Voltage and current expressions for a two-junction superconducting interferometer

Abstract

Articles you may be interested inZero-crossing Shapiro step generated in an asymmetric and nonhysteretic rf-current-driven two-junction superconducting quantum interference deviceThe average voltage and circulating current of a superconducting interferometer containing two Josephson junctions (a dc SQUID) are calculated analytically, in various approximations, as functions of bias current and applied magnetic field or control current. The results are useful in calculations of the noise characteristics of the dc SQUID, as well as in other applications. PACS numbers: 74.50. + r, 85.25. + k [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 132.

Analytical derivation of DC SQUID response

“…Even for ∆l = 0 the voltage response has small constant shift along φ e axis due to ∆i c , ∆r n asymmetries, in accordance with (46). Corresponding terms arising in (42) provide some asymmetry of the voltage response shape which is though quite small for considered case |∆i c |, |∆r n | ≪ 1. Figure 9(b) illustrates effects of the critical current difference ∆i c at ∆r n = 0 and difference of the shunt resistances ∆r n at ∆i c = 0 on the amplitude of the voltage response v * pp for i b , Σi c , Σr n = 2 and l = 1.…”

“…Following works [18,42] we consider the difference phase as a sum of slow-varying ψ − and oscillating ψ ∼ parts. The last one is assumed to be small ψ ∼ ≪ 1 for shunted junctions and the inductance value l ≤ 1.…”

“…Impact of oscillating current circulating in the SQUID can be introduced by oscillating part of the difference phase. Since ψ * ∼ is proportional to the inductance (41), the last two terms in (42) represent SQUID LR-filtering of the circulating current. They vanish in the limit l → 0.…”

“…It is interesting to note that an attempt to average SQUID voltage dynamics in the frame of another analytical approach, which is somewhat similar to the perturbation analysis, was undertaken even before the works [32,35] on HTS SQUIDs. In 1983 Peterson and McDonald proposed their voltage and current expressions for DC SQUID with small but finite inductance [42]. In their method the SQUID difference phase ψ = (φ 1 − φ 2 )/2 (φ 1,2 are the Josephson phases of the first and the second junction) was expressed as a sum of the normalized external magnetic flux φ e and a small correction x, which vanishes with the inductance, ψ = −φ e + x.…”

Sinusoidal response of dc SQUIDs for rf power measurements

“…The dynamic equations describing a dc SQUID are (8) Here the e's are the junction capacitances and the R's are resistances shunting the junctions. Ib is the bias current injected as shown in figure 1.…”