Two-level Tunneling Systems Research Articles

Phonon engineering of atomic-scale defects in superconducting quantum circuits.

Noise within solid-state systems at low temperatures can typically be traced back to material defects. In amorphous materials, these defects are broadly described by the tunneling two-level systems (TLSs) model. TLS have recently taken on further relevance in quantum computing because they dominate the coherence limit of superconducting quantum circuits. Efforts to mitigate TLS impacts have thus far focused on circuit design, material selection, and surface treatments. Our work takes an approach that directly modifies TLS properties. This is achieved by creating an acoustic bandgap that suppresses all microwave-frequency phonons around the operating frequency of a transmon qubit. For embedded TLS strongly coupled to the transmon qubit, we measure a pronounced increase in relaxation time by two orders of magnitude, with the longest T1 time exceeding 5 milliseconds. Our work opens avenues for studying the physics of highly coherent TLS and methods for mitigating noise within solid-state quantum devices.

Spontaneous noise of birefringence in rare-earth doped glasses

We report on first direct observation of spontaneous fluctuations of birefringence in glasses doped with rare-earth (RE) ions. The fluctuations were observed in Nd3+- and Yb3+-doped glasses as polarization noise of the laser beam transmitted through the sample in the region of the RE-ion absorption. The noise was characterized by a flat (“white”) spectrum in the range of frequencies up to 1 GHz and did not show any dependence on magnetic field. The discovered polarization noise is interpreted in terms of structural dynamics of glasses revealed at low temperatures and usually described in the model of tunneling two-level systems (TLS). High sensitivity of the polarization noise technique to this dynamics is related to small homogeneous width of f–f transitions of RE-ions in glasses and small spectral width of the probe laser light. The discovered effect provides a new experimental approach to studying low-temperature structural dynamics of different disordered matrices and interactions of impurities with environment in such media.

Finding defects in glasses through machine learning

Structural defects control the kinetic, thermodynamic and mechanical properties of glasses. For instance, rare quantum tunneling two-level systems (TLS) govern the physics of glasses at very low temperature. Due to their extremely low density, it is very hard to directly identify them in computer simulations. We introduce a machine learning approach to efficiently explore the potential energy landscape of glass models and identify desired classes of defects. We focus in particular on TLS and we design an algorithm that is able to rapidly predict the quantum splitting between any two amorphous configurations produced by classical simulations. This in turn allows us to shift the computational effort towards the collection and identification of a larger number of TLS, rather than the useless characterization of non-tunneling defects which are much more abundant. Finally, we interpret our machine learning model to understand how TLS are identified and characterized, thus giving direct physical insight into their microscopic nature.

Specific heat of thin phonon cavities at low temperature: Very high values revealed by zeptojoule calorimetry

Specific heat of phonon cavities is investigated in order to analyse the effect of phonon confinement on thermodynamic properties. The specific heat of free standing very thin SiN membranes in the low dimensional limit is measured down to very low temperatures (from 6~K to 50~mK). In the whole temperature range, we measured an excess of specific heat orders of magnitude bigger than the typical value observed in amorphous solids. Below 1~K, a cross-over in $c_p$ to a lower power law is seen, and the value of specific heat of thinner membranes becomes larger than that of thicker ones demonstrating a significant contribution coming from the surface. We show that this high value of the specific heat cannot be explained by the sole contribution of 2D phonon modes (Lamb waves). The excess specific heat, being thickness dependent, could come from tunneling two level systems (TLS) that form in low density regions of amorphous solids located on the surfaces. We also show that the specific heat is strongly tuned by the internal stress of the membrane by orders of magnitude, giving unprecedentedly high values, making low stress SiN very efficient for energy storage at very low temperature.

Strain-spectroscopy of strongly interacting defects in superconducting qubits

The proper functioning of some micro-fabricated novel quantum devices, such as superconducting resonators and qubits, is severely affected by the presence of parasitic structural material defects known as tunneling two-level-systems (TLS). Recent experiments have reported unambiguous evidence of the strong interaction between individual (coherent) TLS using strain-assisted spectroscopy. This work provides an alternative and simple theoretical insight that illustrates how to obtain the spectral response of such strongly interacting defects residing inside the amorphous tunnel barrier of a qubit’s Josephson junction. Moreover, the corresponding spectral signatures obtained here may serve to quickly and efficiently elucidate the actual state of these interacting TLS in experiments based on strain or electric-field spectroscopy.

