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arXiv:2107.04131 · Physical Review Applied

Probing Hundreds of Individual Quantum Defects in Polycrystalline and Amorphous Alumina

Chih-Chiao Hung, Liuqi Yu, Neda Foroozani, Stefan Fritz, Dagmar Gerthsen, Kevin D. Osborn

Published Mar 9, 2022• 21 citations
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Abstract

Quantum two-level systems (TLSs) are present in the materials of qubits and are considered defects because they limit qubit coherence. For superconducting qubits, the quintessential Josephson junction barrier is made of amorphous alumina, which hosts TLSs. However, TLSs are not generally understood, either structurally or in atomic composition. In this study, we greatly extend the quantitative data available on TLSs by reporting on the physical dipole moment in two alumina types: polycrystalline $\ensuremath{\gamma}$-${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ and amorphous a-$\mathrm{Al}{\mathrm{O}}_{x}$. To obtain the dipole moments ${p}_{z}$, rather than the less-structural coupling parameter $g$, we tune individual TLSs with a known external electric field in a cavity quantum electrodynamic system. We find a clear difference in the dipole moment distribution from the film types, indicating a difference in TLS structures. A large sample of approximately 400 individual TLSs are analyzed from the polycrystalline film type. Their dipoles along the growth direction ${p}_{z}$ have a mean value of $2.6\ifmmode\pm\else\textpm\fi{}0.3$ debye (D) ($0.54\ifmmode\pm\else\textpm\fi{}0.06\phantom{\rule{0.1em}{0ex}}e$ \AA{}) and standard deviation $\ensuremath{\sigma}=1.6\ifmmode\pm\else\textpm\fi{}0.2\phantom{\rule{0.2em}{0ex}}\mathrm{D}$ ($0.33\ifmmode\pm\else\textpm\fi{}0.03\phantom{\rule{0.1em}{0ex}}e$ \AA{}). The material distribution fits well to a single Gaussian function. Approximately 200 individual TLSs are analyzed from amorphous films. Both the mean ${p}_{z}=4.6\ifmmode\pm\else\textpm\fi{}0.5\phantom{\rule{0.2em}{0ex}}\mathrm{D}$ ($0.96\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.1em}{0ex}}e$ \AA{}) and $\ensuremath{\sigma}=2.5\ifmmode\pm\else\textpm\fi{}0.3\phantom{\rule{0.2em}{0ex}}\mathrm{D}$ ($0.52\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.1em}{0ex}}e$ \AA{}) are larger. Amorphous alumina also has very large ${p}_{z}$, greater than $8.6\phantom{\rule{0.2em}{0ex}}\mathrm{D}$ ($1.8\phantom{\rule{0.1em}{0ex}}e$ \AA{}), in contrast to polycrystalline which has none of this moment. These large moments agree only with oxygen-based TLS models. Based on data and the candidate models (delocalized O and hydrogen-based TLSs), we find polycrystalline alumina has smaller ratio of O-based to H-based TLS than amorphous alumina.

