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IEEE Transactions on Applied Superconductivity

Nonlinear Microwave Circuit Based on Niobium Nanobridges Fabricated With Ne FIB

Parth Bhandari, Laith Meti, Tom Godfrey, Tian Bai, Benjamin White, Gemma Chapman, Edward J. Romans, John C. Gallop, Olena Shaforost, Ling Yun Hao

Published Apr 9, 2026• 0 citations
Publisher

Abstract

Recently the exploration of nonlinear microwave response in superconducting circuits has been extended to Nb nanobridges that can operate at higher magnetic fields, frequencies, and temperatures than their conventional Al counterparts. Nb nanobridge-based Superconducting Quantum Interference Devices (SQUIDs) have shown potential applications in quantum information processing, weak signal detection, and single spin detection. Combining such non-linear elements with circuit Quantum Electrodynamic (QED) elements like coplanar waveguide (CPW) resonators allows the study of the nonlinearity of such systems. In this work we report on the design, fabrication and dispersive microwave readout of a Nb DC nanoSQUID embedded in a superconducting quarter-wavelength resonator. The measured flux-tuneability of the resonance shows a modulation of a few MHz and fits simulations, giving a critical current of 330 μA and a screening parameterβLof 4.07. Following this we present results showing Kerr-type detuning with a pump tone applied to the device.

DOI
10.1109/tasc.2026.3682693

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Recently the exploration of nonlinear microwave response in superconducting circuits has been extended to Nb nanobridges that can operate at higher magnetic fields, frequencies, and temperatures than their conventional Al counterparts. Nb nanobridge-based Superconducting Quantum Interference Devices (SQUIDs) have shown potential applications in quantum information processing, weak signal detection, and single spin detection. Combining such non-linear elements with circuit Quantum Electrodynamic (QED) elements like coplanar waveguide (CPW) resonators allows the study of the nonlinearity of such systems. In this work we report on the design, fabrication and dispersive microwave readout of a Nb DC nanoSQUID embedded in a superconducting quarter-wavelength resonator. The measured flux-tuneability of the resonance shows a modulation of a few MHz and fits simulations, giving a critical current of 330 μA and a screening parameterβLof 4.07. Following this we present results showing Kerr-type detuning with a pump tone applied to the device.
Niobium nanobridge SQUIDs have shown exceptional noise performance with potential applications in quantum information processing, weak signal detection and single spin detection where the nanobridge geometry should enable efficient electromagnetic coupling to implanted spins. Combining such devices with dispersive microwave readout circuitry allows the spin sensitivity to be further improved by overcoming the standard thermal limit. Here we report on the fabrication and dispersive microwave readout of an array of niobium nanobridge rf SQUIDs incorporated into a superconducting resonator, including the optimization of the nanobridge fabrication process by electron beam lithography. We show the measured flux-tuneability of the resonance is in good agreement with theory, and we also discuss how the nonlinearity of the weak-link in the resonator structure allows for the mediation of parametric effects to enhance performance.
Superconducting circuits play a crucial role in the advancement of quantum computing and quantum sensing. Typically such circuits require the presence of a non-linear element, where the engineered anharmonicity (Kerr factor) and resonant linewidth determine the potential applications of the circuit. In this work we have fabricated Nb-based CPW resonators embedded with a DC SQUID incorporating Nb nanobridges as the weak links. We use two-tone spectroscopy to study the non-linear behaviour of the device at 15 mK up to a field of 2.48 mT. Under the application of a blue-detuned pump, the device shows a decrease in the resonant frequency which is used to estimate the Kerr factor. We further apply a red-detuned pump to go beyond the bifurcation threshold and observe the appearance of an additional idler mode with net gain. The gain of the device was maximized by further decreasing the pump frequency, showing a maximum amplification of 15 dB. Finally, we show agreement between the Kerr non-linear oscillator model and the measured transmission spectrum, and highlight further design modifications to improve the gain and bandwidth of such devices.
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.
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 are based on aluminum thin films; 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 prefabricated microwave LCLCLC circuits using neon focused-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 demonstrate that neon focused-ion-beam milling is a promising method for fabricating 3D constriction junctions with flexible parameters and reveal great potential for application of the resulting microwave circuits in hybrid systems with, e.g., magnons and spin ensembles or in flux-mediated optomechanics.
In this licentiate thesis, I present the design, fabrication, and characterization of superconducting parametric resonators, for use in quantum information processing. These devices are quarter-wavelength coplanar waveguide resonators (~5 GHz), terminated at one end by a non-linear inductance provided by a SQUID (superconducting quantum interference device). The SQUID acts as a flux-controlled boundary condition, which effectively changes the electrical length of the resonator. This enables the modulation of the resonant frequency by coupling microwave magnetic flux into the SQUID, using on-chip transmission lines. The modulation occurs on a timescale much faster than the photon loss out of the resonator. The non-linearity provides several different regimes for operating this device. I focused on the parametric regime, in which the non-linear element was being modulated (pumped) at or near twice the resonant frequency. This pumping can lead to amplification and frequency conversion of an incoming signal. It can also give rise to instabilities and self-oscillations "parametric oscillations" - that is, the generation of an intense electric field in the resonator (the creation of photons). Parametric oscillations set in when the pumping strength exceeds a threshold value, and also depends on the pump-frequency detuning from twice the resonance and on the static flux through the SQUID. I characterized the devices over a wide parameter range by doing homodyne detection of the reflected signal or of the emitted field oscillations. In particular, I investigated the damping and two leading nonlinearities, dominating in different operating regimes, which influence the dynamics of the parametric resonator. First, I extracted the Duffing nonlinearity by studying the line width of the resonator as a function of the input signal (without pumping the SQUID). Second, with high pump amplitude, I extracted the pump-induced nonlinearity by determining the threshold parameters (pump amplitude and detuning) for the onset of parametric oscillations; this nonlinearity leads to the generation of higher-order pump terms that complicate the system dynamics, but can be mitigated now that they have been understood. My results validate a recent theoretical model for the classical, non-linear dynamics of parametric resonance, and helps determine workable design parameters. Finally, I helped develop a linearized model −-− the "pumpistor" - describing this device in terms of a flux-controlled impedance. This will be useful when designing more complex circuits. One goal of this work is to demonstrate single-shot measurements on superconducting qubits (quantum bits of information). We will use the parametric resonator as a threshold discriminator, associating the qubit's two energy eigenstates with the parametric oscillations either turning on or not. This would be a very useful device in the quantum engineer's toolbox when designing systems for quantum information processing and communication.
Niobium-based nanobridge superconducting quantum interference devices (SQUIDs) have shown very low noise performance and high-frequency operation. We describe how we are bringing together these two aspects of nanobridge SQUIDs with the aim of realizing single spin-flip detection using microwave inductive readout techniques, where the nanobridge SQUID is integrated into a superconducting coplanar waveguide resonator. Using electron beam lithography (EBL) is ideal for fabricating nanobridge junctions and has the advantage of being easily scalable compared to using a focused ion beam. In this article, we demonstrate that EBL is suitable for fabricating nanobridge junction SQUIDs, and they exhibit very comparable performance to previous focused ion beam milled SQUIDs. Our integrated devices show potential to be used for flux-tunable sensors.