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arXiv:2608.28428

Kerr nonlinearity and three-wave mixing in superconducting resonators hosting Al-InAs weak links

Vittorio Buccheri, Ivo P. C. Cools, Nermin Trnjanin, Ankit Khola, Oleg Shvetsov, Thomas Kanne, Jesper Nygård, Attila Geresdi, Simone Gasparinetti

quant-phSubmitted Aug 28, 2026• Announced Aug 31, 2026• 0 citations
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Abstract

Nonlinear microwave resonators are a versatile tool in quantum information processing, enabling parametric amplification, continuous variable quantum computing, and engineered mode interactions. Many of these applications especially benefit from cubic nonlinearities enabling three-wave mixing; at the same time, they are limited by quartic nonlinearities giving rise to undesired Kerr effects. A recurrent challenge is therefore to engineer resonators with a finite cubic nonlinearity while suppressing quartic terms. Here, we investigate a superconducting resonator hosting two weak links fabricated from an aluminum-capped indium arsenide nanowire. We characterize the Kerr nonlinearity as a function of magnetic flux and gate bias, showing that it can be tuned to zero with either control parameter. Furthermore, we experimentally demonstrate three-wave mixing in a semiconductor-superconductor hybrid device, establishing nonzero cubic nonlinearity. An effective model based on Andreev bound states qualitatively captures the observed trends. Our results validate semiconductor-superconductor hybrid devices as a promising platform for tunable nonlinear superconducting circuits, with applications in parametric amplification, quantum control of bosonic modes, and engineering interactions between microwave modes.

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Nearly quantum limited Josephson parametric amplifiers (JPAs) are essential components in superconducting quantum circuits. However, higher order nonlinearities of the Josephson cosine potential are known to cause gain compression, therefore limiting scalability. In an effort to reduce the fourth order, or Kerr nonlinearity, we realize a parametric amplifier with an Al-InAs superconductor–semiconductor hybrid Josephson junction (JJ). We extract the Kerr nonlinearity of the Al-InAs JJ from two different devices and show that it is three orders of magnitude lower compared to an Al-AlOX junction with identical Josephson inductance. We then demonstrate a four-wave-mixing (4WM) parametric amplifier made with an Al-InAs junction that achieves more than 20 dB of gain and −119 dBm of compression power, which outperforms single resonant JPAs based on Al junctions.

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Near-quantum-limited amplifiers are essential building blocks for high-fidelity readout of superconducting qubits. Josephson parametric amplifiers (JPAs) have been developed to achieve this ultra-low-noise performance [1] in the last two decades by exploiting the quartic term in the nonlinear energy-phase relation of Al-AlO X superconductor-insulator-superconductor Josephson Junctions (SIS JJs). An ongoing research focus is to enhance JPAs’ compression power for processing readout signals in large-scale quantum processors. One approach is to optimize circuit designs to minimize parasitic higher-order nonlinear terms while preserving the quartic nonlinearity for the amplification process. An alternative approach is to make use of new types of JJ devices with small quartic nonlinearity such that parasitic nonlinearities are inherently even lower. Here, we demonstrate that superconductor-semiconductor-superconductor (SSmS) JJs, realized with Al-InAs heterostructures are a promising device to realize quantum-limited amplifiers for superconducting quantum computing. Al-InAs JJs have been used to realize qubits [2] , voltage-tunable resonators [3] , and parametric amplifiers [4] by exploiting critical current tunability via gate voltage ( Fig. 1(a–b) ). In this work, for the first time, we experimentally studied the nonlinear energy-phase relation of Al-InAs JJs and revealed their inherently low quartic nonlinearity. Next, we demonstrate a four-wave-mixing (4WM) parametric amplifier made with an Al-InAs junction that achieves greater than 20 dB of gain, 6 MHz of bandwidth and −119 dBm of compression power.

