Improving the Coherence Time of Superconducting Coplanar Resonators
H. Wang, M. Hofheinz, J. Wenner, M. Ansmann, R. C. Bialczak, M. Lenander, Erik Lucero, M. Neeley, A. D. O'Connell, D. Sank, M. Weides, A. N. Cleland, John M. Martinis
备注：
3 pages, 4 figures for the main paper; total 5 pages, 6 figures including supplementary material. Submitted to Applied Physics Letters
The quality factor and energy decay time of superconducting resonators have been measured as a function of material, geometry, and magnetic field. Once the dissipation of trapped magnetic vortices is minimized, we identify surface two-level states (TLS) as an important decay mechanism. A wide gap between the center conductor and the ground plane, as well as use of the superconductor Re instead of Al, are shown to decrease loss. We also demonstrate that classical measurements of resonator quality factor at low excitation power are consistent with single-photon decay time measured using qubit-resonator swap experiments.
Magnetic-field-resilient superconducting coplanar waveguide (SCPW) resonators are essential for developing integrated quantum circuits of various qubits and quantum memory devices. Molybdenum-Rhenium (MoRe), which is a disordered superconducting alloy forming a highly transparent contact to the graphene and carbon nanotubes (CNTs), would be a promising platform for realizing the field-resilient SCPW resonators combined with graphene- and CNT-based nano-hybrid qubits. We fabricated MoRe SCPW resonators and investigated their microwave transmission characteristics with varying temperature and ex…
Dielectric measurements on insulating materials at cryogenic temperatures can be challenging, depending on the frequency and temperature ranges of interest. We present a technique to study the dielectric properties of bulk dielectrics at GHz frequencies. A superconducting coplanar Nb resonator is deposited directly on the material of interest, and this resonator is then probed in distant-flip-chip geometry with a microwave feedline on a separate chip. Evaluating several harmonics of the resonator gives access to various probing frequencies, in the present studies up to 20 GHz. We demonstrate t…
We characterize low-loss electron-beam evaporated niobium thin films deposited under ultra-high vacuum conditions. Slow deposition yields films with a high superconducting transition temperature ($9.20 \pm 0.06 \rm ~K$) as well as a residual resistivity ratio of $4.8$. We fabricate the films into coplanar waveguide resonators to extract the intrinsic loss due to the presence of two-level-system fluctuators using microwave measurements. For a coplanar waveguide resonator gap of $2~μ\rm m$, the films exhibit filling-factor-adjusted two-level-system loss tangents as low as $1.5 \times 10^{-7}$ wi…
Metallic coplanar microwave resonators are widely employed at room temperature, but their low-temperature performance has received little attention so far. We characterize compact copper coplanar resonators with multiple modes from 2.5 to 20 GHz at temperatures as low as 5 K. We investigate the influence of center conductor width (20 to 100 μm) and coupling gap size (10 to 50 μm), and we observe a strong increase of quality factor (Q) for wider center conductors, reaching values up to 470. The magnetic-field dependence of the resonators is weak, with a maximum change in Q of 3.5% for an applie…
We characterize niobium nitride (NbN) $λ/2$ coplanar waveguide resonators, which were fabricated from a 10nm thick film on silicon dioxide grown by sputter deposition. For films grown at 120°C we report a superconducting critical temperature of 7.4K associated with a normal square resistance of 1k$Ω$ leading to a kinetic inductance of 192pH/$\Box$. We fabricated resonators with a characteristic impedance up to 4.1k$Ω$ and internal quality factors $Q_\mathrm{i} > 10^4$ in the single photon regime at zero magnetic field. Moreover, in the many photons regime, the resonators present high magnetic …
Recent experiments on the coupling of the in-plane motional state of electrons floating on the surface of liquid helium to a microwave resonator have revealed the importance of helium surface fluctuations to the coherence of this motion. Here we investigate these surface fluctuations by studying the resonance properties of a superconducting coplanar waveguide (CPW) resonator filled with superfluid helium, where a significant fraction of the resonator's electromagnetic mode volume is coupled to the surface dynamics of the liquid. We present preliminary results on real-time CPW resonator frequen…
