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arXiv:1511.01760 · Physical Review Applied

High-Kinetic-Inductance Superconducting Nanowire Resonators for Circuit QED in a Magnetic Field

Nodar Samkharadze, Alessandro Bruno, Pasquale Scarlino, Guoji Zheng, David Peter Divincenzo, L. DiCarlo, Lieven M. K. Vandersypen

Published Apr 7, 2016• 290 citations
arXivHTMLPDF

Abstract

Circuit quantum electrodynamics is a powerful approach for scaling up the number of qubits in quantum processors, but the standard planar superconducting microwave resonators are poorly compatible with electron-spin qubits. The authors produce resonators that address the two main hurdles impeding the adoption of such a scaling mechanism for spin qubits: They strongly suppress unwanted vortex generation in magnetic fields up to 6 T, and they are projected to yield ten times the coupling of conventional devices.

DOI
10.1103/physrevapplied.5.044004

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Circuit quantum electrodynamics is a powerful approach for scaling up the number of qubits in quantum processors, but the standard planar superconducting microwave resonators are poorly compatible with electron-spin qubits. The authors produce resonators that address the two main hurdles impeding the adoption of such a scaling mechanism for spin qubits: They strongly suppress unwanted vortex generation in magnetic fields up to 6 T, and they are projected to yield ten times the coupling of conventional devices.
Circuit quantum electrodynamics (QED) employs superconducting microwave resonators as quantum buses. In circuit QED with semiconductor quantum-dot-based qubits, increasing the resonator impedance is desirable as it enhances the coupling to the typically small charge dipole moment of these qubits. However, the gate electrodes necessary to form quantum dots in the vicinity of a resonator inadvertently lead to a parasitic port through which microwave photons can leak, thereby reducing the quality factor of the resonator. This is particularly the case for high-impedance resonators, as the ratio of their total capacitance over the parasitic port capacitance is smaller, leading to larger microwave leakage than for 50-x resonators. Here, we introduce an implementation of on-chip filters to suppress the microwave leakage. The filters comprise a high-kinetic-inductance nanowire inductor and a thin-film capacitor. The filter has a small footprint and can be placed close to the resonator, confining microwaves to a small area of the chip. The inductance and capacitance of the filter elements can be varied over a wider range of values than their typical spiral inductor and interdigitated capacitor counterparts. We demonstrate that the total linewidth of a 6.4 GHz and approximately 3-kx resonator can be improved down to 540 kHz using these filters.
Nonlinear superconducting devices, typically based on Josephson-junction (JJ) nonlinearities, are the basis for superconducting quantum electronics, enabling, e.g., the formation of isolated two-level superconducting qubits and amplifiers. While emerging spin, hybrid spin-superconducting (including Majorana), and nanomagneto-optical quantum systems could benefit tremendously from superconducting nonlinearities, the presence of strong magnetic fields in these systems is incompatible with conventional JJ devices, which are highly sensitive to applied magnetic fields. One potential solution is the use of kinetic inductance (KI) nonlinearity. To date, only linear KI devices have been shown to operate in high magnetic fields, while nonlinear KI device operation in high magnetic fields has received virtually no attention. Here, we study the nonlinearity of superconducting nanowire (NW) KI resonators and their performance as parametric amplifiers for in-plane magnetic fields. We study the Kerr coefficients of NW KI resonators made from 10-nm-thick $\mathrm{Nb}\text{\ensuremath{-}}\mathrm{Ti}\text{\ensuremath{-}}\mathrm{N}$ films with characteristic impedance up to 3 $\mathrm{k}\mathrm{\ensuremath{\Omega}}$, and demonstrate both nondegenerate and degenerate parametric amplification, at magnetic fields up to 2 T. We find that narrow KI resonators of width $0.1\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$ are robust, in terms of gain, dynamic range and noise, to magnetic fields up to approximately 2T2\phantom{\rule{0.2em}{0ex}}\mathrm{T}2T, for up to 12 dB (16 dB) of phase-insensitive (phase-sensitive) gain. In comparison, wider KI resonators of width $1\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{m}$ suffer significant suppression in the gain at fields well below 222 T. Around 8-dB deamplification is also observed for coherent states for a 0.1-$\text{\ensuremath{\mu}}\mathrm{m}$ NW KI resonator, implying the capability of noise squeezing. These results open a pathway to developing nonlinear quantum devices that operate in or generate high magnetic fields such as spin, hybrid spin-superconducting, and magneto-optomechanical devices.
One of the key elements in circuit quantum electrodynamics (cQED) is the superconducting microwave resonator, which can enable strong coupling to and between nanoscale quantum systems, and as a result has emerged as an essential tool for both quantum information and quantum sensing. In this thesis, I will discuss new applications of superconducting resonators in both of these fields, which illustrates how quantum information and quantum sensing can be strongly tied together. As the field of quantum information continues to grow, various platforms for realizing a quantum computer have been proposed. One attractive platform is to control and manipulate the spin of an electron to form spin qubits, which have demonstrated a long coherence time, weak coupling to the environment, and high fidelity single- and two-qubit gates. However, scaling beyond two qubits has proven challenging, as has incorporating long-range coupling, although both are crucial for making spin qubits a scalable quantum computing platform. The confinement of electromagnetic fields in superconducting resonators enables strong coupling to small systems, such as the single electrons of a spin qubit. In the first part of this thesis, I will describe how a singlet-triplet spin qubit coupled to a high-impedance superconducting resonator constitutes