Coupling of two superconductors through a ferromagnet. SFS $\pi$-junctions and intrinsically-frustrated superconducting networks

Reentrant superconducting behavior of the critical supercurrent temperature dependencies has been observed for the Nb-Cu/Ni-Nb Josephson SFS (superconductor–ferromagnet–superconductor) junctions. The $I_{\mathrm{c}}(T)$ oscillations detected are associated with a crossover of the SFS junctions from '$0$'- to '$\pi$'-state that is related to a special feature of superconducting pair flow through a ferromagnet (spatial oscillations of induced superconducting order parameter in presence of the exchange field). A triangular array of the junctions in the $\pi$-state shows evidence for a phase shift of $\pi$ on the $I_{\mathrm{c}}(H)$ dependence. We have argued advantages of the SFS $\pi$-junction use for the quantum bit implementation based on the superconducting loop with quantum Josephson junctions. While designs proposed previously are based on magnetically frustrated superconducting loops, we discuss the advantages offered by the $\pi$-junctions in obtaining naturally degenerate two-level systems.