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Eli M. Levenson-Falk, R. Vijay, I. Siddiqi

We present the driven response at T=30 mK of 6 GHz superconducting resonators constructed from capacitively-shunted three-dimensional (3D) aluminum nanobridge superconducting quantum interference devices (nanoSQUIDs). We observe flux modulation of the resonant frequency in quantitative agreement with numerical calculation and characteristic of near-ideal short weak-link junctions. Under strong microwave excitation, we observe stable bifurcation in devices with coupled quality factor (Q) ranging from 30–3500. Near this bias point, parametric amplification with >20 dB gain, 40 MHz bandwidth, and near quantum-limited noise performance is observed. Our results indicate that 3D nanobridge junctions are attractive circuit elements to realize quantum bits.

arXiv:1101.4672•Applied Physics Letters•Mar 21, 2011•37 citations
Nonlinear microwave resonators are a versatile tool in quantum information processing, enabling parametric amplification, continuous variable quantum computing, and engineered mode interactions. Many of these applications especially benefit from cubic nonlinearities enabling three-wave mixing; at the same time, they are limited by quartic nonlinearities giving rise to undesired Kerr effects. A recurrent challenge is therefore to engineer resonators with a finite cubic nonlinearity while suppressing quartic terms. Here, we investigate a superconducting resonator hosting two weak links fabricated from an aluminum-capped indium arsenide nanowire. We characterize the Kerr nonlinearity as a function of magnetic flux and gate bias, showing that it can be tuned to zero with either control parameter. Furthermore, we experimentally demonstrate three-wave mixing in a semiconductor-superconductor hybrid device, establishing nonzero cubic nonlinearity. An effective model based on Andreev bound states qualitatively captures the observed trends. Our results validate semiconductor-superconductor hybrid devices as a promising platform for tunable nonlinear superconducting circuits, with applications in parametric amplification, quantum control of bosonic modes, and engineering interactions between microwave modes.
Nearly quantum limited Josephson parametric amplifiers (JPAs) are essential components in superconducting quantum circuits. However, higher order nonlinearities of the Josephson cosine potential are known to cause gain compression, therefore limiting scalability. In an effort to reduce the fourth order, or Kerr nonlinearity, we realize a parametric amplifier with an Al-InAs superconductor–semiconductor hybrid Josephson junction (JJ). We extract the Kerr nonlinearity of the Al-InAs JJ from two different devices and show that it is three orders of magnitude lower compared to an Al-AlOX junction with identical Josephson inductance. We then demonstrate a four-wave-mixing (4WM) parametric amplifier made with an Al-InAs junction that achieves more than 20 dB of gain and −119 dBm of compression power, which outperforms single resonant JPAs based on Al junctions.
Near-quantum-limited amplifiers are essential building blocks for high-fidelity readout of superconducting qubits. Josephson parametric amplifiers (JPAs) have been developed to achieve this ultra-low-noise performance [1] in the last two decades by exploiting the quartic term in the nonlinear energy-phase relation of Al-AlO X superconductor-insulator-superconductor Josephson Junctions (SIS JJs). An ongoing research focus is to enhance JPAs’ compression power for processing readout signals in large-scale quantum processors. One approach is to optimize circuit designs to minimize parasitic higher-order nonlinear terms while preserving the quartic nonlinearity for the amplification process. An alternative approach is to make use of new types of JJ devices with small quartic nonlinearity such that parasitic nonlinearities are inherently even lower. Here, we demonstrate that superconductor-semiconductor-superconductor (SSmS) JJs, realized with Al-InAs heterostructures are a promising device to realize quantum-limited amplifiers for superconducting quantum computing. Al-InAs JJs have been used to realize qubits [2] , voltage-tunable resonators [3] , and parametric amplifiers [4] by exploiting critical current tunability via gate voltage ( Fig. 1(a–b) ). In this work, for the first time, we experimentally studied the nonlinear energy-phase relation of Al-InAs JJs and revealed their inherently low quartic nonlinearity. Next, we demonstrate a four-wave-mixing (4WM) parametric amplifier made with an Al-InAs junction that achieves greater than 20 dB of gain, 6 MHz of bandwidth and −119 dBm of compression power.
Three-wave mixing is a key process in superconducting quantum information processing, being involved in quantum-limited amplification and parametric coupling between superconducting cavities. These operations can be implemented by superconducting nonlinear asymmetric inductive element (SNAIL)-based devices that present a Kerr-free flux-bias point where unwanted parasitic effects, such as Stark shift, are suppressed. However, with a single flux-bias parameter, these circuits can only host one Kerr-free point, limiting the range of their applications. In this Letter, we demonstrate how to overcome this constraint by introducing the gradiometric SNAIL, a doubly flux biased superconducting circuit in which both effective inductance and Kerr coefficient can be independently tuned. Experimental data show the capability of the gradiometric SNAIL to suppress the Kerr effect in a three-wave mixing parametric amplifier over a continuum of flux bias points corresponding to a 1.7 GHz range of operating frequencies.
