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Coherence Time Enhancement of Interacting Two-Level Systems in Aluminum Superconducting Resonators

Tamin Tai, Jingnan Cai, Steven M. Anlage

Published Sep 24, 2021• 1 citation
OpenAlex

Abstract

Superconducting resonators are widely used in many applications such as qubit readout for quantum computing applications, and kinetic inductance detectors. These resonators are susceptible to numerous loss and noise mechanisms under microwave excitation, especially the dissipation due to non-equilibrium quasi-particles and two-level systems (TLS), which can result in a decrease of the superconducting intrinsic quality factor ($Q_i$) in high quality superconducting resonators. Particularly in the few-photon and low temperature (T) regime, TLS losses can become a dominant loss mechanism. In this study, novel aluminum half-wavelength resonators are investigated, focusing on the loss properties at extra-low power and low temperature. An unusual increase of $Q_i(T)$ with deceasing temperature is observed. This behavior is attributed to the increase of TLS coherence time ($T_2$) at ultra-low temperatures and powers. This $T_2$ increase is consistent with other work on resonant frequency noise in resonators and measurements of individual TLS, and likely arises from interacting TLS in the aluminum half-wavelength resonators.

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Superconducting quantum devices have gained increasing interest over the past 15 years because of their role as promising candidates for implementing a large-scale quantum computer and as ultra-sensitive detectors. Superconducting resonators are one type of superconducting device which are used in a variety of applications including quantum computing and radioastronomy. They can achieve large quality factors which are important for these applications and a variety of others. Specific examples of these applications include the readout and coupling of superconducting qubits and also microwave kinetic inductance detector arrays for sub-mm wavelength astronomical measurements. High quality factors also enable the study of very subtle features in the electromagnetic response of the resonator. This feature in turn offers provides a method to characterize loss mechanisms which affect the performance of superconducting qubits, by measuring the quality factor of a resonator. Dielectric loss is an example of such a loss mechanism, and is considered to be one of, if not \\it the \\rm major obstacle to overcome in order to construct scalable quantum technologies based on superconducting devices. This type of loss arises from the coupling of the electric field in the device to spurious degrees of freedom which arise naturally the dielectric environment of the device. The fast-growing interest in the physics and applications of superconducting resonators has renewed interest in an improving our fundamental understanding of dielectric loss. This interest involves the study of a much bigger and older question in condensed matter physics; namely, what is the microscopic physics which governs the behaviour and of an amorphous material at low-temperatures? \n \nIn this thesis, we present a systematic study of dielectric loss in amorphous aluminum oxide using superconducting microwave resonators. Measurements of the intrinsic loss tangent over a large temperature range of 40~mK to 1~K are presented and analyzed in detail. Some aspects of the data are well understood in terms of the standard tunnelling two-level system model, while others require a deeper analysis of the electrodynamics of the resonator and insights from more advanced theories. We employ a consistent approach using numerical simulations of the resonator to understand loss mechanisms arising from both an inhomogeneous electric field and multiple dielectric layers. We measure saturation effects which provide insight into coherent properties of two-level system ensembles and the mutual interaction between them. Excellent agreement with the two-level system model is found for intrinsic losses, however the strong dependence on temperature which we observe for saturation effects is not predicted in the standard form of the model. We find that this dependence can be understood in terms of the theory of spectral diffusion which is consistent with a strong mutual interaction between two-level systems contributes to broadening of their spectral linewidths.

