Dissipative two-level systems (TLS) have been a long-standing problem in glassy solids over the last fifty years, and have recently gained new relevance as sources of decoherence in quantum computing. Resonant absorption by TLSs in the dielectric poses a serious limitation to the performance of superconducting qubits; however, the microscopic nature of these systems has yet to be established. Based on first-principles calculations, we propose that hydrogen impurities in Al2O3 are the main source of TLS resonant absorption. Hydrogen is an ubiquitous impurity and can easily incorporate in Al2O3. We find that interstitial H in Al2O3 forms a hydrogen bond (O-H...O). At specific O-O distances, consistent with bond lengths found in amorphous Al2O3 or near Al2O3 surfaces or interfaces, the H atom feels a double well. Tunneling between two symmetric positions gives rise to resonant absorption in the range of 10 GHz, explaining the experimental observations. We also calculate the expected qubit-TLS coupling and find it to lie between 16 and 20 MHz, consistent with experimental measurements.
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 $\ensuremath{\gamma}$-
Al2O3 and amorphous a-
AlOx. To obtain the dipole moments
pz, 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
pz 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
pz, greater than
8.6D (
1.8e \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.
Superconducting qubits are often adversely affected by two-level systems (TLSs) within the Josephson junction, which contribute to decoherence and subsequently limit the performance of the qubit. By treating the TLS as a soft (i.e., low-frequency) bosonic mode localized in real space, we find that a single TLS in either the amorphous-oxide surface or the superconducting bulk may result in a localized “hot spot” of amplified Josephson energy. Such amplification is shown to have a non-negligible effect on the T 1 time of a simple phase qubit, regardless of whether or not the TLS is on resonance with the qubit frequency. With this study, we identify unique fingerprints of TLS defects in the Josephson current and qubit decoherence time.
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.
Reduced transmon qubit
T1 coherence times have been linked to the amorphous oxide layers formed by thin film capacitors during processing. Because Ta or Ta capped Nb capacitors exhibit overall superior qubit performance to those fabricated with Nb capacitors, it has been hypothesized that the amorphous, non-stoichiometric Ta
2O
5−x oxide is less lossy than its Nb
2O
5−x counterpart. The origins of what makes amorphous Ta
2O
5−x less susceptible to accepted decoherence channels is unknown. Here we establish the microscopic features of amorphous Nb
2O
5−x and Ta
2O
5−x using a combination of \textit{ab initio} molecular dynamics and density functional theory calculations. Our simulations establish that oxygen deficiency is less likely to occur in amorphous Ta
2O
5−x than in Nb
2O
5−x for
0≤x≤0.25 and that at a given level of oxygen deficiency the formation of metal Ta-Ta bonds is enhanced. These bonds, which are accommodated by structural flaws in the amorphous network, capture electrons better than in amorphous Nb
2O
5−x. These thermochemical differences quench or highly suppress magnetic moments in amorphous Ta
2O
5−x and eliminate a potential source of quasiparticles and magnetic flux noise. Our calculations also show that hyperfine couplings between Nb nuclei and local magnetic moments in Nb
2O
5−x could form "two-level systems" (TLS) or "two-level fluctuators" (TLF) with energy splittings of 100-1000 MHz or higher. This reveals a new TLS mechanism in amorphous Nb
2O
5−x oxide layers that is unlikely in Ta
2O
5−x. Our work provides fundamental understanding of the materials chemistry and limitations imposed by native oxides of superconducting qubits, which can be used to guide materials selection and processing.
Qubits made from superconducting materials are a mature platform for quantum information science application, such as quantum computing. However, material-based losses are now a limiting factor in reaching the coherence times needed for applications. In particular, knowledge of the atomistic structure and properties of the circuit materials is needed to identify, understand, and mitigate material-based decoherence channels. In this work, we characterize the atomic structure of the native oxide film formed on Nb resonators by comparing fluctuation electron microscopy experiments to density functional theory calculations, finding that an amorphous layer is consistent with an Nb2O5 stoichiometry. Comparing x-ray absorption measurements at the Oxygen K edge with first-principles calculations, we find evidence of d-type magnetic impurities in our sample, known to cause impedance in proximal superconductors. This work identifies the structural and chemical composition of the oxide layer grown on Nb superconductors and shows that soft x-ray absorption can fingerprint magnetic impurities in these superconducting systems.