Electron-phonon interactions in the Andreev bound states of aluminum nanobridge Josephson junctions

We report continuous measurements of quasiparticles trapping and clearing from Andreev bound states in aluminum nanobridge Josephson junctions integrated into a superconducting-qubit-like device. We find that trapping is well modeled by independent spontaneous emission events. Above 80 mK the clearing process is well described by the absorption of thermal phonons, but other temperature-independent mechanisms dominate at low temperature. We find a complex structure in the dependence of the low-temperature clearing rate on the Andreev bound state energy. Our results shed light on quasiparticle behavior in qubitlike circuits.

Figure 1

(a) Images of similar device: A $\lambda /4$ resonator is grounded through a dc SQUID with a pair of symmetric aluminum nanowire junctions. These junctions are approximately $25\mathrm{nm}\times 8\mathrm{nm}\times 100\mathrm{nm}$. (b) The readout drive ${\omega }_d$ is generated at room temperature and attenuated along the path through the dilution refrigerator to the base stage. At 30 mK, pair breaking photons on all inputs and outputs are reduced by K&L 12-GHz low-pass filters and Eccosorb CR110 infrared absorbers. The signal circulates to reflect off our device and pass through a 5.85-GHz low-pass filter. The signal is then amplified by a traveling wave parametric amplifier (TWPA) whose pump is inserted via a directional coupler. The signal exits the dilution refrigerator receiving further amplification by a high-electron-mobility transistor (HEMT) at 4 K and a series of low-noise amplifiers at room temperature. The signal is homodyne demodulated by an IQ mixer and the resulting quadratures are digitized after 15-MHz low-pass filtering. A Keithley source meter sends dc current along the dashed path to a coil in the device package and a vector network analyzer (VNA) is used to measure the resonance as a function of flux.

Figure 2

Measured trap rate (circles) and model (solid lines). The dependence on the trap depth ${\mathrm{\Delta }}_A$ is shown on the left, while temperature dependence is shown on the right. We note the peak in 30 mK data around 9 GHz on the left was observed as a period of significantly larger than normal mean occupation which lasted approximately 1 h in laboratory time. The source of this peak has not been found and it is not reproducible.

Figure 3

Top: The measured release rate vs trap depth and temperature. The top left panel shows the structure in the trap depth dependence which is attributed to the driven electron-photon interactions which dominate at low temperature. In the top right panel, the low-temperature saturation is visible. The gray dashed line indicates the cutoff temperature (90 mK) for the fit. Bottom: The measured release rate minus the low-temperature saturation is shown as circles, while the phonon clearing model [Eq. (7)] is shown as solid curves.

Figure 4

Top: The measured mean occupation (circles) and the corresponding fit (solid) are shown against temperature. Note that a different fit is performed at each value of ${\mathrm{\Delta }}_A$. Bottom: The fit parameter ${\alpha }_M$ vs trap depth. Stars indicate the value of ${\alpha }_M$ for the three curves of the same color displayed in the top panel.

Figure 5

Two sources of estimate for the rate of readout photons clearing QPs from the ABS traps. The measured low-temperature release rate (blue) and the fit parameter from the mean occupation, shown as $\alpha /{\alpha }_M$ (orange), where $\alpha =38.51$ is found from fitting the phonon contribution to the release rate as shown in Fig. 3. We point out that these agree in shape and magnitude despite coming from different sources.