{\mathrm{eq}})$ in the ground and excited states. (c) The energy spectrum $E_q$.Reuse & Permissions