a promising architecture for mediating long-ranged interactions based on a longitudinal coupling between the resonator and qubit. I will discuss the technical developments needed to successfully implement this novel type of interaction in a hybrid spin qubit-resonator device. This type of interaction has several advantages over the more commonly studied transverse coupling scheme: it does not require careful tuning of the qubit frequency to match that of the resonator, which facilitates scaling to a large number of qubits, and also avoids the loss of coherence, which is inevitable in resonant coupling. This type of interaction therefore opens promising paths for generating high-fidelity long-ranged two-qubit coupling by employing superconducting microwave resonators. By adapting techniques used in quantum information, we have also developed a new technique in quantum sensing, where we employ superconducting resonators as a probe of quantum materials such as mesoscopic systems, two-dimensional materials, and heterostructures, which are otherwise challenging to experimentally access with conventional techniques. In the second part of my thesis, I will discuss how implementing cQED techniques from quantum information allows us to probe the symmetry of the order parameter in unconventional superconductors. Unconventional superconductors are not readily available, and we therefore study an engineered system that comprises of interfacing a ferromagnet and superconductor, in which unconventional pairing can be induced into the ferromagnet. This platform allows us to simultaneously excite spin waves, a collective excitation of spins, in the ferromagnet, which opens new directions for studying interactions between coherently coupled magnons (quanta of spin waves) and unconventional superconducting states. Finally, by applying the same technique to a two-dimensional (2D) superconductor, tungsten ditelluride, we leverage this platform in an attempt to study the order parameter of its intrinsic superconducting phase. The nature of the order parameter in this material remains an open question, as both topological and superconducting phases can exist, possibly simultaneously. This work thus demonstrates a unique use of superconducting resonators beyond quantum information applications.
Circuit quantum electrodynamics with qubits based on semiconductor quantum dots can enable long-range two-qubit gates between distant spins, or improve gate-based charge sensing for readout. Compared to conventional resonators, high-impedance resonators improve the coupling to the qubits, but their losses to the quantum dot's leads are also larger. This study implements on-chip filtering using high-kinetic-inductance nanowires and thin-film capacitors to mitigate this source of losses. These filters are very compact and easily extended to a large number of leads, all while preserving state-of-the-art resonator quality factors.
Quantum decoherence due to charge fluctuations is still a problem in many device architectures for quantum computing or metrology, but it can be suppressed by shunting the circuit with a high microwave impedance, known as a $s\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}e$. This study uses the kinetic inductance of a nanowire of disordered superconductor to demonstrate a low-loss, small-capacitance superinductor, in a simpler approach than the traditionally used Josephson-junction arrays. Such nanowire superinductors should have an impact on engineering long-lived superconducting qubits, and quantum-coherent experiments with mesoscopic systems.
As the field of superconducting quantum technology progresses beyond single-qubit control, scalable and multifunctional quantum architectures become increasingly vital. A central challenge is integrating fast, controllable superconducting circuits with components that offer longer coherence, richer physics, or new functionalities. Hybrid quantum systems, where superconducting microwave resonators interface with semiconducting or magnetic subsystems, have the capabilities to fulfil this need, yet they face significant engineering obstacles. Conventional superconducting resonator designs struggle under magnetic field biasing and electrostatic gating, both of which are essential for coupling to spin-based, semiconductor, or magnonic elements.This thesis explores solutions to these bottlenecks through the development of magnetic-field-resilient coplanar stripline (CPS) resonators based on thin-film NbTiN. These resonators retain a stable resonance frequency in in-plane magnetic fields up to 1T, can have high kinetic inductance and offer broad geometrical tunability, enabling strong and ultrastrong coupling to charge- and spin-based quantum systems. In the superconducting–semiconductor domain, we demonstrate high-impedance CPS resonators inductively coupled to Josephson junctions hosting Andreev bound states (ABSs), revealing both coherent pair transitions and single-quasiparticle excitations near the ultrastrong coupling regime. This opens the door to fast, gate-tunable qubits based on microscopic ABSs, distinct from conventional macroscopic qubit architectures, and lays the groundwork for spin–photon hybridisation, non-perturbative light–matter interactions, and parity-based quantum logic.In parallel, this work investigates rare-earth iron garnet (ReIG) ferrimagnetic insulators as low-loss spin-wave media compatible with superconducting devices. In sputtered thin-film thulium iron garnet (TmIG) with perpendicular magnetic anisotropy, we observe deterministic spin-orbit torque switching and multiple magnetisation polarity reversals. These properties showcase the attractiveness of TmIG both for low-dissipation magnonic information transport and as magnetic interfaces for superconducting hybrid devices. Taken together, the results of this thesis establish materials, device concepts, and measurement strategies for novel classes of hybrid quantum systems that combine robust superconducting circuitry, electrostatically tunable semiconductor excitations, and industry-scalable magnetic elements and pave the way for next-generation hybrid quantum systems. More broadly, they provide concrete routes to overcoming limitations of existing hybrid platforms and advance the development of versatile, low-dissipation quantum technologies.