Optimization of Coplanar Waveguide Resonators for ESR Studies on Metals
本文对高导电金属样品附近共面波导谐振器的电磁微波场进行了模拟和解析计算。CPW结构的设计目的是研究金属重费米子系统中的电子自旋共振（ESR），特别是YbRh $_2$ Si $_2$，接近量子临界点。利用CPW谐振器进行ESR实验，可以在mK温度和广泛的自由选择频率范围内进行研究。因此，它是非常感兴趣的，以评估附近的金属样品的共振共面波导结构的性能。在这里，我们研究的微波场在样品表面的波导结构的样品距离的函数和分析的影响的样品上的谐振器的性能。模拟结果揭示了一个最佳的样品距离的微波磁场在样品中最大化，因此最适合ESR研究。
Superconducting coplanar waveguide resonators that can operate in strong magnetic fields are important tools for a variety of high frequency superconducting devices. Magnetic fields degrade resonator performance by creating Abrikosov vortices that cause resistive losses and frequency fluctuations, or suppressing superconductivity entirely. To mitigate these effects we investigate lithographically defined artificial defects in resonators fabricated from NbTiN superconducting films. We show that by controlling the vortex dynamics the quality factor of resonators in perpendicular magnetic fields …
Ultimate sensitivity for quantum magnetometry using nitrogen-vacancy (NV) centers in diamond is limited by number of NV centers and coherence time. Microwave irradiation with a high and homogeneous power density for a large detection volume is necessary to achieve highly sensitive magnetometer. Here, we demonstrate a microwave resonator to enhance the power density of the microwave field and an optical system with a detection volume of 1.4e-3 mm$^3$. The strong microwave field enables us to achieve 48 ns Rabi oscillation which is sufficiently faster than the phase relaxation time of NV centers…
We report on the challenges and limitations of direct coupling of the magnetic field from a circuit resonator to an electron spin bound to a donor potential. We propose a device consisting of a trilayer lumped-element superconducting resonator and a single donor implanted in enriched $^{28}$Si. The resonator impedance is significantly smaller than the practically achievable limit using prevalent coplanar resonators. Furthermore, the resonator includes a nano-scale spiral inductor to spatially focus the magnetic field from the photons at the location of the implanted donor. The design promises …
Separating the influence of hyperfine from spin-orbit interactions in spin-dependent carrier recombination and dissociation processes necessitates magnetic resonance spectroscopy over a wide range of frequencies. We have designed compact and versatile coplanar waveguide resonators for continuous-wave electrically detected magnetic resonance, and tested these on organic light-emitting diodes. By exploiting both the fundamental and higher-harmonic modes of the resonators we cover almost five octaves in resonance frequency within a single setup. The measurements with a common pi-conjugated polyme…
A strategy aimed at decreasing dielectric loss in coplanar waveguides (CPW) and qubits involves the creation of trenches in the underlying substrate within the gaps of the overlying metallization. Participation of contamination layers residing on surfaces and interfaces in these designs can be reduced due to the change in the effective dielectric properties between the groundplane and conductor metallization. Although finite element method approaches have been previously applied to quantify this decrease, an analytical method is presented that can uniquely address geometries possessing small t…
Superconducting quantum circuits are one of the leading quantum computing platforms. To advance superconducting quantum computing to a point of practical importance, it is critical to identify and address material imperfections that lead to decoherence. Here, we use terahertz Scanning Near-field Optical Microscopy (SNOM) to probe the local dielectric properties and carrier concentrations of wet-etched aluminum resonators on silicon, one of the most characteristic components of the superconducting quantum processors. Using a recently developed vector calibration technique, we extract the THz pe…
The in-place growth of suspended carbon nanotubes facilitates the observation of both unperturbed electronic transport spectra and high-Q vibrational modes. For complex structures integrating, e.g., superconducting rf elements on-chip, selection of a chemically and physically resistant material that survives the chemical vapor deposition (CVD) process provides a challenge. We demonstrate the implementation of molybdenum-rhenium coplanar waveguide resonators that exhibit clear resonant behaviour at cryogenic temperatures even after having been exposed to nanotube growth conditions. The properti…