•Apr 9, 2015•1 citation
Superconducting resonators are widely used in many applications such as qubit readout for quantum computing applications, and kinetic inductance detectors. These resonators are susceptible to numerous loss and noise mechanisms under microwave excitation, especially the dissipation due to non-equilibrium quasi-particles and two-level systems (TLS), which can result in a decrease of the superconducting intrinsic quality factor (QiQ_iQi​) in high quality superconducting resonators. Particularly in the few-photon and low temperature (T) regime, TLS losses can become a dominant loss mechanism. In this study, novel aluminum half-wavelength resonators are investigated, focusing on the loss properties at extra-low power and low temperature. An unusual increase of Qi(T)Q_i(T)Qi​(T) with deceasing temperature is observed. This behavior is attributed to the increase of TLS coherence time (T2T_2T2​) at ultra-low temperatures and powers. This T2T_2T2​ increase is consistent with other work on resonant frequency noise in resonators and measurements of individual TLS, and likely arises from interacting TLS in the aluminum half-wavelength resonators.
Superconducting resonators are widely used in many applications such as qubit readout for quantum computing, and kinetic inductance detectors. These resonators are susceptible to numerous loss and noise mechanisms, especially the dissipation due to two-level systems (TLS) which become the dominant source of loss in the few-photon and low temperature regime. In this study, capacitively-coupled aluminum half-wavelength coplanar waveguide resonators are investigated. Surprisingly, the loss of the resonators is observed to decrease with a lowering temperature at low excitation powers and temperatures below the TLS saturation. This behavior is attributed to the reduction of the TLS resonant response bandwidth with decreasing temperature and power to below the detuning between the TLS and the resonant photon frequency in a discrete ensemble of TLS. When response bandwidths of TLS are smaller than their detunings from the resonance, the resonant response and thus the loss is reduced. At higher excitation powers, the loss follows a logarithmic power dependence, consistent with predictions from the generalized tunneling model (GTM). A model combining the discrete TLS ensemble with the GTM is proposed and matches the temperature and power dependence of the measured internal loss of the resonator with reasonable parameters.
Abstract Superconducting resonators are widely used in many applications such as qubit readout for quantum computing, and kinetic inductance detectors. These resonators are susceptible to numerous loss and noise mechanisms, especially the dissipation due to two‐level systems (TLS) which become the dominant source of loss in the few‐photon and low temperature regime. In this study, capacitively‐coupled aluminum half‐wavelength coplanar waveguide resonators are investigated. Surprisingly, the loss of the resonators is observed to decrease with a lowering temperature at low excitation powers and temperatures below the TLS saturation. This behavior is attributed to the reduction of the TLS resonant response bandwidth with decreasing temperature and power to below the detuning between the TLS and the resonant photon frequency in a discrete ensemble of TLS. When response bandwidths of TLS are smaller than their detunings from the resonance, the resonant response and thus the loss is reduced. At higher excitation powers, the loss follows a logarithmic power dependence, consistent with predictions from the generalized tunneling model (GTM). A model combining the discrete TLS ensemble with the GTM is proposed and matches the temperature and power dependence of the measured internal loss of the resonator with reasonable parameters.
Superconducting microwave resonators are critical to quantum computing and sensing technologies. Additionally, they are common proxies for superconducting qubits when determining the effects of performance-limiting loss mechanisms such as from two-level systems (TLSs). The extraction of these loss mechanisms is often performed by measuring the internal quality factor Qi as a function of power or temperature. In this work, we investigate large temporal fluctuations of Qi at low powers over periods of 12–16 h (relative standard deviation σQi/Qi=13%). These fluctuations are ubiquitous across multiple resonators, chips, and cooldowns. We are able to attribute these fluctuations to variations in the TLS loss tangent due to two main indicators. First, measured fluctuations decrease as power and temperature increase. Second, for interleaved measurements, we observe correlations between low- and medium-power Qi fluctuations and an absence of correlations with high-power fluctuations. Agreement with the TLS loss tangent mean is obtained by performing measurements over a time span of a few hours. We hypothesize that, in addition to decoherence, due to coupling to individual near-resonant TLS, superconducting qubits are affected by these observed TLS loss tangent fluctuations.
