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arXiv:cond-mat/0501236

Nonlinear Coupling in Nb/NbN Superconducting Microwave Resonators

Baleegh Abdo, Eran Segev, Oleg Shtempluck, Eyal Buks

Published Jan 11, 2005• 4 citations
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Abstract

In this experimental study we show that the coupling between Nb/NbN superconducting microwave resonators and their feedline can be made amplitude dependent. We employ this mechanism to tune the resonators into critical coupling condition, a preferable mode of operation for a wide range of applications. Moreover we examine the dependence of critical coupling state on other parameters such as temperature and magnetic field. Possible novel applications based on such nonlinear coupling are briefly discussed.

DOI
10.48550/arxiv.cond-mat/0501236

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In this experimental study we show that the coupling between Nb/NbN superconducting microwave resonators and their feedline can be made amplitude dependent. We employ this mechanism to tune the resonators into critical coupling condition, a preferable mode of operation for a wide range of applications. Moreover we examine the dependence of critical coupling state on other parameters such as temperature and magnetic field. Possible novel applications based on such nonlinear coupling are briefly discussed.
We present a tunable coupler scheme that allows us to tune the coupling strength between a feedline and a superconducting resonator in situ over a wide range. In this scheme, we shunt the feedline with a 50-Ω lumped-element nonlinear transmission line made from a 20 nm NbTiN film. By injecting a DC current, the nonlinear kinetic inductance changes and the effective impedance shunting the resonator periodically varies from a short to an open, which tunes the coupling strength and coupling quality factor Qc. We have demonstrated Qc tuning over a factor of 40, between Qc∼5.5×104 and Qc∼2.3×106, for a 4.5 GHz resonator by applying a DC current less than 3.3 mA. Our tunable coupler scheme is easy to implement and may find broad applications in superconducting detector and quantum computing/information experiments.
Abstract Superconducting resonators and parametric amplifiers are important components in scientific systems such as kinetic inductance detector arrays, frequency-domain multiplexers for other superconducting bolometers, spin-ensemble based memories, and circuit quantum electrodynamics demonstrators. In this paper, we report microwave measurements of superconducting Ti, Nb, and NbN resonators and their use as parametric amplifiers. These half-wave resonators were fabricated under near identical sputtering and lithographic conditions to ensure a like-for-like comparison of material properties. We report a wide range of properties and behaviours in terms of transition temperatures, resistivities, rate-limiting nonlinear response times, nonlinear dissipation, signs of the nonlinear inductances and their dependences on temperature and resonance harmonic. We have successfully operated Nb and NbN resonators as high gain parametric amplifiers, achieving greater than 20 dB of power amplification. We have shown that for a half-wave resonator, amplification can be realised not only in the fundamental resonance but also in the higher harmonic resonances. Further, for materials with high transition temperatures, e.g. Nb and NbN, amplification can be achieved at ∼ 4 K, i.e. a temperature maintained by a pulse tube cooler. Finally, in materials systems that have very fast response times, e.g. NbN, we have found that a cross-harmonic type of amplification can be achieved by placing pump tone in a different resonant mode as the signal and the idler. This wide range of observations will have important implications on the design and application of superconducting parametric amplifiers.
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In the circuit quantum electrodynamics architecture, both the resonance frequency and the coupling of superconducting qubits to microwave field modes can be controlled via external electric and magnetic fields to explore qubit-photon dynamics in a wide parameter range. Here, we experimentally demonstrate and analyze a scheme for tuning the coupling between a transmon qubit and a microwave resonator using a single coherent drive tone. We treat the transmon as a three-level system, with the qubit subspace defined by the ground and the second excited states. If the drive frequency matches the difference between the resonator and the qubit frequencies, a Jaynes-Cummings-type interaction is induced, which is tunable in both amplitude and phase. We show that coupling strengths of about 10 MHz can be achieved in our setup, limited only by the anharmonicity of the transmon qubit. This scheme has been successfully used to generate microwave photons with a controlled temporal shape [M. Pechal et al., Phys. Rev. X 4, 041010 (2014)] and can be directly implemented with superconducting quantum devices featuring larger anharmonicity for higher coupling strengths.
We propose tunable superconducting split-ring resonators (SRRs) employing nonlinear Josephson inductance. A fraction of SRR is replaced by Nb-AlOx-Nb Josephson tunnel junctions connected in parallel and forming a superconducting quantum interference device, whose inductance is sensitive to the external dc magnetic field. Due to the lumped nature of the Josephson inductance, the SRR can be made very compact, and its resonance frequency can be tuned by applying magnetic field. We present the model, results of extensive electromagnetic-simulation and experimental data for the SRR weakly coupled to a transmission line within frequency range of 11–13 GHz.