Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1501.05865 · Physical Review Letters

Projected Dipole Moments of Individual Two-Level Defects Extracted Using Circuit Quantum Electrodynamics

Bahman Sarabi, Aruna N. Ramanayaka, Alexander L. Burin, F. C. Wellstood, Kevin D. Osborn

Published Apr 22, 2016• 68 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.116.167002

Related papers

Probing Hundreds of Individual Quantum Defects in Polycrystalline and Amorphous Alumina

Chih-Chiao Hung, Liuqi Yu, Neda Foroozani +3 more

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.

arXiv:2107.04131•Physical Review Applied•Mar 9, 2022•21 citations

Cavity quantum electrodynamics using a near-resonance two-level system: Emergence of the Glauber state

B. Sarabi, Aruna N. Ramanayaka, Alexander L. Burin +2 more

Random tunneling two-level systems (TLSs) in dielectrics have been of interest recently because they adversely affect the performance of superconducting qubits. The coupling of TLSs to qubits has allowed individual TLS characterization, which has previously been limited to TLSs within (thin) Josephson tunneling barriers made from aluminum oxide. Here, we report on the measurement of an individual TLS within the capacitor of a lumped-element LC microwave resonator, which forms a cavity quantum electrodynamics (CQED) system and allows for individual TLS characterization in a different structure and material than demonstrated with qubits. Due to the reduced volume of the dielectric (80 μm3), even with a moderate dielectric thickness (250 nm), we achieve the strong coupling regime as evidenced by the vacuum Rabi splitting observed in the cavity spectrum. A TLS with a coherence time of 3.2 μs was observed in a film of silicon nitride as analyzed with a Jaynes-Cummings spectral model, which is larger than seen from superconducting qubits. As the drive power is increased, we observe an unusual but explicable set of continuous and discrete crossovers from the vacuum Rabi split transitions to the Glauber (coherent) state.

arXiv:1405.0264•Applied Physics Letters•Apr 27, 2015•20 citations

Giant Two-Level Systems in a Granular Superconductor

M Donnell Kristen, Jan Nicolas Voss, Micha Wildermuth +4 more

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.

arXiv:2307.09078•Physical Review Letters•May 22, 2024•14 citations

Quantum sensors for microscopic tunneling systems

Alexander Bilmes, Serhii Volosheniuk, Jan David Brehm +2 more

Abstract The anomalous low-temperature properties of glasses arise from intrinsic excitable entities, so-called tunneling Two-Level-Systems (TLS), whose microscopic nature has been baffling solid-state physicists for decades. TLS have become particularly important for micro-fabricated quantum devices such as superconducting qubits, where they are a major source of decoherence. Here, we present a method to characterize individual TLS in virtually arbitrary materials deposited as thin films. The material is used as the dielectric in a capacitor that shunts the Josephson junction of a superconducting qubit. In such a hybrid quantum system the qubit serves as an interface to detect and control individual TLS. We demonstrate spectroscopic measurements of TLS resonances, evaluate their coupling to applied strain and DC-electric fields, and find evidence of strong interaction between coherent TLS in the sample material. Our approach opens avenues for quantum material spectroscopy to investigate the structure of tunneling defects and to develop low-loss dielectrics that are urgently required for the advancement of superconducting quantum computers.

arXiv:2011.14327•npj Quantum Information•Feb 5, 2021•32 citations

Experimentally revealing anomalously large dipoles in the dielectric of a quantum circuit

Liuqi Yu, Shlomi Matityahu, Yaniv Jacob Rosen +5 more

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.

arXiv:2110.10747•Scientific Reports•Oct 10, 2022•6 citations

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

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.

arXiv:2203.05054•Physical Review Applied•Feb 2, 2023•12 citations
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.
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{\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 $2.6\ifmmode\pm\else\textpm\fi{}0.3$ 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{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.
Random tunneling two-level systems (TLSs) in dielectrics have been of interest recently because they adversely affect the performance of superconducting qubits. The coupling of TLSs to qubits has allowed individual TLS characterization, which has previously been limited to TLSs within (thin) Josephson tunneling barriers made from aluminum oxide. Here, we report on the measurement of an individual TLS within the capacitor of a lumped-element LC microwave resonator, which forms a cavity quantum electrodynamics (CQED) system and allows for individual TLS characterization in a different structure and material than demonstrated with qubits. Due to the reduced volume of the dielectric (80 μm3), even with a moderate dielectric thickness (250 nm), we achieve the strong coupling regime as evidenced by the vacuum Rabi splitting observed in the cavity spectrum. A TLS with a coherence time of 3.2 μs was observed in a film of silicon nitride as analyzed with a Jaynes-Cummings spectral model, which is larger than seen from superconducting qubits. As the drive power is increased, we observe an unusual but explicable set of continuous and discrete crossovers from the vacuum Rabi split transitions to the Glauber (coherent) state.
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.
Abstract The anomalous low-temperature properties of glasses arise from intrinsic excitable entities, so-called tunneling Two-Level-Systems (TLS), whose microscopic nature has been baffling solid-state physicists for decades. TLS have become particularly important for micro-fabricated quantum devices such as superconducting qubits, where they are a major source of decoherence. Here, we present a method to characterize individual TLS in virtually arbitrary materials deposited as thin films. The material is used as the dielectric in a capacitor that shunts the Josephson junction of a superconducting qubit. In such a hybrid quantum system the qubit serves as an interface to detect and control individual TLS. We demonstrate spectroscopic measurements of TLS resonances, evaluate their coupling to applied strain and DC-electric fields, and find evidence of strong interaction between coherent TLS in the sample material. Our approach opens avenues for quantum material spectroscopy to investigate the structure of tunneling defects and to develop low-loss dielectrics that are urgently required for the advancement of superconducting quantum computers.
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.
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.