Anomalous low-energy properties in amorphous solids and the interplay of electric and elastic interactions of tunneling two-level systems

Tunneling two-level systems (TLSs), generic to amorphous solids, dictate the low-temperature properties of amorphous solids and dominate noise and decoherence in quantum nano-devices. The properties of the TLSs are generally described by the phenomenological standard tunneling model. Yet, significant deviations from the predictions of this model found experimentally suggest the need for a more precise model in describing TLSs. Here we show that the temperature dependence of the sound velocity, dielectric constant, specific heat, and thermal conductivity, can be explained using an energy-dependent TLS density of states reduced at low energies due to TLS-TLS interactions. This reduction is determined by the ratio between the strengths of the TLS-TLS interactions and the random potential, which is enhanced in systems with dominant electric dipolar interactions.

Quantum sensors for microscopic tunneling systems

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.

Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature.

This work concerns the theoretical description of the quantum dynamics of molecular junctions with thermal fluctuations and probability losses. To this end, we propose a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. Along the lines discussed in [A. Sergi et al., Symmetry 10 518 (2018)], we adopt the operator-valued Wigner formulation of quantum mechanics (wherein the density matrix depends on the points of the Wigner phase space associated to the system) and derive a non-linear equation of motion. Moreover, we introduce a model for a non-Hermitian quantum single-molecule junction (nHQSMJ). In this model the leads are mapped to a tunneling two-level system, which is in turn coupled to a harmonic mode (i.e., the molecule). A decay operator acting on the two-level system describes phenomenologically probability losses. Finally, the temperature of the molecule is controlled by means of a Nosé-Hoover chain thermostat. A numerical study of the quantum dynamics of this toy model at different temperatures is reported. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction. The possibility that the formalism here presented can be extended to treat both more quantum states () and many more classical modes or atomic particles () is highlighted.

High frequency atomic tunneling yields ultralow and glass-like thermal conductivity in chalcogenide single crystals

Crystalline solids exhibiting glass-like thermal conductivity have attracted substantial attention both for fundamental interest and applications such as thermoelectrics. In most crystals, the competition of phonon scattering by anharmonic interactions and crystalline imperfections leads to a non-monotonic trend of thermal conductivity with temperature. Defect-free crystals that exhibit the glassy trend of low thermal conductivity with a monotonic increase with temperature are desirable because they are intrinsically thermally insulating while retaining useful properties of perfect crystals. However, this behavior is rare, and its microscopic origin remains unclear. Here, we report the observation of ultralow and glass-like thermal conductivity in a hexagonal perovskite chalcogenide single crystal, BaTiS3, despite its highly symmetric and simple primitive cell. Elastic and inelastic scattering measurements reveal the quantum mechanical origin of this unusual trend. A two-level atomic tunneling system exists in a shallow double-well potential of the Ti atom and is of sufficiently high frequency to scatter heat-carrying phonons up to room temperature. While atomic tunneling has been invoked to explain the low-temperature thermal conductivity of solids for decades, our study establishes the presence of sub-THz frequency tunneling systems even in high-quality, electrically insulating single crystals, leading to anomalous transport properties well above cryogenic temperatures.

Internal friction measurements of low energy excitations in amorphous germanium thin films

Motivated to create a germanium analog to nearly two-level-tunneling-system (TLS)-free amorphous silicon, six germanium films, all about 350 nm thick, were deposited by molecular beam epitaxy onto substrates held at temperatures between room temperature and 280∘C. The internal friction and speed of sound of the films was measured between 375 mK and 300 K. Although the intent was to study amorphous thin films, those grown at 200∘C and higher were shown to be at least partially crystalline. The tunneling strength C, a measure of the interaction between phonons and two-level tunneling systems, decreased monotonically with increasing substrate growth temperature, and for films grown on substrates at temperatures above room temperature, C was below the glassy range. The lowest value for an amorphous film, for the 160∘C-grown film, was C=1.9×10−5.

Comparing amorphous silicon prepared by electron-beam evaporation and sputtering toward eliminating atomic tunneling states

It has previously been shown that amorphous silicon (a-Si) thin films can be produced free of tunneling two-level systems (TLS) by e-beam evaporation onto substrates held at elevated temperatures, and there appears to be a strong anticorrelation between the atomic density of these films and the number density of TLS. We have prepared a-Si films with higher atomic density using magnetron sputtering at substrate temperatures comparable to those used in the e-beam studies. We compare the atomic densities measured using Rutherford backscattering and the shear moduli, the speeds of sound, and the densities of TLS calculated using internal friction measurements at cryogenic temperatures of sputtered a-Si films to those of the e-beam films. Our results show that despite their higher atomic densities, sputtered a-Si films prepared at elevated substrate temperatures have lower speeds of sound and higher densities of TLS, which we attribute to the different film growth mechanism from that of e-beam evaporation. We conclude that a collaborative improvement of both local structure and network connectivity, determined by atomic density and speed of sound, respectively, to approach their crystalline values is required to eliminate atomic tunneling states.

Why Phonon Scattering in Glasses is Universally Small at Low Temperatures.

