Recovery dynamics of a gap-engineered transmon after a quasiparticle burst

Abstract

Ionizing radiation impacts create bursts of quasiparticle density in superconducting qubits. These bursts temporarily degrade qubit coherence which can be detrimental for quantum error correction. Here, we experimentally resolve quasiparticle bursts in 3D gap-engineered transmon qubits by continuously monitoring qubit transitions. Gap engineering allows us to reduce the burst detection rate by a factor of five. This reduction falls four orders of magnitude short of that expected if the quasiparticles were to quickly thermalize to the cryostat temperature. We associate the limited effect of gap engineering with the slow thermalization of the phonons in our chips after the burst.

Figures (2)

• Figure 1: (a) Parity-switching rate ($\Gamma$) as a function of the fridge temperature ($T$) for devices with different film thicknesses. The film thickness is used as a knob to control the gap difference $\:\delta\Delta$ at the qubit junction. Down (up)-pointing triangles represent rate $\Gamma_0$ ($\Gamma_1$) conditioned on the qubit residing in the ground (excited) state. When $\:\delta\Delta > hf_q$, the gap difference is efficient in obstructing the tunneling of resident QPs. Correspondingly, $\Gamma_1$ follows an Arrhenius law with the activation exponent $\:\delta\Delta - hf_q$, i.e., $\Gamma_1\propto \exp\left(-\left[\:\delta\Delta - hf_q\right] / \:k_\mathrm{B} T\right)$. This regime is realized in the big- and medium-$\:\delta\Delta$ device (left and middle panels). For the small-$\:\delta\Delta$ device (right panel), $\:\delta\Delta < hf_q$, and the gap difference is not effective at preventing the tunneling of resident QPs. The observed rate $\Gamma_1$ for the small-$\:\delta\Delta$ device is the highest among the measured devices. Comparing the data for $\Gamma_1$ and $\Gamma_0$ to theory (solid lines) allows us to extract $\:\delta\Delta$ and the resident QP density for all three devices. The resulting fit parameters are shown in Table \ref{['tab:table1']}. Notably, $\Gamma^\mathrm{ph}$ and $\:x_{\mathrm{QP}}^\mathrm{ne}$ for the three devices are of the same order of magnitude despite being fabricated individually. We attribute this consistency to the shared electromagnetic and radiation environment provided by the multiplexed package noauthor_see_nodate. (b) Exponential suppression of the resident QP tunneling rate, $\Gamma_1-\Gamma_1^\mathrm{ph}$, in state $|1\rangle$. Different points correspond to devices with different $\:\delta\Delta-\:hf_q$, different cooldowns, and temperatures noauthor_see_nodate. For convenience of comparison between different devices, the rate is normalized by the resident QP density, $\:\gamma^\mathrm{QP}_1\coloneqq (\Gamma_1-\Gamma_1^\mathrm{ph})/\:x_{\mathrm{QP}}^\mathrm{ne}$. When the gap difference surpasses the qubit energy, the normalized tunneling rate decreases exponentially with increasing $\:(\delta\Delta-hf_q)/k_\mathrm{B} T$. The inset shows the full dependence of $\:\gamma^\mathrm{QP}_1$ on $\:(\delta\Delta-hf_q)/k_\mathrm{B} T$. The normalized rate diverges when $\:\delta\Delta=\:hf_q$ but becomes temperature-insensitive for $\:\delta\Delta<\:hf_q$. The gray-shaded regions in the main plot and inset represent the theoretical prediction for the rate for a range of additional parameters such as $E_J$ or $E_C$.
• Figure 2: (a) Schematic of how a high-energy impact leads to a QP burst. The collision of high-energy particles ionizes electron-hole pairs in the substrate. When the electron-hole pairs recombine, they generate high-energy phonons (green waves). These phonons have enough energy to break Cooper pairs in superconducting films, thereby generating numerous QPs. Tunneling of these QPs across the junction increases the qubit relaxation rate. (b) Pulse sequence for detecting QP bursts. Every 5.7 $\mathrm{\mu s}$, the qubit is read-out, then projected into $\ket{1}$. (c) Histogram of the qubit relaxation event counts within a 1 ms window. Different colors correspond to different devices. In the absence of bursts, we expect the histograms to represent a Poisson process. The most likely number of relaxation events is determined by the steady-state coherence time $T_1^{\rm steady}$. The positions of the observed maxima are consistent with measured steady-state relaxation times ($T_1^{\rm steady} \approx 100 \mathrm{\mu s}$). We associate clear deviation from the Poissonian statistics in the tails of the distributions with the rare QP bursts. To the right of the black line, the measured counts for both devices are dominated by QP bursts. Post-selecting events based on this threshold thus allows fair comparison of the burst occurrence rate in the big-$\:\delta\Delta$ and small-$\:\delta\Delta$ devices. The larger $\:\delta\Delta$ yields roughly five times fewer detected burst events according to this criteria. (d) A readout trace during a QP burst. After the burst begins, the qubit experiences an excess number of relaxation events. During the burst, the number of relaxation events in several 1 ms bins exceeds the threshold in panel (c). It allows us to identify the burst. (e) Excess qubit relaxation rate $\Delta\Gamma_{10}$ after high-energy impacts, averaged over all observed burst events. The bursts are identified according to the threshold defined in panel (c). Exponential fit results are shown with solid lines. The extracted burst duration, see the legend, is insensitive to $\:\delta\Delta$. The inset shows the qubit temperature, $T_q$, during bursts in the big-$\:\delta\Delta$ device (see noauthor_see_nodate for the measurement protocol). We observe $T_q$ abruptly increases from the background value (50 mK) to $\approx90$ mK and stays consistently elevated for over 5 ms. We attribute this increase to elevated QP temperature during the burst. We note that the 50 mK background likely does not reflect the real temperature of the sample. Excess of $\ket{1}$ measurements primarily stems from measurement errors.