We investigate the performance of niobium nitride superconducting coplanar waveguide resonators towards hybrid quantum devices with magnon-photon coupling. We find internal quality factors ~ 20000 at 20 mK base temperature, in zero magnetic field. We find that by reducing film thickness below 100 nm internal quality factor greater than 1000 can be maintained up to parallel magnetic field of ~ 1 T and perpendicular magnetic field of ~ 100 mT. We further demonstrate strong coupling of microwave photons in these resonators, with magnons in chromium trichloride, a van der Waals antiferromagnet, wh…
We present a systematic analysis of the internal losses of superconducting coplanar waveguide microwave resonators based on niobium thin films on silicon substrates. In particular, we investigate losses introduced by Nb/Al interfaces in the center conductor, which is important for experiments where Al based Josephson junctions are integrated into Nb based circuits. We find that these interfaces can be a strong source for two-level state (TLS) losses, when the interfaces are not positioned at current nodes of the resonator. In addition to TLS losses, for resonators including Al, quasiparticle l…
Superconducting boron doped silicon is a promising material for integrated silicon quantum devices. In particular, its low electronic density and moderate disorder make it a suitable candidate for the fabrication of large inductances with low losses at microwave frequencies. Here, we study experimentally the electrodynamics of superconducting silicon thin layers patterned in coplanar waveguide resonators, targeting three key properties: kinetic inductance, internal losses, and the variation of these quantities with the read-out power. We report the first observation in a doped semiconductor of…
We numerically and experimentally investigate the phononic loss for superconducting resonators fabricated on a piezoelectric substrate. With the help of finite element method simulations, we calculate the energy loss due to electromechanical conversion into bulk and surface acoustic waves. This sets an upper limit for the resonator internal quality factor $Q_i$. To validate the simulation, we fabricate quarter wavelength coplanar waveguide resonators on GaAs and measure $Q_i$ as function of frequency, power and temperature. We observe a linear increase of $Q_i$ with frequency, as predicted by …
We report on the on-chip detection of microwaves in the frequency range around 100GHz. For the purpose of detection, we employ a discrete transport channel triggered in a superconducting single-electron transistor by photon-assisted tunneling of quasiparticles. The technique is successfully applied to observe the spectrum of the dressed states of a model cQED system consisting of a superconducting coplanar resonator coupled to a quantum Josephson oscillator. The dressed states appear as typical resonance anticrossing exhibiting, in our case, an expectedly wide frequency splitting corresponding…
We report on electron spin resonance (ESR) measurements of phosphorus donors localized in a 200 square micron area below the inductive wire of a lumped element superconducting resonator. By combining quantum limited parametric amplification with a low impedance microwave resonator design we are able to detect around 20000 spins with a signal-to-noise ratio (SNR) of 1 in a single shot. The 150 Hz coupling strength between the resonator field and individual spins is significantly larger than the 1 - 10 Hz coupling rates obtained with typical coplanar waveguide resonator designs. Due to the large…
We report measurements of a superconducting coplanar waveguide resonator (CPWR) coupled to a sphere of yttrium-iron garnet. The non-uniform CPWR field allows us to excite various magnon modes in the sphere. Mode frequencies and relative coupling strengths are consistent with theory. Strong coupling is observed to several modes even with, on average, less than one excitation present in the CPWR. The time response to square pulses shows oscillations at the mode splitting frequency. These results indicate the feasibility of combining magnonic and planar superconducting quantum devices.