We present a novel view of the standard model of tunneling two level systems (TLSs) to explain the puzzling universal value of a quantity, C∼3×10^{-4}, that characterizes phonon scattering in glasses below 1K as reflected in thermal conductivity, ultrasonic attenuation, internal friction, and the change in sound velocity. Physical considerations lead to a broad distribution of phonon-TLS couplings that (1)exponentially renormalize tunneling matrix elements, and (2)reduce the TLS density of states through TLS-TLS interactions. We find good agreement between theory and experiment for a variety of individual glasses.

In Which Cases and Why the Standard Model of Tunneling Two-Level Systems Describes the Low-Temperature Inner Dynamics of Real Glasses Inadequately

Experiments carried out in recent years using single-molecule spectroscopy to study the low-temperature dynamics of some molecular solid-state media with a disordered internal structure made it possible to obtain new information on the dynamics of such media at the local level. In some substances, the time-dependent behavior of the majority of individual spectra of single fluorescent molecules introduced into the studied medium as a local spectral probe corresponded to the predictions of the standard model of tunneling two-level systems. In others, the behavior of most of the spectra of single molecules was more complicated, which it is difficult to describe in the framework of the standard model. This paper is devoted to the analysis of the results of studies of low-temperature spectral dynamics of single fluorescent molecules in a number of disordered molecular systems (amorphous polyisobutylene, toluene, cumene, propylene carbonate). The observed deviations from the predictions of the theory are associated with the microstructure of the systems under study and the sample shape. Possible reasons for the deviations of the observed local spectral dynamics from the predictions of the standard model of tunneling two-level systems are discussed. Inadequately.

Manipulation of Glassy State in Amorphous Selenium by Low-temperature Internal Friction Measurements

We have studied the thickness and quench-rate dependent internal friction of amorphous selenium (a-Se) thin films deposited at room temperature. The internal friction of a-Se films exhibit a temperature independent plateau below 1 K followed by a broad maximum at 10 K. The plateau, which is seen in almost all amorphous solids, is caused by dissipation by two-level tunneling systems (TLS), whose origin is still unknown. The maximum is caused by thermal relaxation over the same energy barrier that induces TLS. The internal friction and shear modulus are almost thickness independent from 100 nm to 10 µm. Unlike other elemental amorphous materials, the sufficiently low glass transition temperature (Tg) of a-Se (only about 10 K above room temperature) allows in-situ quench-rate dependent study of TLS. The amorphous structure resets itself by a thermal equilibration cycle above Tg. We show that a faster quench rate freezes a-Se to a lower density structure with a higher TLS density and vice versa. The changes are reversible supporting a relationship between different quenched states and the density of TLS. Our study shows that a-Se can be a simple monatomic amorphous system to constrain models for the origin of TLS in amorphous solids.

Correlating the nanostructure of Al-oxide with deposition conditions and dielectric contributions of two-level systems in perspective of superconducting quantum circuits

This work is concerned with Al/Al-oxide(AlOx)/Al-layer systems which are important for Josephson-junction-based superconducting devices such as quantum bits. The device performance is limited by noise, which has been to a large degree assigned to the presence and properties of two-level tunneling systems in the amorphous AlOx tunnel barrier. The study is focused on the correlation of the fabrication conditions, nanostructural and nanochemical properties and the occurrence of two-level tunneling systems with particular emphasis on the AlOx-layer. Electron-beam evaporation with two different processes and sputter deposition were used for structure fabrication, and the effect of illumination by ultraviolet light during Al-oxide formation is elucidated. Characterization was performed by analytical transmission electron microscopy and low-temperature dielectric measurements. We show that the fabrication conditions have a strong impact on the nanostructural and nanochemical properties of the layer systems and the properties of two-level tunneling systems. Based on the understanding of the observed structural characteristics, routes are suggested towards the fabrication of Al/AlOx/Al-layers systems with improved properties.

Transmission-line resonators for the study of individual two-level tunneling systems

Parasitic two-level tunneling systems (TLS) emerge in amorphous dielectrics and constitute a serious nuisance for various microfabricated devices, where they act as a source of noise and decoherence. Here, we demonstrate a new test bed for the study of TLS in various materials which provides access to properties of individual TLS as well as their ensemble response. We terminate a superconducting transmission-line resonator with a capacitor that hosts TLS in its dielectric. By tuning TLS via applied mechanical strain, we observe the signatures of individual TLS strongly coupled to the resonator in its transmission characteristics and extract the coupling components of their dipole moments and energy relaxation rates. The strong and well-defined coupling to the TLS bath results in pronounced resonator frequency fluctuations and excess phase noise, through which we can study TLS ensemble effects such as spectral diffusion, and probe theoretical models of TLS interactions.

