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arXiv:2203.05054 · Physical Review Applied

Modeling Dielectric Loss in Superconducting Resonators: Evidence for Interacting Atomic Two-Level Systems at the Nb/Oxide Interface

Noah Gorgichuk, Tobias Junginger, Rogério de Sousa

Published Feb 2, 2023• 12 citations
arXivHTMLPDF

Abstract

While several experiments claim that two-level system (TLS) defects in amorphous surfaces and interfaces are responsible for energy relaxation in superconducting resonators and qubits, none can provide quantitative explanation of their data in terms of the conventional noninteracting TLS model. Here a model that interpolates between the interacting and noninteracting TLS loss tangent is proposed to perform numerical analysis of experimental data and extract information about TLS parameters and their distribution. As a proof of principle, the model is applied to TESLA cavities that contain only a single lossy material in their interior, the niobium-niobium oxide interface. The best fits show interacting TLSs with a sharp modulus of electric dipole moment for both thin ($5\phantom{\rule{0.2em}{0ex}}\mathrm{nm}$) and thick ($100\phantom{\rule{0.2em}{0ex}}\mathrm{nm}$) oxides, indicating that the TLSs are ``atomic'' instead of ``glassy.'' The proposed method can be applied to other devices with multiple material interfaces and substrates, with the goal of elucidating the nature of TLSs causing energy loss in resonators and qubits.

