Magnetic landscape of NbTiN superconducting resonators under radio-frequency excitation

Abstract

Planar superconducting resonators are essential components in quantum circuits and highly sensitive sensors. However, their performance is often compromised by magnetic flux penetration, as the interaction of flux quanta and the induced radio-frequency (RF) currents in the superconducting thin film leads to significant energy dissipation. At low operating temperatures, this issue is aggravated as thermomagnetic instabilities can trigger the sudden propagation of magnetic flux avalanches. An important open question is whether the RF excitation itself stimulates the nucleation and propagation of magnetic flux avalanches in the superconducting thin film. The literature remains inconclusive on this point, partly due to the lack of compelling evidence for this phenomenon. In this work, we address this issue by unprecedented direct visualization of magnetic flux penetration through Faraday rotation imaging under simultaneous RF excitation. We demonstrate that the avalanche activity exhibits a weak dependence on the RF intensity for RF excitations within the linear Campbell regime. However, magnetic flux bursts clearly influence the RF transmission properties of the device. Furthermore, it is possible to unambiguously associate a particular avalanche event with a jump in resonance frequency. This enables us to identify the loci of most deleterious events and understand the distinct origins of upward and downward frequency shifts. These observations are supported by electromagnetic simulations in which local changes of the kinetic inductance mimic flux avalanches and confirm the invasive character of the MOI technique. The insights gained from this study aim to contribute to the broader understanding of the magnetic resilience of superconducting resonators, with the goal of improving their efficiency and stability.

Figures (5)

• Figure 1: (a) Experimental setup combining RF excitation of three multiplexed quarter-wavelength resonators and simultaneous magneto-optical imaging of the sample. The inset shows the typical components of the indicator placed on top of the device: the transparent gadolinium galium garnet (GGG) substrate, the 3 µm thick optically active indicator Bi:YIG, and a fully reflective mirror. In the final experiments, the mirror has been removed to avoid eddy currents induced in this metallic layer. In addition, the inset shows the geometry of the sample along with the labeling as resonator 1, 2, and 3. (b)-(d) Transmission coefficient $S_{21}$ in the vicinity of the three resonance frequencies at 3.3 K and with a RF power of -30 dBm. The black curves represent the fit obtained by following the procedure explained in khalil_analysis_2012. (e) Relative change of the resonance frequency, $\delta f_r = f_r(T) - f_r(T = 3.33$ K), as a function of temperature. The lines are fit to \ref{['Eq1']}. The inset shows the resonance frequency peak shape as a function of excitation power. (f) Magnetic field dependence of the resonance frequency for an applied out-of-plane magnetic field, cycled from 0 mT $\rightarrow$ 3.3 mT $\rightarrow$ -3.3 mT $\rightarrow$ 0 mT, with dark arrows indicating the sweeping direction. The green arrow indicates the situation pictured in the panel (g) and corresponding to the transmission parameter for two consecutive applied magnetic fields. The dotted box indicates the magnetic field interval studied in \ref{['Fig4']}.
• Figure 2: (a)-(d) Magnetic flux penetration after a zero-field cooling during a magnetic field sweep from 0 mT $\rightarrow$ 3.3 mT $\rightarrow$ -3.3 mT $\rightarrow$ 0 mT at a base temperature of 3.2 K. Images were taken at 0.67 mT ($\mu_0 H_{app} \nearrow$), 1.33 mT ($\mu_0 H_{app} \nearrow$), 0.59 mT ($\mu_0 H_{app} \searrow$) and -0.71 mT ($\mu_0 H_{app} \searrow$), respectively. (e)-(g) Transmission coefficient $S_{21}$ for the resonator alone, with the indicator and with the indicator without mirror, respectively, at 3.3, 5.1, 6.4 and 7.1 K. (h, i) Evolution of the relative change in resonance frequency, $\delta f_r = f_r(d) - f_r(d = 100~\text{µm})$, and quality factor with decreasing distance between sample and indicator. The gray lines represent the width of the central microstrip line.
• Figure 3: (a) Schematic of the experimental protocol followed to characterize the influence a RF sweep on magnetic flux avalanches. This protocol is applied after a ZFC. (b)-(e) Avalanche activity appearing after waiting $\Delta t$ when increasing the magnetic field. (b) and (c) show the avalanches appearing after $\Delta t =2$ s for a control measurement and during a RF sweep respectively. (d) and (e) show the avalanches appearing after $\Delta t=6$ s for the control measurement and during the RF sweep respectively. (f)-(h) Histogram of the frequency jump sizes appearing during a magnetic field sweep for -30 dBm, -20 dBm and -15 dBm. Each graph results from 10 magnetic field sweeps with a constant field step of 0.0216 mT. (i) Cumulative probability of the frequency jump sizes for the three RF powers applied.
• Figure 4: (a)-(c) Resonance frequency as a function of applied magnetic field of resonator 1, 2 and 3, respectively. (d)-(i) MOI images related to the intervals of magnetic field defined in (a)-(c). Each new avalanche is colored with respect to where it nucleates, where resonator 1 is green, resonator 2 is red, resonator 3 is blue, whereas avalanches forming at the feedline and the border edges are colored in orange. The field range and magnetic history correspond to the dotted box indicated in Figure 1(f).
• Figure 5: (a) Simulated $S_{21}$ spectrum of the resonance peak for a superconducting area that is modeled using the same kinetic inductance ($L_k$) as the rest of the material, an increased kinetic inductance (10*$L_k$) and finally, with a resistive component ($R_{RF})$. (b) Illustration of the simulated current density at resonance at an applied power of +13 dBm, superposed with the subdivisions considered in the following. (c) Simulated relative change in resonance frequency as a function of the position of the simulated area. The triangle markers corresponds to the outer areas and the dots to the inner ones, as shown in (b). Furthermore, the marker colors correspond to the position of the considered areas. (d) Change in resonance frequency as a function of the current density squared at the center conductor near the simulated area. (e) Simulated relative change in resonance frequency as a function of the contact length with the edge of the conductor. The upper inset shows the change in resonance frequency as a function of the area of the simulated patch, while the lower inset illustrates the contact length and area of the simulated patch.