We report a theoretical study of the low-frequency impedance of a Josephson junction chain whose parameters vary in space. Our goal is to find the optimal spatial profile which maximizes the total inductance of the chain without shrinking the low-frequency window where the chain behaves as an inductor. If the spatial modulation is introduced by varying the junction areas, we find that the best result is obtained for a spatially homogeneous chain, reported earlier in the literature. An improvement over the homogeneous result can be obtained by representing the junctions by SQUIDs with different loop areas, so the inductances can be varied by applying a magnetic field. Still, we find that this improvement becomes less important for longer chains.
We report a theoretical study of the low-frequency impedance of a Josephson junction chain whose parameters vary in space. Our goal is to find the optimal spatial profile which maximizes the total inductance of the chain without shrinking the low-frequency window where the chain behaves as an inductor. If the spatial modulation is introduced by varying the junction areas, we find that the best result is obtained for a spatially homogeneous chain, reported earlier in the literature. An improvement over the homogeneous result can be obtained by representing the junctions by SQUIDs with different loop areas, so the inductances can be varied by applying a magnetic field. Still, we find that this improvement becomes less important for longer chains.
We propose a way to control the Josephson energy of a single Josephson junction embedded in a one-dimensional superconducting metamaterial: an inhomogeneous superconducting loop, made out of a superconducting nanowire or a chain of Josephson junctions. The Josephson energy is renormalized by the electromagnetic modes propagating along the loop. We study the behavior of the modes as well as of their frequency spectrum when the capacitance and the inductance along the loop are spatially modulated. We show that, depending on the amplitude of the modulation, the renormalized Josephson energy is either larger or smaller than the one found for a homogeneous loop. Using typical experimental parameters for Josephson junction chains and superconducting nanowires, we conclude that this mode engineering can be achieved with currently available metamaterials.
It is customary to use arrays of superconducting quantum interference devices (SQUIDs) for implementing magnetic field-tunable inductors. Here, we demonstrate an equivalent tunability in a (SQUID-free) array of single Al/AlOx/Al Josephson tunnel junctions. With the proper choice of junction geometry, a perpendicularly applied magnetic field bends along the plane of the superconductor and focuses into the tunnel barrier region due to a demagnetization effect. Consequently, the Josephson inductance can be efficiently modulated by the Fraunhofer-type supercurrent interference. The elimination of SQUIDs not only simplifies the device design and fabrication but also facilitates a denser packing of junctions, and, hence, a higher inductance per unit length. As an example, we demonstrate a transmission line, the characteristic impedance of which is field-tuned in the range of 4–8 kΩ, centered around the important value of the resistance quantum h/(2e)2≈6.5 kΩ.
Superinductances are superconducting circuit elements that combine a large inductance with a low parasitic capacitance to ground, resulting in a characteristic impedance exceeding the resistance quantum RQ=h/(2e)2≃6.45kΩ. In recent years, these components have become key enablers for emerging quantum circuit architectures. However, achieving high characteristic impedance while maintaining scalability and fabrication robustness remains a major challenge. In this work, we present two fabrication techniques for realizing superinductances based on vertically stacked Josephson junctions. Using a multi-angle Manhattan (MAM) process and a zero-angle (ZA) evaporation technique -- in which junction stacks are connected pairwise using airbridges -- we fabricate one-dimensional chains of stacks that act as high-impedance superconducting transmission lines. Two-tone microwave spectroscopy reveals the expected n scaling of the impedance with the number of junctions per stack. The chain fabricated using the ZA process, with nine junctions per stack, achieves a characteristic impedance of ∼16kΩ, a total inductance of 5.9μH, and a maximum frequency-dependent impedance of 50kΩ at 1.4 GHz. Our results establish junction stacking as a scalable, robust, and flexible platform for next-generation quantum circuits requiring ultra-high impedance environments.
We propose a scheme to implement a tunable, wide frequency-band dissipative environment using a double chain of Josephson junctions. The two parallel chains consist of identical superconducting quantum interference devices (SQUIDs), with magnetic-flux tunable inductance, coupled to each other at each node via a capacitance much larger than the junction capacitance. Thanks to this capacitive coupling, the system sustains electromagnetic modes with a wide frequency dispersion. The internal quality factor of the modes is maintained as high as possible, and the damping is introduced by a uniform coupling of the modes to a transmission line, itself connected to an amplification and readout circuit. For sufficiently long chains, containing several thousands of junctions, the resulting admittance is a smooth function versus frequency in the microwave domain, and its effective dissipation can be continuously monitored by recording the emitted radiation in the transmission line. We show that by varying in situ the SQUIDs' inductance, the double chain can operate as a tunable ohmic resistor in a frequency band spanning up to 1 GHz, with a resistance that can be swept through values comparable to the resistance quantum ${R}_{q}=h/(4{e}^{2})\ensuremath{\simeq}6.5\phantom{\rule{4pt}{0ex}}\text{k}\mathrm{\ensuremath{\Omega}}$. We argue that the circuit complexity is within reach using current Josephson junction technology.
We report on experiments with superconducting Josephson metamaterials. In such a material, conventional split ring resonators are replaced by superconducting loops that are interrupted by Josephson junctions, so called rf-SQUIDs. Like the split ring resonators, they can be seen as LCresonators that couple to the magnetic component of the incoming wave. The advantage of superconducting thin-film metamaterials is that due to the tunable intrinsic inductance of the Josephson junction, the resonance frequency of the rf-SQUID can be changed by applying an external dc magnetic field. We present experimental results that show the tunability of the resonance frequency of these devices.
Abstract Superconducting quantum interference devices (SQUIDs) with 3D nano-bridge junctions can be miniaturized into nano-SQUIDs that are able to sense a few spins in a large magnetic field. Among all device parameters, the inductance is key to the performance of SQUIDs with 3D nano-bridge junctions. Here, we measured the critical-current magnetic flux modulation curves of 12 devices with three design types using a current strip-line directly coupled to the SQUID loop. A best flux modulation depth of 71% was achieved for our 3D Nb SQUID. From the modulation curves, we extracted the inductance values of the current stripe-line in each design and compared them with the corresponding simulation results of InductEX. In this way, London penetration depths of 110 and 420 nm were determined for our Nb (niobium) and NbN (niobium nitride) films, respectively. Furthermore, we showed that inductances of 11 and 119 pH for Nb and NbN 3D nano-bridge junctions, respectively, dominated the total inductance of our SQUID loops which are 23 pH for Nb and 255 pH for NbN. A screening parameter being equal to one suggests optimal critical currents of 89.6 and 8.1 μ A for Nb and NbN SQUIDs, respectively. Additionally, intrinsic flux noise of 110 ± 40 n Φ 0 /(Hz) 1/2 is calculated for the Nb SQUIDs with 3D nano-bridge junctions by Langevin simulation.