DOI
10.1103/physrevapplied.19.024006

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While several experiments claim that two-level system (TLS) defects in amorphous surfaces and interfaces are responsible for energy relaxation in superconducting resonators and qubits, none can provide quantitative explanation of their data in terms of the conventional noninteracting TLS model. Here a model that interpolates between the interacting and noninteracting TLS loss tangent is proposed to perform numerical analysis of experimental data and extract information about TLS parameters and their distribution. As a proof of principle, the model is applied to TESLA cavities that contain only a single lossy material in their interior, the niobium-niobium oxide interface. The best fits show interacting TLSs with a sharp modulus of electric dipole moment for both thin (5nm5\phantom{\rule{0.2em}{0ex}}\mathrm{nm}5nm) and thick (100nm100\phantom{\rule{0.2em}{0ex}}\mathrm{nm}100nm) oxides, indicating that the TLSs are atomic'' instead of glassy.'' The proposed method can be applied to other devices with multiple material interfaces and substrates, with the goal of elucidating the nature of TLSs causing energy loss in resonators and qubits.
noise caused by microscopic two-level systems (TLS) is known to be very detrimental to the performance of superconducting quantum devices but the nature of these TLS is still poorly understood. Recent experiments with superconducting resonators indicates that interaction between TLS in the oxide at the film-substrate interface is not negligible. Here we present data on the loss and frequency noise from two different Nb resonators with and without Pt capping and discuss what conclusions can be drawn regarding the properties of TLS in amorphous oxides. We also estimate the concentration and dipole moment of the TLS.
1/f noise caused by microscopic two-level systems (TLS) is known to be very detrimental to the performance of superconducting quantum devices but the nature of these TLS is still poorly understood. Recent experiments with superconducting resonators indicates that interaction between TLS in the oxide at the film-substrate interface is not negligible. Here we present data on the loss and 1/f frequency noise from two different Nb resonators with and without Pt capping and discuss what conclusions can be drawn regarding the properties of TLS in amorphous oxides. We also estimate the concentration and dipole moment of the TLS.
Quantum two-level systems (TLSs) commonly found at low temperature in amorphous and disordered materials are responsible for decoherence in superconducting Josephson junction qubits particularly because they absorb energy of coherent qubit oscillations in the microwave frequency range. In planar Josephson resonators with oxide interfaces this absorption is characterized by an anomalously weak loss tangent dependence on the field in the non-linear regime that conflicts with the theoretical expectations and the observations in amorphous dielectrics. It was recently suggested that this anomalous absorption is due to TLS dynamic interactions. Here we show that such interactions cannot lead to the observed loss-tangent field dependence and suggest the alternative explanation assuming that TLS dipole moments ppp are distributed according to the specific power law P(p)∝1/p3−ηP(p) \propto 1/p^{3-η}P(p)∝1/p3−η (0≤η<10\leq η<10≤η<1). This assumption, indeed, results in the observed loss tangent behavior. The hypothesis of a power law distribution is supported both by the recent measurements of individual TLS dipole moments and the theoretical model of TLS formation due to the long-range dipole-dipole interaction, thus connecting the anomalous absorption with the possible solution of the long-standing problem of the nature of TLSs.
Superconducting films are inherently limited by losses due to two-level system (TLS) defects within the amorphous oxide layers surrounding them and from quasiparticles in the film. In this thesis I will discuss novel theoretical and experimental methods toward understanding superconducting resonator loss from deleterious surface TLS defects as well as a loss transition from non-equilibrium quasiparticles in granular TiN. I will show using finite element solver software that a resonator with submicron linewidth and linespacing can be used to better characterize and simulate surface TLS as part of a circuit QED system. I have observed individual surface TLS and found coupling values in the range of g/2π =50 kHz -280 kHz with a maximum dipole moment pz-max = 4.5 Debye (.93 eÅ). I have found in in simulation of experiment that over 80% of the strongly coupled TLS reside within 50 nm of the corner between the Metal-Substrate (MS) and Substrate-Air (SA) interface. Additionally I have studied a loss transition from non-equilibrium quasiparticles in TiN films. These films exhibit an anomalous loss dependence on substrate treatment and film thickness. The films of interest are ones grown thin on oxidized substrates, which exhibit an order of magnitude decrease in internal quality factor (Qi) relative to either thicker ˝films or films grown without the oxidized substrate. These films additionally exhibit a grain size on average of 7.5 nm, a higher inhomogeneous gap, a transition to lower stress and a preference for the [111] crystal growth. The temperature dependence of the conductivity is fit and a factor of two difference in quasiparticle lifetime is found between the two films where the thinner film has a shorter lifetime. A two gap quasiparticle trapping model is fit to the temperature dependent loss data. The data is consistent with a model where non-equilibrium quasi-particles are trapped in low gapped grains on the inside of the films. From these works and others presented in my thesis the understanding of TLSs on surfaces and non-equilibrium quasiparticles in TiN has improved. This will help illuminate some of the most important absorption mechanisms plaguing superconducting qubits and resonators.
Quantum sensing and computation can be realized with superconducting microwave circuits. Qubits are engineered quantum systems of capacitors and inductors with non-linear Josephson junctions. They operate in the single-excitation quantum regime, photons of 27μ27 μ27μeV at 6.5 GHz. Quantum coherence is fundamentally limited by materials defects, in particular atomic-scale parasitic two-level systems (TLS) in amorphous dielectrics at circuit interfaces.[1] The electric fields driving oscillating charges in quantum circuits resonantly couple to TLS, producing phase noise and dissipation. We use coplanar niobium-on-silicon superconducting resonators to probe decoherence in quantum circuits. By selectively modifying interface dielectrics, we show that most TLS losses come from the silicon surface oxide, and most non-TLS losses are distributed throughout the niobium surface oxide. Through post-fabrication interface modification we reduced TLS losses by 85% and non-TLS losses by 72%, obtaining record single-photon resonator quality factors above 5 million and approaching a regime where non-TLS losses are dominant. [1]Müller, C., Cole, J. H. & Lisenfeld, J. Towards understanding two-level-systems in amorphous solids: insights from quantum circuits. Rep. Prog. Phys. 82, 124501 (2019)
Quantum two-level systems (TLSs) intrinsic to glasses induce decoherence in many modern quantum devices, such as superconducting qubits. Although the low-temperature physics of these TLSs is usually well-explained by a phenomenological standard tunneling model of independent TLSs, the nature of these TLSs, as well as their behavior out of equilibrium and at high energies above 1 K, remain inconclusive. Here we measure the non-equilibrium dielectric loss of TLSs in amorphous silicon using a superconducting resonator, where energies of TLSs are varied in time using a swept electric field. Our results show the existence of two distinct ensembles of TLSs, interacting weakly and strongly with phonons, where the latter also possesses anomalously large electric dipole moment. These results may shed new light on the low temperature characteristics of amorphous solids, and hold implications to experiments and applications in quantum devices using time-varying electric fields.