We review the physical basis of and recent developments in ferromagnetic Josephson junctions with a focus on the π state, which is useful for applications to superconducting devices. Among various novel phenomena that emerge from the interaction between the superconductor and ferromagnet, the π state (junction) works as a phase shifter in superconducting devices, and several proposals and demonstrations of applications to quantum computing elements (qubits), classical superconducting logic circuits, and cryogenic memory have been presented. As a new research trend in superconducting spintronics, we also introduce recent interesting works on the long-range Josephson effect caused by spin-triplet Cooper pairs.
A controllable \ensuremath{\pi}-SQUID is a DC SQUID (direct-current superconducting quantum interference device) with two controllable \ensuremath{\pi} junctions as weak links. A controllable \ensuremath{\pi} junction consists of a superconducting--normal metal--superconducting Josephson junction with two additional contacts to the normal region of the junction. By applying a voltage
Vc over these contacts it is possible to control the state of the junction, i.e., a conventional (0) state or a \ensuremath{\pi} state, depending on the magnitude of
Vc. We demonstrate experimentally that, by putting one junction into a \ensuremath{\pi} state, a screening current is generated around the SQUID loop at an integer external flux. To be able to do this, we have fabricated controllable $\ensuremath{\pi}$ junctions, based on Cu-Nb or Ag-Nb, in a new geometry. We show that at 1.4 K only the Ag-Nb device shows the transition to a \ensuremath{\pi} state as a function of
Vc consistent with theoretical predictions. In a controllable \ensuremath{\pi}-SQUID based on Nb-Ag we observe, apart from a screening current at integer external flux, a phase shift of \ensuremath{\pi} of the ${V}_{\mathrm{SQUID}}\ensuremath{-}B$ oscillations under a suitable current bias, depending on the magnitude of
Vc.Encoding a qubit in logical quantum states with wave functions characterized by disjoint support and robust energies can offer simultaneous protection against relaxation and pure dephasing. One of the most promising candidates for such a fully protected superconducting qubit is the 0-π circuit [Brooks et al., Phys. Rev. A 87, 052306 (2013)]. Here we realize the proposed circuit topology in an experimentally obtainable parameter regime, where the ground-state degeneracy is lifted but the qubit is still largely noise protected. More precisely, the logical states of this qubit feature disjoint support and are exponentially protected against relaxation and exponentially (first order) protected against dephasing due to charge (flux) noise. We name the resultant device the "soft 0-π qubit."Multitone spectroscopy measurements reveal the energy-level structure of the system, which can be precisely described by a simple two-mode Hamiltonian. Using a Raman-type protocol, we exploit a higher-lying charge-insensitive energy level of the device to realize coherent population transfer and logical operations. The measured relaxation (T1 = 1.6 ms) and dephasing (TR = 9 μs, T2E = 25μs) times demonstrate that the soft 0-π circuit not only broadens the family of superconducting qubits but also constitutes an important step toward quantum computing with intrinsically protected superconducting qubits.