Quasiparticle Dynamics in Epitaxial $\mathrm{Al}$-$\mathrm{In}\mathrm{As}$ Planar Josephson Junctions

Quasiparticle (QP) effects play a significant role in the coherence and fidelity of superconducting quantum circuits. The Andreev bound states of high-transparency Josephson junctions can act as low-energy traps for QPs, providing a mechanism for studying the dynamics and properties of both the QPs and the junction. Using locally injected and thermal QPs, we study QP loss and QP poisoning in epitaxial $\mathrm{Al}$-$\mathrm{In}\mathrm{As}$ Josephson junctions incorporated in a superconducting quantum interference device (SQUID) galvanically shorting a superconducting resonator to ground. We observe changes in the resonance line shape and frequency shifts consistent with QP trapping into and clearing out of the ABSs of the junctions when the junctions are phase biased. By monitoring the QP trapping and clearing mechanisms in time, we find a time scale of $\mathcal{O}(1\text{μ}\mathrm{s})$ for these QP dynamics, consistent with the presence of phonon-mediated QP-QP interactions. Our measurements suggest that electron-phonon interactions play a significant role in the relaxation mechanisms of our system, while electron-photon interactions and electron-phonon interactions govern the clearing mechanisms. Our results highlight the QP-induced dissipation and complex QP dynamics in superconducting quantum circuits fabricated on superconductor-semiconductor heterostructures.

Popular Summary

Standard Josephson tunnel junctions, formed by two superconducting layers sandwiching a nm-thick insulating barrier, conduct current through the tunneling of Cooper pairs. Current in a Josephson junction based on indium arsenide, however, is carried by coherent reflections of normal electrons and holes at the two interfaces forming Andreev bound states. These states have their own spectrum, and understanding their dynamics is key in many mesoscopic and topological superconductivity. We show that these states form low-energy bound states that can act like traps for unassuming quasiparticles. While it was predicted there should be a very low density of quasiparticles in superconducting circuits at operating temperatures of 20 mK, it has been observed that the density is much larger than expected. In standard transmon circuits, tunneling of quasiparticles across a Josephson junction can cause dissipation. In hybrid indium arsenide-based junctions, the quasiparticles can actually fall into the Andreev bound states, causing a measurable decrease in the current through the device, an act known as quasiparticle poisoning. Understanding the quasiparticle poisoning effect is key in using the mesoscopic junctions for superconducting qubit or topological quantum computing platforms based on Majorana bound states, as poisoning can interfere with the users fault-tolerant operation.

In this work we show that with two Josephson junctions forming a superconducting quantum interference device, we are able to detect the poisoning of Andreev bound states by quasiparticles. These quasiparticles are thermally activated and injected deliberately by an injector on the same chip. We are also able to clear the trapped quasiparticles from the junctions, and by studying the rates of trapping and clearing, we uncover mechanisms behind quasiparticle poisoning in indium arsenide junctions, such as electron-phonon interactions and local suppression of the superconducting gap.

Our work provides insights to quasiparticle poisoning dynamics in indium arsenide Josephson junctions, relevant for superconducting circuits and topological quantum computing platforms based on Majorana bound states.

Figure 1

The Andreev spectrum and the device design. (a) The calculated energy spectrum of the Andreev bound states in a wide $\mathrm{Al}$-$\mathrm{In}\mathrm{As}$ junction. The results obtained are for a JJ with width $w=1\text{μ}\mathrm{m}$, normal region length $l=100\mathrm{nm}$, length of the superconductor $l_{\mathrm{sc}}=2\text{μ}\mathrm{m}$, superconducting gap $\mathrm{\Delta }=210\text{μ}\mathrm{eV}$, carrier density $n=4\times {10}^{11}{\mathrm{cm}}^{-2}$, and effective electron mass $m^{\ast }=0.04m_e$, where $m_e$ is the electron mass. (b) A histogram of the transparencies of the ABS modes in (a) extracted from fitting the modes to Eq. (1). (c) The circuit diagram of the CPW-SQUID device. A transmission-line resonator with frequency $f_0$ is coupled capacitively to a feed line characterized by an external quality factor $Q_{\mathrm{ext}}$ and directly connected to a superconducting loop with two Josephson junctions (JJs), each with inductance $L_J$. A flux $\mathrm{\Phi }$ threads the loop. Separately, a two-terminal “injector” JJ is placed $1.6\mathrm{mm}$ away from the SQUID, serving to inject QPs to the circuit by biasing one terminal with voltage $V_{\mathrm{inj}}$ and grounding the other terminal. (d)–(f) Optical images of (d) the CPW-SQUID device, (e) the SQUID, and (f) the injector junction, where the etched mesa is shown in dark blue, epitaxial $\mathrm{Al}$ in light blue, and gates in gold.

Figure 2

The flux tuning. (a) The magnitude of the complex transmission $|S_{21}|$ as a function of magnetic flux $\mathrm{\Phi }/{\mathrm{\Phi }}_0$. (b) The corresponding line cuts.