DOI
10.1103/physrevapplied.17.034025

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Quantum two-level systems (TLSs) are present in the materials of qubits and are considered defects because they limit qubit coherence. For superconducting qubits, the quintessential Josephson junction barrier is made of amorphous alumina, which hosts TLSs. However, TLSs are not generally understood, either structurally or in atomic composition. In this study, we greatly extend the quantitative data available on TLSs by reporting on the physical dipole moment in two alumina types: polycrystalline \ensuremathγ\ensuremath{\gamma}\ensuremathγ-Al2O3{\mathrm{Al}}_{2}{\mathrm{O}}_{3}Al2​O3​ and amorphous a-AlOx\mathrm{Al}{\mathrm{O}}_{x}AlOx​. To obtain the dipole moments pz{p}_{z}pz​, rather than the less-structural coupling parameter ggg, we tune individual TLSs with a known external electric field in a cavity quantum electrodynamic system. We find a clear difference in the dipole moment distribution from the film types, indicating a difference in TLS structures. A large sample of approximately 400 individual TLSs are analyzed from the polycrystalline film type. Their dipoles along the growth direction pz{p}_{z}pz​ have a mean value of 2.6\ifmmode±\else\textpm\fi0.32.6\ifmmode\pm\else\textpm\fi{}0.32.6\ifmmode±\else\textpm\fi0.3 debye (D) (0.54\ifmmode±\else\textpm\fi0.06e0.54\ifmmode\pm\else\textpm\fi{}0.06\phantom{\rule{0.1em}{0ex}}e0.54\ifmmode±\else\textpm\fi0.06e \AA{}) and standard deviation \ensuremathσ=1.6\ifmmode±\else\textpm\fi0.2D\ensuremath{\sigma}=1.6\ifmmode\pm\else\textpm\fi{}0.2\phantom{\rule{0.2em}{0ex}}\mathrm{D}\ensuremathσ=1.6\ifmmode±\else\textpm\fi0.2D (0.33\ifmmode±\else\textpm\fi0.03e0.33\ifmmode\pm\else\textpm\fi{}0.03\phantom{\rule{0.1em}{0ex}}e0.33\ifmmode±\else\textpm\fi0.03e \AA{}). The material distribution fits well to a single Gaussian function. Approximately 200 individual TLSs are analyzed from amorphous films. Both the mean pz=4.6\ifmmode±\else\textpm\fi0.5D{p}_{z}=4.6\ifmmode\pm\else\textpm\fi{}0.5\phantom{\rule{0.2em}{0ex}}\mathrm{D}pz​=4.6\ifmmode±\else\textpm\fi0.5D (0.96\ifmmode±\else\textpm\fi0.1e0.96\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.1em}{0ex}}e0.96\ifmmode±\else\textpm\fi0.1e \AA{}) and \ensuremathσ=2.5\ifmmode±\else\textpm\fi0.3D\ensuremath{\sigma}=2.5\ifmmode\pm\else\textpm\fi{}0.3\phantom{\rule{0.2em}{0ex}}\mathrm{D}\ensuremathσ=2.5\ifmmode±\else\textpm\fi0.3D (0.52\ifmmode±\else\textpm\fi0.05e0.52\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.1em}{0ex}}e0.52\ifmmode±\else\textpm\fi0.05e \AA{}) are larger. Amorphous alumina also has very large pz{p}_{z}pz​, greater than 8.6D8.6\phantom{\rule{0.2em}{0ex}}\mathrm{D}8.6D (1.8e1.8\phantom{\rule{0.1em}{0ex}}e1.8e \AA{}), in contrast to polycrystalline which has none of this moment. These large moments agree only with oxygen-based TLS models. Based on data and the candidate models (delocalized O and hydrogen-based TLSs), we find polycrystalline alumina has smaller ratio of O-based to H-based TLS than amorphous alumina.
Material-based two-level systems (TLSs), appearing as defects in low-temperature devices including superconducting qubits and photon detectors, are difficult to characterize. In this study we apply a uniform dc electric field across a film to tune the energies of TLSs within. The film is embedded in a superconducting resonator such that it forms a circuit quantum electrodynamical system. The energy of individual TLSs is observed as a function of the known tuning field. By studying TLSs for which we can determine the tunneling energy, the actual p_{z}, dipole moments projected along the uniform field direction, are individually obtained. A distribution is created with 60 p_{z}. We describe the distribution using a model with two dipole moment magnitudes, and a fit yields the corresponding values p=p_{1}=2.8±0.2 D and p=p_{2}=8.3±0.4 D. For a strong-coupled TLS the vacuum-Rabi splitting can be obtained with p_{z} and tunneling energy. This allows a measurement of the circuit's zero-point electric-field fluctuations, in a method that does not need the electric-field volume.
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.
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.
Disordered thin films are a common choice of material for superconducting, high impedance circuits used in quantum information or particle detector physics. A wide selection of materials with different levels of granularity are available, but, despite low microwave losses being reported for some, the high degree of disorder always implies the presence of intrinsic defects. Prominently, quantum circuits are prone to interact with two-level systems (TLS), typically originating from solid state defects in the dielectric parts of the circuit, like surface oxides or tunneling barriers. We present an experimental investigation of TLS in granular aluminum thin films under applied mechanical strain and electric fields. The analysis reveals a class of strongly coupled TLS having electric dipole moments up to 30 eÅ, an order of magnitude larger than dipole moments commonly reported for solid state defects. Notably, these large dipole moments appear more often in films with a higher resistivity. Our observations shed new light on granular superconductors and may have implications for their usage as a quantum circuit material.
We perform ab initio calculations of hydrogen-based tunneling defects in alumina to identify deleterious two-level systems (TLS) in superconducting qubits. The defects analyzed include bulk hydrogenated Al vacancies, bulk hydrogen interstitial defects, and a surface OH rotor. The formation energies of the defects are first computed for an Al- and O-rich environment to give the likelihood of defect occurrence during growth. The potential energy surfaces are then computed and the corresponding dipole moments are evaluated to determine the coupling of the defects to an electric field. Finally, the tunneling energy is computed for the hydrogen defect and the analogous deuterium defect, providing an estimate of the TLS energy and the corresponding frequency for photon absorption. We predict that hydrogenated cation vacancy defects will form a significant density of GHz frequency TLSs in alumina.
While two-level systems (TLSs) are ubiqitous in solid state systems, microscopic understanding of their nature remains an outstanding problem. Conflicting phenomenological models are used to describe TLSs in seemingly similar materials when probed with different experimental techniques. Specifically, bulk measurements in amorphous solids have been interpreted using the model of a tunneling atom or group of atoms, whereas TLSs observed in the insulating barriers of Josephson junction qubits have been understood in terms of tunneling of individual electrons. Motivated by recent experiments studying TLSs in Josephson junctions, especially the effects of elastic strain on TLS properties, we analyze the interaction of the electronic TLS with phonons. We demonstrate that strong polaronic effects lead to dramatic changes in TLS properties. Our model gives a quantitative understanding of the TLS relaxation and dephasing as probed in Josephson junction qubits, while providing an alternative interpretation of bulk experiments. We demonstrate that a model of polaron dressed electronic TLS leads to estimates for the density and distribution of parameters of TLSs consistent with bulk experiments in amorphous solids. This model explains such surprising observations of recent experiments as the existence of minima in the energy of some TLSs as a function of strain and makes concrete predictions for the character of TLS dephasing near such minima. We argue that better understanding of the microscopic nature of TLSs can be used to improve properties of quantum devices, from an enhancement of relaxation time of TLSs to creating new types of strongly interacting optomechanical systems.