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arXiv:cond-mat/0112433 · Applied Physics Letters

Simple phase bias for superconducting circuits

Johannes Majer, J. R. Butcher, Johan E. Mooij

Published May 13, 2002• 73 citations
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Abstract

A superconducting phase-bias tool, based on a trapped fluxoid in a ring, is proposed and demonstrated. It can provide arbitrary phase values and is simple to fabricate. The phase bias has been realized in two superconducting quantum interference devices, where the critical current versus magnetic flux is shown to be shifted by π/2 and π.

DOI
10.1063/1.1478150

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A superconducting phase-bias tool, based on a trapped fluxoid in a ring, is proposed and demonstrated. It can provide arbitrary phase values and is simple to fabricate. The phase bias has been realized in two superconducting quantum interference devices, where the critical current versus magnetic flux is shown to be shifted by π/2 and π.
A dc superconducting quantum interference device (SQUID) consisting of a symmetric ring circuit with four Josephson junctions and two independent external currents I1{I}_{1}I1​ and I2{I}_{2}I2​, which enter the circuit at different points, has a phase boundary between the fully superconducting and the normal states that is different from that of a conventional SQUID. The control current I2{I}_{2}I2​ modifies the magnetic flux (\ensuremath{\varphi}) periodicity and the value of the maximum measuring current I1m{I}_{1m}I1m​(\ensuremath{\varphi}). For values of I2{I}_{2}I2​>Ic{I}_{c}Ic​ (critical current of Josephson junction) the fully resistive state exists over flux intervals centered around (n+(1/2)${\ensuremath{\varphi}}_{0}$, where n is an integer and ${\ensuremath{\varphi}}_{0}$ is the fluxoid quantum. A superconducting circuit without Josephson junctions is suggested which should have a phase boundary similar to that found here. Minimization procedures which are usually employed in analyzing SQUID's are discussed.
Abstract Superconducting circuits represent a versatile playground to explore novel quantum phenomena and a platform to realize quantum bits (qubits). Superconducting qubits hinge on the coherent tunneling of Cooper pairs across the insulating barrier of a Josephson junction. This qubit implementation is, however, plagued with the variability of the fabricated junction, along with the need for magnetic tunability of the qubit transition frequency. Alternatively, a dual to the Josephson effect—referred to as quantum phase slips—allows for a coherent coupling of flux states and has been used to build phase-slip qubits. In this paper, we propose coupling flux states of a superconducting ring using a bias voltage. By solving the time-dependent Ginzburg–Landau equations, we demonstrate that the bias voltage locally suppresses the density of Cooper pairs, thereby forming a weak link where phase slips occur. Moreover, we show that a voltage-biased superconducting ring serves as an electrically-controlled magnetic memory. The work presented in this paper is an important step towards realizing electrically-tunable superconducting devices, such as qubits and SQUIDs.
Abstract Applying a radian phase shift other than 2π is a key issue for superconducting circuits, such as flux qubits. The magnetic flux is useful when generating a phase shift. However, a quantized magnetic flux accompanying a trapped vortex in a superconductor does not have a phase shifter function. The magnetic flux generated by an external field generates noise. In this study, we propose a phase bias system that does not require an external field during operation. We confirm the phase shift of a direct current superconducting interference device (SQUID) placed on an ultrathin superconducting Nb bilayer with a through-hole by cooling it to a temperature below the superconducting transition temperature with an external field. Although the cause of the phase shift in our system is unclear, we believe that it may be caused by a fractional quantum in the bilayer. When the SQUID is replaced by a qubit, the phase shift can be applied to a phase bias.
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 d-wave pairing symmetry in high-critical temperature superconductors makes it possible to realize superconducting rings with built-in pi phase shifts. Such rings have a twofold degenerate ground state that is characterized by the spontaneous generation of fractional magnetic flux quanta with either up or down polarity. We have incorporated pi phase-biased superconducting rings in a logic circuit, a flip-flop, in which the fractional flux polarity is controllably toggled by applying single flux quantum pulses at the input channel. The integration of p rings into conventional rapid single flux quantum logic as natural two-state devices should alleviate the need for bias current lines, improve device symmetry, and enhance the operation margins.
Leveraging the quantization properties inherent in superconductors, we present the development of an intrinsic superconducting phase battery. This advancement is achieved by integrating a ferromagnetic π-phase Josephson junction (π-JJ) within a superconducting ring. The core innovation lies in harnessing the potential energy of the π-JJ to generate an intrinsic circulating current, thereby inducing a phase difference as the current goes through the geometric inductance. This mechanism allows for tuning the phase bias φ (0 < φ < π) through an arrangement of the geometric inductance in the battery. We integrate the intrinsic phase batteries into superconducting quantum interference devices, where we verified the effectiveness of the induced phase bias. The polarity of the phase battery is determined by the direction of the intrinsic circulating current, which can be initialized by an external magnetic field. The design methodology for precise intrinsic phase bias has been established. Our findings not only show the feasibility of generating an intrinsic and adjustable phase bias using established fabrication techniques but also open new avenues for enhancing the design, efficiency, and functionality of superconducting electronics, promising to accelerate advancements in digital and quantum computing technologies.