Figure 3

The effect of QP injection and clearing. (a) Line cuts for zero and half flux at zero and finite injector bias, $V_{\mathrm{inj}}$. The half-flux case shows a more pronounced broadening and frequency shift upon QP injection. (b) Line cuts for different flux values at $V_{\mathrm{inj}}=10\mathrm{mV}$ and photon number = 2, with and without an applied clearing tone of frequency $f_{\mathrm{clear}}=18\mathrm{GHz}$. The finite-flux cases show the original line shape is somewhat restored with the application of the clearing tone, while the zero-flux case shows no change.

Figure 4

Microwave loss due to QP effects. The (a),(c),(e) internal quality factor $Q_{\mathrm{int}}$ and (b),(d),(f) frequency shift $\mathrm{\Delta }{f}_r$ as a function of: (a),(b) the voltage bias of the injector junction $V_{\mathrm{inj}}$ at $T=15\mathrm{mK}$, (c),(d) the temperature $T$ without QP injection ($V_{\mathrm{inj}}=0\mathrm{mV}$) and (e),(f) the photon number $\overline{n}$ at $T=15\mathrm{mK}$. $\mathrm{\Delta }{f}_r$ is calculated by subtracting the leftmost $f_r$ value of each data set on the horizontal axis. The solid lines show fits to models for the dependence of $Q_{\mathrm{int}}$ on $T$ and $\overline{n}$ and to the dependence of $f_r$ on $T$.

Figure 5

QP trapping and clearing. (a) The protocol for QP clearing. (i) While the in-phase (I) and quadrature (Q) components are measured, a constant $V_{\mathrm{inj}}=10\mathrm{mV}$ being applied such that a finite QP density populates the trap states. (ii) A 100-$\text{μ}\mathrm{s}$-long clearing-tone pulse with $f_{\mathrm{clear}}=18\mathrm{GHz}$ is applied, which clears out the QPs. (iii) The clearing-tone pulse ends and QPs fall back into the trap states. (b) An example measurement of the I response over time $t$. The region where the clearing-tone pulse is on is shaded in green. The clearing time $t_{\mathrm{clear}}$ and the trapping $t_{\mathrm{trap}}$ are extracted from an exponential fit of the I or Q response to the start (bottom left plot) and end of the pulse (bottom right plot), respectively. (c)–(e) The trapping and clearing times as a function of $\mathrm{\Phi }/{\mathrm{\Phi }}_0$, $V_{\mathrm{inj}}$, and the temperature $T$, respectively: (c) $V_{\mathrm{inj}}=10\mathrm{mV}$, $T=15\mathrm{mK}$; (d) $\mathrm{\Phi }/{\mathrm{\Phi }}_0=0.49$, $T=15\mathrm{mK}$; (e) $\mathrm{\Phi }/{\mathrm{\Phi }}_0=0.49$, $V_{\mathrm{inj}}=0\mathrm{mV}$.

Figure 6

A schematic of the chip design. The chip has three $\lambda /4$ CPWs shunted to ground through a SQUID loop (RS2, RS3, and RS4) and one bare resonator (R1). The design also includes two injector junctions (IJ1 and IJ2). In this work, we focus on RS3, R1, and IJ1.

Figure 7

A schematic of the material heterostructure with a junction, made of $\mathrm{Al}$ superconducting contacts and an $\mathrm{In}\mathrm{As}$ surface quantum well. A layer of $\mathrm{Al}\mathrm{O}$${}_x$ is deposited as a gate dielectric, followed by a patterned $\mathrm{Al}$ gate.

Figure 8

A schematic of the cryogenic and room-temperature measurement setup.

Figure 9

(a) The extracted resonant frequencies $f_r$ from Fig. 2 as a function of the out-of-plane magnetic field $B_{\perp }$. The periodicity of the oscillations is found by finding the $B_{\perp }$ values at the maximum of each oscillation. (b) The extracted resonant frequencies and fit for the SQUID oscillation using Eq. (D1).

Figure 10

(a) A three-dimensional diagram of the QCage sample holder. (b) A cross-section view of the sample holder showing the Au-plated (Be-Cu) frames that create the inner cavity and the superconducting shielding.

Figure 11

A histogram of the Andreev-trap depth ${\mathrm{\Delta }}_A$ at half flux extracted from the ABS modes calculated in Fig. 1.

Figure 12

(a) An example measurement of the I response over time $t$ for two different values of $V_{\mathrm{inj}}$ at ${\mathrm{\Phi }}_{\mathrm{ext}}/{\mathrm{\Phi }}_0=0.5$ and at a temperature of $T=15$ mKe. The region where the pulse is maximum is shaded in green. (b),(c) Regions that we fit to extract the clearing and trapping times are shown in (b) and (c) respectively. For the injector voltage biases of $V_{\mathrm{inj}}=2\mathrm{mV}$ and $V_{\mathrm{inj}}=0\mathrm{mV}$.