Magnetic Phase Control of a Thick SNS Weak Link: Proposed experimental scheme

TL;DR

The paper investigates whether a thick SNS weak link can achieve strong local magnetic control of the Josephson phase using an on-chip microcoil, challenging the assumption that loopless junctions have negligible phase coupling. Within a classical RSJ/RCSJ framework combined with linear circuit theory, it shows that a thick SNS bridge with parameters $L_{\text{kin}}$, $C$, $M$, and a plasma mode of frequency $\omega_p$ and quality factor $Q$ can yield a phase–flux coefficient $\alpha(d,\omega)$ amplified near resonance to $|\alpha|\sim 0.3$–$0.6$, i.e., a significant fraction of an ideal dc SQUID. The authors provide a practical experimental scheme to extract an operational $\alpha_{\mathrm{exp}}(d,\omega)$ by comparing Shapiro steps under direct RF drive and magnetic drive from the same microcoil, enabling a direct test of the predicted strong coupling. If realized, this would enable compact, locally addressable phase control in superconducting circuits without macroscopic loops, with broad implications for dense qubit/resonator networks and tunable on-chip phase shifters.

Abstract

In contrast to the extensive literature on thin tunnel junctions and traditional SQUID geometries, there is almost no quantitative experimental data on magnetic control of the Josephson phase in thick SNS weak links. The standard view is that in such compact structures without macroscopic loops the local magnetic coupling to the phase is negligibly small, which in practice forces one to use bulky SQUID devices for phase control. We show that this view is overly restrictive. We consider a thick SNS bridge with an on-chip microcoil placed directly above it, which controls the Josephson phase via strong phase-flux coupling enhanced near the Josephson plasma resonance. In the proposed configuration realistic thick SNS weak links, with normal-layer thickness d of order xi, can achieve phase-flux efficiencies of order 30-60 percent of an ideal dc SQUID. Within a standard RSJ/RCSJ model and linear circuit theory we show that this unexpectedly strong coupling arises from the combination of a large kinetic inductance of the thick SNS bridge and resonant amplification of about 15-35 dB, rather than from any exotic microphysics. The proposed experiment, a comparative analysis of Shapiro steps driven by a direct RF signal and by the magnetic field of the same microcoil, provides a direct and quantitative method to measure the phase-flux response of a thick SNS junction. If confirmed experimentally, such structures may become compact phase elements capable of locally controlling the Josephson phase without a macroscopic loop and enabling dense, locally addressable phase control in superconducting quantum circuits.

Figures (6)

• Figure 1: Cross-sectional sketch of the proposed device (not to scale). A superconducting strip is interrupted by a thick SNS weak link of length $L_W$ and thickness $d$. An on-chip microcoil above the insulating layer carries an AC current $I_{\mathrm{AC}}$, generating a local AC magnetic field $B_{\mathrm{AC}}(t)$ through the weak link. A DC bias current $I_{\mathrm{DC}}$ flows along the superconducting strip. This figure defines the geometric parameters used in the classical Josephson--circuit model.
• Figure 2: Same geometry as Fig. \ref{['fig:device']}, with the hatched, dashed region indicating the local field-active volume where the microcoil field penetrates the thick SNS weak link and neighbouring superconducting material. In the classical description this is the effective phase-sensitive region that determines the flux $\Phi_{\mathrm{ext}}(t)$ entering the phase--flux coefficient $\alpha(d,\omega)$.
• Figure 3: Illustrative dependence of the magnitude of the static phase--flux coefficient $|\alpha_{\text{static}}(d)|$ on the ratio $d/\xi$ between the normal-layer thickness and the coherence length, within the classical model of Sec. \ref{['sec:theory']}. Thin tunnel junctions ($d\ll\xi$) and overly thick weak links ($d\gg\xi$) exhibit weak coupling, while a thick SNS bridge with $d\sim\xi$ can reach a strong-coupling regime with $|\alpha_{\text{static}}|\sim 0.3$--$0.6$, indicated by the shaded band.
• Figure 4: Frequency dependence of the magnitude of the phase--flux coefficient $|\alpha(d,\omega)|$ obtained from the linearised RCSJ model. At low frequencies $\omega\ll\omega_p$ one recovers the quasistatic value $\alpha_{\mathrm{static}}$, while near the plasma resonance $\omega\simeq\omega_p$ the coupling is enhanced to $\alpha_{\mathrm{res}}\approx \alpha_{\mathrm{static}} Q$ in agreement with Eq. \ref{['eq:alpha_res_Q']}, with $Q$ the quality factor of the mode.
• Figure 5: Illustrative phase-field simulation for a thick SNS weak link driven by a local microcoil. The panels demonstrate that a localised drive predominantly excites a single standing-wave-like effective phase mode confined to the central part of the bridge.