Superconducting circuits present a promising platform with which to realize a quantum refrigerator. Motivated by this, we fabricate and perform spectroscopy of a gated Cooper-pair box, capacitively coupled to two superconducting coplanar waveguide resonators with different frequencies. We experimentally demonstrate the strong coupling of a charge qubit to two superconducting resonators, with the ability to perform voltage driving of the qubit at GHz frequencies. We go on to discuss how the measured device could be modified to operate as a cyclic quantum refrigerator by terminating the resonato…
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 in order to develop a comprehensive understanding and mitigation strategy of these fluctuations. Here we use a frequency-locked loop to track the resonant-frequency jitter of three different resonator types---one niobium-nitride superinductor, one aluminium coplanar waveguide, and one aluminium cavity---and we observe strikingly similar random-tel…
We demonstrate microwave-mediated distant magnon-magnon coupling on a superconducting circuit platform, incorporating chip-mounted single-crystal Y$_3$Fe$_5$O$_{12}$ (YIG) spheres. Coherent level repulsion and dissipative level attraction between the magnon modes of the two YIG spheres are demonstrated. The former is mediated by cavity photons of a superconducting resonator, and the latter is mediated by propagating photons of a coplanar waveguide. Our results open new avenues towards exploring integrated hybrid magnonic networks for coherent information processing on a quantum-compatible supe…
We demonstrate strong magnon-photon coupling of a thin-film permalloy device fabricated on a coplanar superconducting resonator. A coupling strength of 0.152 GHz and a cooperativity of 68 are found for a 30-nm-thick permalloy stripe. The coupling strength is tunable by rotating the biasing magnetic field or changing the volume of permalloy. We also observe an enhancement of magnon-photon coupling in the nonlinear regime of the superconducting resonator, which is mediated by the nucleation of dynamic flux vortices. Our results demonstrate a critical step towards future integrated hybrid systems…
The problem of coupling multiple spin ensembles through cavity photons is revisited by using PyBTM organic radicals and a high-$T_c$ superconducting coplanar resonator. An exceptionally strong coupling is obtained and up to three spin ensembles are simultaneously coupled. The ensembles are made physically distinguishable by chemically varying the $g$ factor and by exploiting the inhomogeneities of the applied magnetic field. The coherent mixing of the spin and field modes is demonstrated by the observed multiple anticrossing, along with the simulations performed within the input-output formali…
We report on fast tunability of an electromagnetic environment coupled to a superconducting coplanar waveguide resonator. Namely, we utilize a recently-developed quantum-circuit refrigerator (QCR) to experimentally demonstrate a dynamic tunability in the total damping rate of the resonator up to almost two orders of magnitude. Based on the theory it corresponds to a change in the internal damping rate by nearly four orders of magnitude. The control of the QCR is fully electrical, with the shortest implemented operation times in the range of 10 ns. This experiment constitutes a fast active rese…
We have observed period-tripling subharmonic oscillations, in a superconducting coplanar waveguide resonator operated in the quantum regime, $k_B T \ll \hbarω$. The resonator is terminated by a tunable inductance that provides a Kerr-type nonlinearity. We detected the output field quadratures at frequencies near the fundamental mode, $ω/2π\sim 5\,$GHz, when the resonator was driven by a current at $3ω$ with an amplitude exceeding an instability threshold. The output radiation was red-detuned from the fundamental mode. We observed three stable radiative states with equal amplitudes and phase-sh…
Lossy dielectrics are a significant source of decoherence in superconducting quantum circuits. In this report, we model and compare the dielectric loss in bulk and interfacial dielectrics in titanium nitride (TiN) and aluminum (Al) superconducting coplanar waveguide (CPW) resonators. We fabricate isotropically trenched resonators to produce a series of device geometries that accentuate a specific dielectric region's contribution to resonator quality factor. While each dielectric region contributes significantly to loss in TiN devices, the metal-air interface dominates the loss in the Al device…
