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arXiv:1607.08146 · Physical review. B./Physical review. B

Quantum paraelectricity probed by superconducting resonators

Dejan Davidovikj, Nicola Manca, Herre S. J. van der Zant, Andrea D. Caviglia, Gary Alexander Steele

Published Jun 28, 2017• 17 citations
arXivHTMLPDF

Abstract

Superconducting coplanar waveguide (CPW) resonators are powerful and versatile tools used in areas ranging from radiation detection to circuit quantum electrodynamics. Their potential for low intrinsic losses makes them attractive as sensitive probes of electronic properties of bulk materials and thin films. Here we use superconducting MoRe CPW resonators to investigate the high-frequency (up to 0.3 GHz) and low-temperature (down to 3.5 K) permittivity of ${\mathrm{SrTiO}}_{3}$, a nonlinear dielectric on the verge of a ferroelectric transition (quantum paraelectricity). We perform a quantitative analysis of its dielectric properties as a function of external dc bias (up to $\ifmmode\pm\else\textpm\fi{}15\phantom{\rule{0.16em}{0ex}}\mathrm{V}$), rf power, and mode number and discuss our results within the framework of the most recent theoretical models. We also discuss the origin of a fatigue effect that reduces the tunability of the dielectric constant of ${\mathrm{SrTiO}}_{3}$, which we relate to the presence of oxygen vacancies.

DOI
10.1103/physrevb.95.214513

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Superconducting coplanar-waveguide (CPW) resonators are one of the key devices in circuit quantum electrodynamics (cQED). Their performance can be limited by dielectric losses in the substrate and in the material interfaces. Reliable modeling is required to aid in the design of low-loss CPW structures for cQED. We analyze the geometric dependence of the dielectric losses in CPW structures using finite-element modeling of the participation ratios of the lossy regions. In a practical scenario, uncertainties in the the dielectric constants and loss tangents of these regions introduce uncertainties in the theoretically predicted participation ratios. We present a method for combining loss simulations with measurements of two-level-system-limited quality factors and resonance frequencies of CPW resonators. Namely, we solve an inverse problem to find model parameters producing the measured values. High quality factors are obtainable by properly designing the cross-sectional geometries of the CPW structures, but more accurate modeling and design methods for low-loss CPW resonators are called for major future improvements. Our nonlinear optimization methodology for solving the aforementioned inverse problem is a step in this direction.
Superconducting coplanar waveguide (SCPW) resonators have a wide range of applications due to the combination of their planar geometry and high quality factors relative to normal metals. However, their performance is sensitive to both the details of their geometry and the materials and processes that are used in their fabrication. In this paper, we study the dependence of SCPW resonator performance on materials and geometry as a function of temperature and excitation power. We measure quality factors greater than 2 × 106 at high excitation power and 6 × 105 at a power comparable to that generated by a single microwave photon circulating in the resonator. We examine the limits to the high excitation power performance of the resonators and find it to be consistent with a model of radiation loss. We further observe that while in all cases the quality factors are degraded as the temperature and power are reduced due to dielectric loss, the size of this effect is dependent on resonator materials and geometry. Finally, we demonstrate that the dielectric loss can be controlled in principle using a separate excitation near the resonance frequencies of the resonator.
Superconducting resonators are powerful tools widely used in circuit Quantum Electrodynamics [1]. High-quality factors, tunability, and several implemented layouts make them ideal circuital elements for various applications from quantum metrology [2], to quantum computation [3] and quantum information [4]. Here, we report on the simulation and design of superconducting Coplanar Waveguide (CPW) resonators whose resonance frequencies are in the range of 4–8 GHz. Typical properties of superconducting resonators employed in standard transmon qubits can be achieved by designing a λ/4 resonator made by Niobium (Nb) and modeling the capacitive coupling to provide a high-quality factor useful for its future employments in more advanced quantum circuits [5]. Nb gives the advantage of better stability of the superconducting properties of the material against the application of a magnetic field, compared those achievable by Aluminum (Al), thus guaranteeing an additional degree of freedom in the implementation of complex quantum architectures [5]–[7].
Superconducting coplanar waveguide (CPW) microwave resonators in quantum circuits are the best components for reading and changing the state of artificial atoms because of their excellent coupling to quantum systems. This coupling forms the basis of the developing circuit quantum electrodynamic architecture. In quantum processors, oscillators are used to store and transmit quantum information using microwave-frequency wave packets. However, the presence of amorphous thin-film defects is deleterious and can result in an irrevocable loss of coherent information with uncontrolled degrees of freedom. Although there has been extensive research into techniques to reduce the coherent loss of such devices, the precise structure of amorphous dielectric layers on surfaces and interfaces and their associated loss mechanism are being actively studied. In particular, planar superconducting resonators are very sensitive to defects on their surfaces, such as two-level systems in oxidized metals and nonequilibrium quasiparticles, making these devices suitable probes for the different loss mechanisms. In this work, we present the design, fabrication, and characterization of Nb CPW resonators with different surface treatments with self-assembled monolayers (SAMs), which mitigate the growth of oxides in superconducting circuits. We demonstrate SAM-passivated resonators having internal quality factors of greater than 10 6 at a single-photon excitation power (measured at 100 mK), which were probed using scanning electron microscopy, X-ray photoelectron spectroscopy, and transmission electron microscopy to demonstrate the efficiency of our surface treatment. Finally, we compared the improvements in the experimental quality factors to those obtained by numerical simulation.
The objective of this thesis is to evaluate a generic process for fabrication and characterization of the Superconductive coplanar waveguide (CPW) resonators. Superconductive CPW resonators with various lengths and shapes are designed to investigate their electrical and magnetic properties as well as resonance properties and sensitivities. In the first part of thesis, two different models are introduced in order to estimate the nonlinear kinetic inductance of a superconducting CPW resonator. The first model is based on Bean critical-state model and the second one is based on current dependence of London penetration depth. The existence of a shift in resonant frequency of Superconductive CPW resonator caused by a non-linear kinetic inductance is also shown experimentally. Simulations were carried out to estimate the nonlinear kinetic inductance due to the self- induced magnetic field penetration. The rest of the thesis is concerned with development of very smooth Aluminum (Al) thin films with RMS (Root Mean Square) roughness 1~nm and CAD (Computer Aid Design) of superconductive CPW resonators. Experimental investigation of a generic fabrication technique for superconductive CPW resonator is carried out. Many resonators are fabricated with different design parameters, such as centerline or gap width, film thickness and gap capacitors length. The fabrication process is described in detail. Electron Beam Lithography is used to fabricate Nb and Al CPW resonators which are coupled to outer conductors via gap capacitors. We have fabricated GHz frequency CPW resonators with quality factors, Q up 5X10^5.
Materials that feature very high permittivity and very low losses at low temperatures offer interesting opportunities for improving the performance of a variety of microwave-optical devices such as phase shifters and quantum transducers. In this Letter, superconducting Al coplanar waveguide resonators between 4 and 6 GHz were used to determine the complex permittivity and loss of thin film SrTiO3 on Si at cryogenic temperatures. We report a permittivity of 1950 ± 140 and a high-power loss tangent (tan δSTO) of 3.4 ± 0.1×10−4 at millikelvin temperatures. To further investigate the potential of SrTiO3 for use in emerging quantum technology applications, the transition of tan δSTO into the single photon regime was analyzed. Our findings reveal a loss scaling that aligns closely with a two-level system loss mechanism. We observe a nearly two orders of magnitude difference in tan δSTO between high and low input power levels, consistent with that two-level system loss picture.