High quality factor, i.e. low loss, microwave resonators are important for quantum information storage and addressing. In this work we study the resonance frequency and loss in superconducting coplanar waveguide resonators as a function of power and temperature. We find that there is increased loss at low power and low temperature. The increased loss is attributed to the existence of two-level systems (TLS) at the surfaces, interfaces, and in the bulk of insulators deposited on the structures. We show that both the temperature dependence of the resonant frequency and the power dependence of the loss can be used to find the TLS contribution to the loss. The TLS intrinsic loss tangent derived from the frequency shift data at high power is shown to agree well with the direct loss measurement at low power. The former allows for a relatively fast measurement of the TLS loss. As an example, we measure the properties of amorphous AlOXdeposited on the resonators and find a TLS loss tangent of 1 × 10-3.
High quality factor, i.e. low loss, microwave resonators are important for quantum information storage and addressing. In this work we study the resonance frequency and loss in superconducting coplanar waveguide resonators as a function of power and temperature. We find that there is increased loss at low power and low temperature. The increased loss is attributed to the existence of two-level systems (TLS) at the surfaces, interfaces, and in the bulk of insulators deposited on the structures. We show that both the temperature dependence of the resonant frequency and the power dependence of the loss can be used to find the TLS contribution to the loss. The TLS intrinsic loss tangent derived from the frequency shift data at high power is shown to agree well with the direct loss measurement at low power. The former allows for a relatively fast measurement of the TLS loss. As an example, we measure the properties of amorphous AlOXdeposited on the resonators and find a TLS loss tangent of 1 × 10-3.
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.
In a number of recent experiments with microwave high quality superconducting coplanar waveguide resonators an anomalously weak power dependence of the quality factor has been observed. We argue that this observation implies that the monochromatic radiation does not saturate the two level systems (TLS) located at the interface oxide surfaces of the resonator and suggests the importance of their interactions. We estimate the microwave loss due to interacting TLS and show that the interactions between TLS lead to a drift of their energies that result in a much slower, logarithmic dependence of their absorption on the radiation power in agreement with the data.
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.
Microscopic two-level systems (TLSs) are known to contribute to loss in resonant superconducting microwave circuits. This loss increases at low power and temperatures as the TLSs become unsaturated. We find that the loss is dependent on both the substrate-superconductor interface and the roughness of the surfaces. A native, oxide-free interface reduced the loss due to TLSs. However, a rough surface in the CPW gap did not cause more TLS loss, but the overall loss was significantly increased for the roughest surfaces.
The loss in superconducting microwave resonators at low-photon numbers and low temperatures is not well understood but has implications for achievable coherence times in superconducting qubits. We have fabricated single-layer resonators with a high quality factor by patterning a superconducting aluminum film on a sapphire substrate. Four resonator geometries were studied with resonant frequencies ranging from 5 to 7 GHz: a quasi-lumped element resonator, a coplanar strip waveguide resonator, and two hybrid designs that contain both a coplanar strip and a quasi-lumped element. Transmitted power measurements were taken at 30 mK as a function of frequency and probe power. We find that the resonator loss, expressed as the inverse of the internal quality factor, decreases slowly over four decades of photon number in a manner not merely explained by loss from a conventional uniform spatial distribution of two-level systems in an oxide layer on the superconducting surfaces of the resonator.
In this master's thesis, I present the design, fabrication, and characterisation of superconducting microwave resonators. These resonators are quarter-wavelength coplanar waveguide resonators, operating at resonance frequencies between 4 GHz and 8 GHz. This kind of resonator is a key component in several applications, ranging from quantum computation devices to parametric amplifiers. Minimising the losses (achieving high internal quality factors) in these resonators is important to maximise performance of the applications they are used for. During the thesis work, we have studied several possible changes to improve the resonator quality.\n\nFabrication of the resonators was done in the Nanofabrication Laboratory at Chalmers University of Technology, and consist of the following steps: cleaning a sapphire or silicon wafer, depositing a layer of superconducting niobium, photolithography, and etching the waveguide. We then measured the resonators in a cryogen-free dilution refrigerator, at a temperature of 10 mK. The measurements consisted of a power sweep, in order to quantify the quality factor at high and low excitation powers. As an example, the first resonator we fabricated had a quality factor of 4.3 x 10^4 at high power (about 10^5 photons in the resonator), and quality factor of 3.7 x 10^4 at the single-photon level.\n\nWe then investigated different loss mechanisms that we expect to negatively affect the quality factor, and how to reduce this loss. Firstly, to reduce radiation losses and magnetic vortex losses, we reduced the lateral dimensions of the resonator. Secondly, as two-level system (TLS) losses are believed to mainly reside at the surfaces of the materials and interfaces between them, we etched into the substrate to selectively move a part of the TLS away from the resonator. We also studied the effect of the meandering of the resonator on the quality factor, as well as using two different etching gasses.\n\nBy gathering all this data, we were then able to compare the different combinations to see the effect of the changing parameters. In conclusion, the reduced lateral dimensions and the removal of part of the substrate indeed reduce the losses, as expected from the theory. We also found interesting behaviour with regards to the meandering, namely that having a meandered structure negatively affects the quality factor.\n\nCombining all results, we can give a guideline for the fabrication of resonators in the future, which gave us a quality factor up to 4.9 x 10^5 at high excitation power, and 3.0 x 10^5 at the single photon level.