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Physics-Uspekhi

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

V. V. Ryazanov, V. A. Oboznov, A. V. Veretennikov, A. Yu. Rusanov, Alexander A. Golubov, J. Aarts

Published Oct 1, 2001• 12 citations
Publisher

Abstract

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 Ic(T) oscillations detected are associated with a crossover of the SFS junctions from '0'- to 'π'-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 π-state shows evidence for a phase shift of π on the Ic(H) dependence. We have argued advantages of the SFS π-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 π-junctions in obtaining naturally degenerate two-level systems.

DOI
10.1070/1063-7869/44/10s/s18

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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 Ic(T) oscillations detected are associated with a crossover of the SFS junctions from '0'- to 'π'-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 π-state shows evidence for a phase shift of π on the Ic(H) dependence. We have argued advantages of the SFS π-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 π-junctions in obtaining naturally degenerate two-level systems.
π-junction qubit based on superconducting quantum interference device ring has been already proposed. In this qubit, a quantum two-level system is spontaneously generated without any bias flux applied. Flux qubit with a single π-junction concerns the large inductance L of the loop, which makes the qubit vulnerable to decoherence caused by magnetic fluctuations in the environment. To overcome this difficulty one can use three-junction π-qubit, comprising three π-junctions in a loop with negligible small inductance or unharmonic two-junction interferometer exploiting non-sinusoidal current-phase relations of the junctions. In the paper we theoretically investigate the macroscopic quantum dynamics of proposed qubits. The measurement process in two types of qubits has been analyzed in the frame of Lindblad equation formalism. Different mechanisms giving a non-sinusoidal CPR in SFS structures are analyzed as well. It is shown, that the largest second harmonic can be obtained for the SFS junction in the "clean" limit with a thin ferromagnet layer at low temperature.
We report on the functionality of a Nb-based superconducting single flux quantum (SFQ) toggle flip-flop (TFF) circuit, comprising a complementary superconductor–ferromagnet–superconductor (SFS) Josephson π-junction. The SFS junction was used as a phase shifting element inserted in the storage loop of the TFF. The fabricated circuits demonstrated correct functionality with the operation parameter ranges of ± 20%. The application of SFS π-junctions makes the SFQ circuits very compact, may substantially improve their stability, and may also be suitable for integration with Josephson quantum circuits (qubits).
The superconducting phase qubit combines Josephson junctions into superconducting loops and defines one of the promising solid state device implementations for quantum computing. While conventional designs are based on magnetically frustrated superconducting loops, here we discuss the advantages offered by πππ-junctions in obtaining naturally degenerate two-level systems. Starting from a basic five-junction loop, we show how to construct degenerate two-level junctions and superconducting phase switches. These elements are then effectively engineered into a superconducting phase qubit which operates exclusively with switches, thus avoiding permanent contact with the environment through external biasing. The resulting superconducting phase qubits can be understood as the macroscopic analogue of the `quiet' s-wave-d-wave-s-wave Josephson junction qubits introduced by Ioffe {\it et al.} [Nature {\bf 398}, 679 (1999)].
We fabricated Josephson junctions (JJs) between the d-wave superconductor (SC) YBa2Cu3O7-x (YBCO) and the s-wave SC Nb (ds-JJs) on graphoepitaxially buffered MgO substrates, studied ds-JJs at temperatures down to 30 mK and employed these JJs in π-loops. Current-voltage characteristics of ds-JJs oriented along the [100] axis of YBCO exhibited up to a factor of 200 higher critical current densities than ds-JJs oriented along the [110] axis of YBCO. The critical currentIcI_{c}Ic​and theIcRnI_{c}R_{n}Ic​Rn​product of [100]-oriented 3 μm wide ds-JJs are ∼70 μA and ∼200 μV, respectively, at 4.2 K. Rectangular arrays of up to 40 000 π-loops based on such ds-JJs were investigated using a low temperature scanning superconducting quantum interference device (SQUID) microscope. We observed ordering of spontaneously generated half integer magnetic flux quanta in the π-loops correlated with minute spurious background magnetic fields, as well as with configurations and mutual coupling of the π-loops. We manipulated the magnetic states of the π-loops by the local application of magnetic fields using nearby planar coils. This paper paves the way for the use of π-loops in computations that are based on annealing processes.
A superconducting-phase quantum bit (qubit) involves three or more Josephson junctions combined into a superconducting loop and defines one of the promising solid-state device implementations for quantum computing. Recently, so called $\ensuremath{\pi}$ junctions, Josephson junctions with a ground state characterized by a \ensuremath{\pi}-phase shift across, have attracted much attention. We show how to make use of such $\ensuremath{\pi}$ junctions in the construction of superconducting phase qubits and discuss the advantage over conventional designs based on magnetically frustrated loops. Starting from a basic five-junction loop with one $\ensuremath{\pi}$ junction, we show how to construct effective junctions with degenerate minima characterized by phase shifts 0 and $\ensuremath{\pi}$ and superconducting-phase switches. These elements are then combined into a superconducting-phase qubit which operates exclusively with switches, thus avoiding permanent contact with the environment through external biasing. The resulting superconducting-phase qubits can be understood as the macroscopic analog of the ``quiet'' s-wave--d-wave--s-wave Josephson-junction qubits introduced by Ioffe et al. [Nature (London) 398, 679 (1999)].
We adopt superconductor/ferromagnet/insulator/superconductor (SFIS) Josephson junctions (JJs) as both switching JJs and intrinsic π phase shifters in superconductor digital circuits. The critical current density (Jc) and characteristic voltage (Vc) of the SFIS junctions are about 22 A/cm2 and 22 μV, respectively. The intrinsic π phase shift is confirmed by measuring the suppressed nominal critical current Icn and half-period-shifted modulation pattern of a π–π–π superconducting quantum interference device (SQUID) that contains three π-JJs in a superconducting loop. A single-flux-quantum (SFQ) circuit composed of a DC/SFQ, Josephson transmission line (JTL), and SFQ/DC converter based on SFIS JJs alone is demonstrated at 4.2 K. The energy dissipation of the SFQ/DC converter decreases by 80% because some JJs are self-biased by the π phase shifter. The intrinsic circulating currents induced by the π phase shifters lead to a narrow bias margin (±5%) and even error function, which can be solved by parameters optimization or circuit initialization in the future. The half-modulation period (Φ0/2) of a half-flux-quantum (HFQ) SQUID (a partial HFQ JTL) exhibits propagation of HFQ between π–π–π SQUIDs, indicating that more complex HFQ circuits can be developed with π-JJs alone in the future.