Single-Quasiparticle Trapping in Aluminum Nanobridge Josephson Junctions

We present microwave measurements of a high quality factor superconducting resonator incorporating two aluminum nanobridge Josephson junctions in a loop shunted by an on-chip capacitor. Trapped quasiparticles (QPs) shift the resonant frequency, allowing us to probe the trapped QP number and energy distribution and to quantify their lifetimes. We find that the trapped QP population obeys a Gibbs distribution above 75 mK, with non-Poissonian trapping statistics. Our results are in quantitative agreement with the Andreev bound state model of transport, and demonstrate a practical means to quantify on-chip QP populations and validate mitigation strategies in a cryogenic environment.

Figure 1

(a) Andreev bound state energies for $\tau =1$ (solid lines) and $\tau =0.5$ (dashed lines). The Andreev gap ${\mathrm{\Delta }}_A$ is illustrated for the $\tau =1$ channel. (b) Simplified measurement schematic. The resonator is biased with a static flux $\mathrm{\Phi }$; measurements are performed by passing a weak probe tone ($f_{\mathrm{probe}}$, blue) through a circulator and analyzing the reflected signal. A strong excitation tone ($f_{\mathrm{exc}}$, red) may be applied via a directional coupler in order to alter the distribution of QPs in the junctions. (c) False-color SEM image of device, showing the nano-SQUID (circled), meander inductor (orange), and IDC (blue). (d) False-color SEM image of the nanobridge junction, showing the bridge (orange) connecting the thick banks (blue and green, highlighting the two deposition layers).

Figure 2

(a) Resonance line shapes versus flux, plotted as a function of frequency detuning from the 0-QP resonance. The Lorentzian present at 0 flux develops multiple broad humps as flux increases. (b) Temperature dependence of the resonance line shape, showing the decrease in QP trapping as temperature rises. All data are shown at $\varphi =0.464$. At low temperature, multiple humps are resolvable, indicating multiple QP trapping numbers. At higher temperatures, first the 2-QP and then the 1-QP peak shrink, leading to a Lorentzian resonance. At even higher temperature ($T=250\mathrm{mK}$), the resonance broadens, shrinks, and moves to lower frequency; we attribute this to loss originating from bulk QP transport in the resonator.

Figure 3

Frequency response at 75 mK for $\varphi =0$ (top, red) and 0.464 (bottom, blue), illustrating the change in resonance line shape. Traces are vertically offset for clarity. The black curves are fits using Eq. (3) with ${\overline{n}}_{\text{trap}}=0$ and 0.49. Inset: ${\overline{n}}_{\text{trap}}$ (left axis, black circles) at $\varphi =0.464$ and extracted values of $x_{\mathrm{QP}}$ (right axis, red squares) as a function of temperature.

Figure 4

Resonance traces taken with the radiator on, showing a Lorentzian line shape at 0 flux (right, red) and a Lorentzian convolved with a Gaussian (with a lower center frequency) at $\varphi =0.432$ (left, blue). Fits using the high-${\overline{n}}_{\text{trap}}$ Gaussian approximation are shown in black. The dashed black line is a fit constrained by a single parameter ${\overline{n}}_{\text{trap}}=7$, while the solid lines allow the width and center point of the convoluted Gaussian-Lorentzian to vary independently (${\overline{n}}_{\text{trap}}=19$ and 7, respectively). The zero-flux data is well fit by a Lorentzian, indicating ${\overline{n}}_{\text{trap}}=0$.

Figure 5

Spectroscopy data, showing the shift in the 0-QP peak height versus flux $\varphi$ and excitation tone frequency $f_{\mathrm{exc}}$, referred to its height with the excitation tone off. The data show a threshold excitation frequency which grows with flux, consistent with ${\mathrm{\Delta }}_A(\varphi )$, and a height shift which grows with flux, indicating a growing ${\overline{n}}_{\text{trap}}$.