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arXiv:cond-mat/0609614 · Applied Physics Letters

Noise properties of superconducting coplanar waveguide microwave resonators

Jiansong Gao, Jonas Zmuidzinas, Benjamin A. Mazin, Henry G. LeDuc, Peter K. Day

Published Mar 5, 2007• 216 citations
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Abstract

The authors have measured noise in thin-film superconducting coplanar waveguide resonators. This noise appears entirely as phase noise, equivalent to a jitter of the resonance frequency. In contrast, amplitude fluctuations are not observed at the sensitivity of their measurement. The ratio between the noise power in the phase and amplitude directions is large, in excess of 30dB. These results have important implications for resonant readouts of various devices such as detectors, amplifiers, and qubits. They suggest that the phase noise is due to two-level systems in dielectric materials.

DOI
10.1063/1.2711770

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The authors have measured noise in thin-film superconducting coplanar waveguide resonators. This noise appears entirely as phase noise, equivalent to a jitter of the resonance frequency. In contrast, amplitude fluctuations are not observed at the sensitivity of their measurement. The ratio between the noise power in the phase and amplitude directions is large, in excess of 30dB. These results have important implications for resonant readouts of various devices such as detectors, amplifiers, and qubits. They suggest that the phase noise is due to two-level systems in dielectric materials.
We present measurements of the temperature and power dependence of the resonance frequency and frequency noise of superconducting niobium thin-film coplanar waveguide resonators carried out at temperatures well below the superconducting transition (Tc=9.2K). The noise decreases by nearly two orders of magnitude as the temperature is increased from 120to1200mK, while the variation of the resonance frequency with temperature over this range agrees well with the standard two-level system (TLS) model for amorphous dielectrics. These results support the hypothesis that TLSs are responsible for the noise in superconducting microresonators and have important implications for resonator applications such as qubits and photon detectors.
Excess phase noise has been observed in microwave kinetic inductance detectors (MKIDs) which prevents the noise-equivalent power (NEP) of current detectors from reaching theoretical limits. One characteristic of this excess noise is its dependence on the power of the readout signal: the phase noise decreases as the readout power increases. We investigated this power dependence in a variety of devices, varying the substrate (silicon and sapphire), superconductor (aluminum and niobium) and resonator parameters (resonant frequency, quality factor and resonator geometry). We find that the phase noise has a power law dependence on the readout power, and that the exponent is -1/2 in all our devices. We suggest that this phase noise is caused by coupling between the high-Q microwave resonator that forms the sensitive element of the MKID and two-level systems associated with disorder in the dielectric material of the resonator. The physical situation is analogous to the resonance fluorescence in quantum optics, and we are investigating the application of resonance fluorescence theory to MKID phase noise.
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 SrTiO3{\mathrm{SrTiO}}_{3}SrTiO3​, 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 SrTiO3{\mathrm{SrTiO}}_{3}SrTiO3​, which we relate to the presence of oxygen vacancies.
Frequency instability of superconducting resonators and qubits leads to dephasing and time-varying energy loss and hinders quantum processor tune-up. Its main source is dielectric noise originating in surface oxides. Thorough noise studies are needed to develop a comprehensive understanding and mitigation strategy of these fluctuations. We use a frequency-locked loop to track the resonant frequency jitter of three different resonator types—one niobium nitride superinductor, one aluminum coplanar waveguide, and one aluminum cavity—and we observe notably similar random telegraph signal fluctuations. At low microwave drive power, the resonators exhibit multiple, unstable frequency positions, which, for increasing power, coalesce into one frequency due to motional narrowing caused by sympathetic driving of two-level system defects by the resonator. In all three devices, we identify a dominant fluctuator whose switching amplitude (separation between states) saturates with increasing drive power, but whose characteristic switching rate follows the power law dependence of quasi-classical Landau-Zener transitions.
The addition of nonlinearity to an harmonic resonator provides a route to complex dynamical behaviour of resonant modes, including coupling between them. We present a superconducting device that makes use of the nonlinearity of Josephson junctions to introduce a controlled, tunable, nonlinear inductance to a thin film coplanar waveguide resonator. Considering the device as a potential quantum optical component in the microwave regime, we create a sensitive bifurcation amplifier and then demonstrate spectroscopy of other resonant modes via the intermode coupling. We find that the sensitivity of the device approaches within a factor two quantitative agreement with a quantum model by Dykman but is limited by a noise that has its source(s) on-chip.
We measure frequency- and dissipation-quadrature noise in superconducting microresonators with sensitivity near the vacuum noise level using a Josephson parametric amplifier. At an excitation power of 100 nW, frequency noise rises orders of magnitude above the vacuum noise, but no excess dissipation-quadrature noise is observed above the vacuum noise level. Our results suggest that using quantum amplifiers in dissipation measurement may greatly improve the sensitivity of microresonator readout, which has important implications for applications such as detectors, qubits, and nanomechanical oscillators.