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arXiv:2108.11006 · Applied Physics Express

Half-integer Shapiro-steps in superconducting qubit with a π-Josephson junction

Michiyasu Mori, Sadamichi Maekawa

Published Aug 25, 2021• 2 citations
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Abstract

Abstract A superconducting quantum interference device (SQUID) comprising 0- and π-Josephson junctions (JJs), called π-SQUID, is studied by the resistively shunted junction model. The π-SQUID shows half-integer Shapiro-steps (SS) under microwave irradiation at the voltage V = ( ℏ / 2 e ) Ω ( n / 2 ) , with angular frequency Ω and half-integer n/2 in addition to integer n. We show that the π-SQUID can be a π-qubit with spontaneous loop currents by which the half-integer SS are induced. Making the 0- and π-JJs equivalent is a key for the half-integer SS and realizing the π-qubit.

DOI
10.35848/1882-0786/ac211d

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Abstract A superconducting quantum interference device (SQUID) comprising 0- and π-Josephson junctions (JJs), called π-SQUID, is studied by the resistively shunted junction model. The π-SQUID shows half-integer Shapiro-steps (SS) under microwave irradiation at the voltage V = ( ℏ / 2 e ) Ω ( n / 2 ) , with angular frequency Ω and half-integer n/2 in addition to integer n. We show that the π-SQUID can be a π-qubit with spontaneous loop currents by which the half-integer SS are induced. Making the 0- and π-JJs equivalent is a key for the half-integer SS and realizing the π-qubit.
A high-Tc dc superconducting quantum interference device (SQUID) with three Josephson junctions (JJs) in series in each of its arms has been fabricated. Its Shapiro steps were studied using microwave (rf) radiation of 10 GHz and weak magnetic fields. The appearance of giant Shapiro steps and of some of half-integer steps was observed. Separation between the adjacent Shapiro steps could be tuned by rf magnetic fields and small external dc magnetic fields. This phenomenon was analyzed by phase locking the JJs in the SQUID.
Integer and half-integer Shapiro step amplitudes in the current-voltage characteristics of symmetric superconducting quantum interference devices (SQUIDS), containing more than one Josephson junction on each arm, are analytically calculated for small values of the parameter β and in the absence of noise. This analysis is made possible by the reduction of the dynamical equations of the multiple-junction SQUID to the dynamical equation of a single Josephson junction possessing a nonconventional current-phase relation.
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.
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.
The Shapiro effect is known, with regular steps in the voltage–current characteristic of a Josephson junction in the presence of microwave radiation, and so are its applications. In asymmetric two-junction SQUIDs (superconducting quantum interference devices), in particular the interactions between various current contributions in the two junctions lead to more varied and richer conditions. In this paper, we discuss the possibility and the impacts of a kind of internal Shapiro effect in some portions of the parameter space of the asymmetric high-TC SQUID with overdamped junctions and large loop inductance. In this predicted phenomenon, the required high-frequency radiation is produced spontaneously in the interior of the SQUID. The main message is the importance of achieving a set of nine parameters for the device whose voltage–current characteristics show no indication of spike–step-like structures.
A zero-crossing Shapiro step (ZCSS) in an asymmetric and nonhysteretic two-junction superconducting quantum interference device (SQUID) driven by one sinusoidal rf signal is presented. The operation is based on imbalanced evolution of the junction phases owing to the tilted interference diagrams. Dependence of ZCSS generation upon the frequency and amplitude of a rf signal was numerically obtained. A test circuit was designed and fabricated using a Nb∕AlOx∕Nb junction technology. When we irradiated a rf signal of 10GHz, a ZCSS at the voltage position of the first order was observed. The polarity of the step voltage was switched by a dc control flux to the SQUID loop. The experimental bias-current versus voltage and control-current versus voltage curves were quantitatively reproduced by numerical simulation.