Tunable low-temperature dissipation scenarios in palladium nanomechanical resonators

We study dissipation in palladium (Pd) nanomechanical resonators at low temperatures in the linear response regime. Metallic resonators have shown characteristic features of dissipation due to tunneling two-level systems (TLS). The system described here offers a unique tunability of the dissipation scenario by adsorbing hydrogen (${\text{H}}_{2}$), which induces a compressive stress. The intrinsic stress is expected to alter TLS behavior. We find a sublinear $\ensuremath{\sim}{T}^{0.4}$ dependence of dissipation in a limited temperature regime. As seen in TLS dissipation scenarios, we find a logarithmic increase of frequency from the lowest temperatures till a characteristic temperature ${T}_{\text{co}}$ is reached. In samples without ${H}_{2},\phantom{\rule{0.16em}{0ex}}{T}_{\text{co}}\ensuremath{\sim}1\phantom{\rule{0.16em}{0ex}}\text{K}$ was seen, whereas with ${\text{H}}_{2}$ it is clearly reduced to $\ensuremath{\sim}700\phantom{\rule{0.16em}{0ex}}\text{mK}$. Based on standard TLS phenomena, we attribute this to enhanced phonon-TLS coupling in samples with compressive strain. We also find that with ${\text{H}}_{2}$ there is a saturation in low-temperature dissipation, which may possibly be due to super-radiant interaction between TLS and phonons. We discuss the data in the scope of TLS phenomena and similar data for other systems.

Symmetry reduction for tunneling defects due to strong couplings to phonons

Tunneling two-level systems (TLSs) are ubiquitous in amorphous solids, and form a major source of noise in systems such as nano-mechanical oscillators, single electron transistors, and superconducting qubits. Occurance of defect tunneling despite their coupling to phonons is viewed as a hallmark of weak defect–phonon coupling. This is since strong coupling to phonons results in significant phonon dressing and suppresses tunneling in two-level tunneling defects effectively. Here we determine the dynamics of a tunneling defect in a crystal strongly coupled to phonons incorporating the full 3D geometry in our description. We find that inversion symmetric tunneling is not dressed by phonons whereas other tunneling pathways are dressed by phonons and, thus, are suppressed by strong defect–phonon coupling. We provide the linear acoustic and dielectric response functions for a tunneling defect in a crystal for strong defect–phonon coupling. This allows direct experimental determination of the defect–phonon coupling. The singling out of inversion-symmetric tunneling states in single tunneling defects is complementary to their dominance of the low energy excitations in strongly disordered solids as a result of inter-defect interactions for large defect concentrations. This suggests that inversion symmetric TLSs play a unique role in the low energy properties of disordered solids.

Universality of thermal transport in amorphous nanowires at low temperatures

Thermal transport properties of amorphous materials at low temperatures are governed by the interaction between phonons and localized excitations referred to as tunneling two level systems (TLS). The temperature variation of the thermal conductivity of these amorphous materials is considered as universal and is characterized by a quadratic power law. This is well described by the phenomenological TLS model even though its microscopic explanation is still elusive. Here, by scaling down to the nanometer scale amorphous systems much below the bulk phonon-TLS mean free path, we probed the robustness of that model in restricted geometry systems. Using very sensitive thermal conductance measurements, we demonstrate that the temperature dependence of the thermal conductance of silicon nitride nanostructures remains mostly quadratic independently of the nanowire section. It is not following the cubic power law in temperature as expected in a Casimir-Ziman regime of boundary limited thermal transport. This shows a thermal transport counter intuitively dominated by phonon-TLS interactions and not by phonon-boundary scattering in the nanowires. This could be ascribed to an unexpected high density of TLS on the surfaces which still dominates the phonon diffusion processes at low temperatures and explains why the universal quadratic temperature dependence of thermal conductance still holds for amorphous nanowires.

Elastic Measurements of Amorphous Silicon Films at mK Temperatures

The low temperature properties of glass are distinct from those of crystals due to the presence of poorly understood low-energy excitations. The tunneling model proposes that these are atoms tunneling between nearby equilibria, forming tunneling two level systems (TLSs). This model is rather successful, but it does not explain the remarkably universal value of the mechanical dissipation $Q^{-1}$ near 1 kelvin. The only known exceptions to this universality are the $Q^{-1}$ of certain thin films of amorphous silicon, carbon and germanium. Recently, it was found that $Q^{-1}$ of amorphous silicon (a-Si) films can be reduced by two orders of magnitude by increasing the temperature of the substrate during deposition. According to the tunneling model, the reduction in $Q^{-1}$ at 1 kelvin implies a reduction in $P_{0}\gamma ^{2}$, where $P_{0}$ is the density of TLSs and $\gamma $ is their coupling to phonons. In this preliminary report, we demonstrate elastic measurements of a-Si films down to 20 mK. This will allow us, in future work, to determine whether $P_{0}$ or $\gamma $ is responsible for the reduction in $Q^{-1}$ with deposition temperature.