Nonlinear microwave circuits are key elements for many groundbreaking research directions and technologies, such as quantum computation and quantum sensing. The majority of microwave circuits with Josephson nonlinearities to date is based on aluminum thin films, and therefore they are severely restricted in their operation range regarding temperatures and external magnetic fields. Here, we present the realization of superconducting niobium microwave resonators with integrated, three-dimensional (3D) nanobridge-based superconducting quantum interference devices. The 3D nanobridges (constriction weak links) are monolithically patterned into pre-fabricated microwave LC circuits using neon ion beam milling, and the resulting quantum interference circuits show frequency tunabilities, flux responsivities and Kerr nonlinearities on par with comparable aluminum nanobridge devices, but with the perspective of a much larger operation parameter regime. Our results reveal great potential for application of these circuits in hybrid systems with e.g. magnons and spin ensembles or in flux-mediated optomechanics.
Hybrid quantum systems play an essential role in efforts towards the advancements of quantum information technology and quantum sensing by bridging distinct technological platforms. In particular, hybrid systems comprising superconducting microwave circuits are being pursued intensely in light of existing achievements in superconducting qubits and precise quantum control in microwave circuits. Their realization relies on the design of superconducting resonators capable of coupling to an oscillatory mode of a second quantum system, facilitating the probing and manipulation of one via the other. In order to accommodate the coupled system, its particular constraints and requirements must be respected, which may be quite extreme from the perspective of established superconducting circuit design and operation. Overcoming this challenge has proved to be a substantial obstacle for the attainment of strongly coupled hybrid systems, despite spectacular advances in superconducting microwave circuits individually. In this work, we examine two approaches tackling this issue for different hybrid quantum systems, focusing on the optimization and characterization of the superconducting circuits. The first device aims at a superconductor-atom hybrid system through the coupling to Rydberg-Rydberg transitions in ultra-cold Rb-87 atoms trapped near the superconducting chip. Using simulations in conjunction with theoretical considerations, we demonstrate a comprehensive geometry parameter optimization procedure for maximum coupling rate. Presenting an experimental implementation of the resulting circuit, we validate its suitability for use under the intended operation conditions, including the option of tuning the electronic transition frequencies using a dc voltage. Secondly, we investigate a device designed for applications in large magnetic in-plane fields used to mediate coupling to integrated micromechanical oscillators; more specifically it is a flux-tunable SQUID resonator comprising Josephson nano-constrictions as nonlinear inductive components. Performing a thorough characterization of its frequency and Kerr anharmonicity tuning behavior at fields up to several hundred mT, we discover a pronounced asymmetry in its flux response at large fields. We show this asymmetry to be caused by the nano-constrictions turning into Josephson diodes, develop an intuitive macroscopic model for its field-induced emergence and reconstruct the diode current-phase relation from the flux tuning data. Several figures of merit informing the suitability of the SQUID resonators for optomechanical systems as well as other applications are improved by the diode effect, highlighting the potential of Josephson diodes in superconducting microwave circuits. Our results provide a promising stepping stone for the advancement of hybrid systems involving superconducting microwave circuits, putting new and exciting operation and coupling regimes within reach.
We present the driven response at T=30 mK of 6 GHz superconducting resonators constructed from capacitively-shunted three-dimensional (3D) aluminum nanobridge superconducting quantum interference devices (nanoSQUIDs). We observe flux modulation of the resonant frequency in quantitative agreement with numerical calculation and characteristic of near-ideal short weak-link junctions. Under strong microwave excitation, we observe stable bifurcation in devices with coupled quality factor (Q) ranging from 30–3500. Near this bias point, parametric amplification with >20 dB gain, 40 MHz bandwidth, and near quantum-limited noise performance is observed. Our results indicate that 3D nanobridge junctions are attractive circuit elements to realize quantum bits.