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arXiv:2507.09339 · Applied Physics Letters

Superinductor-based ultrastrong coupling in a superconducting circuit

Alba Torras-Coloma, Luca Cozzolino, Ariadna Gómez-del-Pulgar-Martínez, E. Bertoldo, P. Forn-Díaz

Published Nov 24, 2025• 1 citation
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Abstract

We present an ultrastrong superinductor-based coupling mechanism in a circuit consisting of a flux qubit galvanically coupled to an LC resonator. The coupling inductor is fabricated with granular aluminum, a superinductor material able to provide large surface inductances. Despite the low persistent current exhibited by the qubit, Ip=11.6 nA, spectroscopy measurements reveal a Bloch–Siegert shift of 23 MHz and a coupling fraction of g/ωr≃0.13, entering the perturbative ultrastrong coupling regime. An independent estimate of the coupler inductance by low-temperature resistance measurements leads to Lc=(0.74±0.14) nH, which is compatible with g/ωr≳0.1. Our results show that superinductors are a promising resource to study ultrastrong coupling physics in high-coherence circuits using flux qubits with small loop areas and low persistent currents.

DOI
10.1063/5.0293790

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We present an ultrastrong superinductor-based coupling mechanism in a circuit consisting of a flux qubit galvanically coupled to an LC resonator. The coupling inductor is fabricated with granular aluminum, a superinductor material able to provide large surface inductances. Despite the low persistent current exhibited by the qubit, Ip=11.6 nA, spectroscopy measurements reveal a Bloch–Siegert shift of 23 MHz and a coupling fraction of g/ωr≃0.13, entering the perturbative ultrastrong coupling regime. An independent estimate of the coupler inductance by low-temperature resistance measurements leads to Lc=(0.74±0.14) nH, which is compatible with g/ωr≳0.1. Our results show that superinductors are a promising resource to study ultrastrong coupling physics in high-coherence circuits using flux qubits with small loop areas and low persistent currents.
Superconducting inductors with impedance surpassing the resistance quantum, i.e., superinductors, are important for quantum technologies because they enable the development of protected qubits, enhance coupling to systems with small electric dipole moments, and facilitate the study of phase-slip physics. We demonstrate superinductors with densely packed meandered traces of granular aluminum ( grAl ) with inductances up to 4 µH, achieving impedances exceeding 100 k in the 4–8 GHz range. Ring resonators made with grAl meandered superinductors exhibit quality factors on the order of 10 5 in the single-photon regime, and low nonlinearity on the order of tens of hertz. Depending on the grAl resistivity, at 10 Hz, we measure frequency-noise spectral densities in the range of 10 2 – 10 3 Hz / Hz . In some devices, in the single-photon regime, we observe a positive Kerr coefficient of unknown origin. Using more complex fabrication, the devices could be released from the substrate, either freestanding or suspended on a membrane, thereby further improving their impedance by a factor of 3.
We report on ultrastrong coupling between a superconducting flux qubit and a resonant mode of a system comprised of two superconducting coplanar stripline resonators coupled galvanically to the qubit. With a coupling strength as high as 17.517.5%17.5 of the mode frequency, exceeding that of previous circuit quantum electrodynamics experiments, we observe a pronounced Bloch-Siegert shift. The spectroscopic response of our multimode system reveals a clear breakdown of the Jaynes-Cummings approximation. In contrast to earlier experiments, the high coupling strength is achieved without making use of an additional inductance provided by a Josephson junction.
Superinductors are inductors whose microwave characteristic impedances are greater than the resistance quantum, RQ=h/(2e)2approx6.5kOmegaR_{Q}=h/(2e)^{2}approx6.5kOmegaRQ​=h/(2e)2approx6.5kOmega. They can be implemented using Josephson junction chains and high kinetic inductance nanowires. In this dissertation, we explore applications of superinductors in both implementations in superconducting quantum circuits. The dissertation consists of three parts. In the first part, we discuss the fluxon-parity-protected qubit consisting of a Cooper-pair box (CPB) shunted by a superinductor made of a chain of coupled asymmetric Superconducting Quantum Interference Devices (CASQUIDs). The spectroscopic measurement of a prototype of the fluxon-parity-protected qubit was performed. We observed almost complete suppression of the single fluxon tunneling across the CPB due to the destructive Aharonov-Casher interference when the offset charge on the CPB island was set to eee mod(2eee). A fluxon-parity-protected qubit with a higher superinductance can potentially be used to perform fault-tolerant Clifford gates. In the second part, we studied the microwave losses in high-kinetic-inductance granular Aluminum films using superconducting coplanar-waveguide (CPW) resonators made of the films. We observed that the intrinsic losses in these resonators at low temperatures were limited by resonator coupling to the two-level systems (TLS) in the environment. The demonstrated internal quality factors are comparable with those for CPW resonators made of conventional superconductors. The characterized granular Aluminum films can be used to fabricate superinductors for a wide range of applications in quantum metrology and quantum information processing. In the third part, we discuss the one-dimensional Josephson metamaterial made of a similar structure as the superinductor used in the fluxon-parity-protected qubit. The metamaterial demonstrated strong Kerr nonlinearity with the Kerr constant tunable over a wide range from positive to negative values by the magnetic field. The metamaterial is promising for use as an active medium for quantum-limited Josephson traveling-wave parametric amplifiers.
We investigate the ultrastrong tunable coupler for coupling of superconducting resonators. The obtained coupling constant exceeds 1 GHz, and the wide-range tunability is achieved for both antiferromagnetics and ferromagnetics from $\ensuremath{-}1086$ to 604 MHz. The ultrastrong coupler is composed of a rf superconducting quantum interference device (SQUID) and dc SQUID as tunable junctions, which connect to resonators via shared aluminum thin-film meander lines enabling such a huge coupling constant. The spectrum of the coupler obviously shows the breaking of the rotating-wave approximation, and our circuit model treating the Josephson junction as a tunable inductance reproduces the experimental results well. The ultrastrong coupler is expected to be utilized in quantum annealing circuits and/or noisy intermediate-scale quantum devices with dense connections between qubits.
We design superinductors made of strongly disordered superconductors for implementation in ``hybrid'' superconducting quantum circuits. The superinductors are fabricated as meandered nanowires made from granular aluminum films. Optimization of the device geometry enables the realization of superinductors with an inductance of approximately 1 $\ensuremath{\mu}\mathrm{H}$ and a self-resonance frequency of over 3 GHz. These compact superinductors are attractive for a wide range of applications, from superconducting circuits for quantum computing to microwave elements of cryogenic parametric amplifiers and kinetic inductance photon detectors.