As superconducting kinetic inductance detectors (KIDs) continue to grow in popularity for sensitive submillimeter detection and other applications, there is a drive to advance toward lower-loss devices. We present measurements of diagnostic thin-film aluminum coplanar waveguide (CPW) resonators designed to inform ongoing KID development at NASA Goddard Space Flight Center. The resonance frequencies span f0f_0f0​ = 3.5-4 GHz and include quarter-wave and half-wave resonators with varying coupling capacitor designs. We present measurements of the device film properties and an analysis of the dominant mechanisms of loss in the resonators measured in a dark environment, demonstrating quality factors of Qi−1≈3.64−8.57 ×10−8Q_i^{-1} \approx 3.64-8.57\ \times 10^{-8}Qi−1​≈3.64−8.57 ×10−8. We observe an enhanced level of suppression in the loss contributions from two-level systems (TLS) at intermediate-to-high read powers, and a regime at these powers and low temperatures where contributions from intrinsic processes Qi−1Q_i^{-1}Qi−1​,other dominate the total loss. We also observe deviations from the standard TLS loss model at low powers and temperatures below 60 mK, and use a modified model to describe this behavior.
Measuring the internal quality factor of coplanar waveguide superconducting resonators is an established method of determining small losses in superconducting devices. Often, resonator losses are attributed to two-level system (TLS) defects using a power dependent model for the quality factor. However, excess non-equilibrium quasiparticles can also limit the quality factor of superconducting resonators. Here, a two-temperature, power and temperature dependent model is used to evaluate resonator losses for titanium nitride and aluminum coplanar waveguide resonators with loss tangents of 10−5–10−6. This model enables a set of parameters to describe both the internal quality factor and fractional frequency shift of the resonator across a broad range of average cavity photon numbers, from 1 to 106, and temperatures between those limited by the experimental apparatus near 50 mK and thermal quasiparticle dominated. The presented model also offers potential insight into observing the temperature and power dependence of TLS–TLS interactions in these resonators.
Superconducting quantum devices have gained increasing interest over the past 15 years because of their role as promising candidates for implementing a large-scale quantum computer and as ultra-sensitive detectors. Superconducting resonators are one type of superconducting device which are used in a variety of applications including quantum computing and radioastronomy. They can achieve large quality factors which are important for these applications and a variety of others. Specific examples of these applications include the readout and coupling of superconducting qubits and also microwave kinetic inductance detector arrays for sub-mm wavelength astronomical measurements. High quality factors also enable the study of very subtle features in the electromagnetic response of the resonator. This feature in turn offers provides a method to characterize loss mechanisms which affect the performance of superconducting qubits, by measuring the quality factor of a resonator. Dielectric loss is an example of such a loss mechanism, and is considered to be one of, if not \\it the \\rm major obstacle to overcome in order to construct scalable quantum technologies based on superconducting devices. This type of loss arises from the coupling of the electric field in the device to spurious degrees of freedom which arise naturally the dielectric environment of the device. The fast-growing interest in the physics and applications of superconducting resonators has renewed interest in an improving our fundamental understanding of dielectric loss. This interest involves the study of a much bigger and older question in condensed matter physics; namely, what is the microscopic physics which governs the behaviour and of an amorphous material at low-temperatures? \n \nIn this thesis, we present a systematic study of dielectric loss in amorphous aluminum oxide using superconducting microwave resonators. Measurements of the intrinsic loss tangent over a large temperature range of 40~mK to 1~K are presented and analyzed in detail. Some aspects of the data are well understood in terms of the standard tunnelling two-level system model, while others require a deeper analysis of the electrodynamics of the resonator and insights from more advanced theories. We employ a consistent approach using numerical simulations of the resonator to understand loss mechanisms arising from both an inhomogeneous electric field and multiple dielectric layers. We measure saturation effects which provide insight into coherent properties of two-level system ensembles and the mutual interaction between them. Excellent agreement with the two-level system model is found for intrinsic losses, however the strong dependence on temperature which we observe for saturation effects is not predicted in the standard form of the model. We find that this dependence can be understood in terms of the theory of spectral diffusion which is consistent with a strong mutual interaction between two-level systems contributes to broadening of their spectral linewidths.