Gate-Tunable Transmon Using Selective-Area-Grown Superconductor-Semiconductor Hybrid Structures on Silicon

We present a gate-voltage-tunable transmon qubit (gatemon) based on planar $\mathrm{In}\mathrm{As}$ nanowires that are selectively grown on a high-resistivity silicon substrate using III-V buffer layers. We show that low-loss superconducting resonators with an internal quality of $2\times {10}^5$ can readily be realized using these substrates after the removal of buffer layers. We demonstrate coherent control and readout of a gatemon device with a relaxation time, $T_1\approx 700\mathrm{ns}$, and dephasing times, $T_2^{\ast }\approx 20\mathrm{ns}$ and $T_{2,\mathrm{echo}}\approx 1.3\mu \mathrm{s}$. Further, we infer a high junction transparency of $0.4$–$0.9$ from an analysis of the qubit anharmonicity.

Figure 1

Qubit devices and microwave properties. (a) Optical micrograph of the T-shaped qubit island that is capacitively coupled to a readout cavity. (b) Enlarged optical micrograph of the junction region. The junction is positioned on about a $1$-$\mu \mathrm{m}$-thick mesa. (c) Schematic of material stack around the junction. The $\mathrm{In}\mathrm{As}$ region (green) is proximitized by the epitaxial $\mathrm{Al}$ (light blue) and the junction is formed by selectively removing a short segment of the $\mathrm{Al}$. (d) Scanning electron micrograph of the junction area. The mesa consists of $\mathrm{Ga}\mathrm{As}$, $\mathrm{Ga}\mathrm{P}$, and $400\mathrm{nm}$ of $\mathrm{Si}$. The top gate metal climbs the mesa with the help of cross-linked PMMA. (inset) Cross section of the nanowire with the dielectric growth mask consisting of ${\mathrm{Si}\mathrm{O}}_x$ and ${\mathrm{Al}\mathrm{O}}_x$. (e) (Left) The $\mathrm{Ga}$ and $\mathrm{P}$ concentrations of the material stack as a function of depth measured with secondary-ion mass spectrometry. (Center) Schematic of the corresponding material stack. (Right) Internal quality factor of test resonators as a function of photon number for an etch depth into the $\mathrm{Si}$ of $120\mathrm{nm}$ (red), $390\mathrm{nm}$ (blue), and $720\mathrm{nm}$ (green).

Figure 2

Qubit anharmonicity. (a) Resonator response $V_H$ as a function of gate top gate voltage $V_G$ and drive frequency $f_{\mathrm{drive}}$. The qubit is driven through the gate line with microwave pulses with a relatively high-power $P_{\mathrm{rf}}$ on chip such that the $|0⟩\to |1⟩$ with frequency $f_{01}$ and the $|0⟩\to |2⟩$ with frequency $f_{02}/2$ are measured. (b). Extracted anharmonicity $-\alpha /h$ as a function of qubit frequency $f_{01}$ and $\mathrm{\Sigma }{T}_i=(h{f}_{01}{)}^2/(2\mathrm{\Delta }{E}_C)$. Dashed lines indicate model prediction for an ideal QPC (red), two channels with equal transmission (green), and the tunneling limit (black).

Figure 3

Coherent oscillations. (a) The main panel shows Rabi oscillations as a function of drive power on-chip $P_{\mathrm{drive}}$ and pulse length $\tau$ at fixed drive frequency $f_{\mathrm{drive}}=4.47\mathrm{GHz}$. The pulse sequence used is shown above the plot. The lower panel shows a line cut at $P_{\mathrm{drive}}=-89\mathrm{dBm}$ (white dotted line) from the main panel. The solid line is a fit to the data using a damped sinusoid with a linear contribution. (b) The main panel shows Ramsey fringes as a function of delay $\tau$ between $R_{\mathrm{X}}^{\pi /2}$ pulses and $f_{\mathrm{drive}}$. The pulse sequence is shown above. The lower panel shows a line cut at $f_{\mathrm{drive}}=4.353\mathrm{GHz}$ (white dotted line) with a fit to a damped oscillation yielding $T_2^{\ast }\approx 15\mathrm{ns}$. For better visibility, we subtract the average value of $V_H$ for each horizontal line cut in the main panels of (a) and (b).

Figure 4

Qubit lifetimes. (a) Pulse sequences for lifetime measurements. (b) The $T_1$ and $T_{2,\mathrm{echo}}$ measurements of the qubit at $f_q\approx 4.48\mathrm{GHz}$. The $T_{2,\mathrm{echo}}$ data are offset by $+0.09\mathrm{mV}$. (c) Lifetimes as a function of $f_{\mathrm{q}}$. The $T_1$ and $T_{2,\mathrm{echo}}$ times are measured with the pulse sequences shown in (a). The $T_2^{\ast }$ time is extracted from the power dependence of the linewidth of the qubit in spectroscopy (Appendix pp5).

Figure 5

Example data and fit of the resonator with an etch depth of 720 nm (see Fig. 1) at $P_{\mathrm{on}\mathrm{chip}}=-149\mathrm{dBm}$. (a) Raw data (black) and fit (red) of the trajectory of $S_{21}$ in the complex plane. (b) The $S_{21}$ data and fit after correcting for the cable delay [36, 37]. Panels (c) and (d) show the magnitude and phase of $S_{21}$ of the data in (a) with the corresponding fits.

Figure 6

Coherent oscillations. (a) Rabi oscillations as a function of $f_{\mathrm{drive}}$ at the same gate point as in Fig. 3 and $P_{\mathrm{drive}}=-82\mathrm{dBm}$. (b) Rabi oscillations from Fig. 3 with the on-chip drive amplitude $V_{\mathrm{drive}}$. (c) Extracted Rabi frequency ${\mathrm{\Omega }}_{\mathrm{Rabi}}/2\pi$ as a function of $V_{\mathrm{drive}}$. The red line is a linear fit of the form ${\mathrm{\Omega }}_{\mathrm{Rabi}}/2\pi =m\cdot V_{\mathrm{drive}}$ for $V_{\mathrm{drive}}<8.1\mu \mathrm{V}$, with $m$ the fit parameter. (d) Simulated Rabi frequency ${\mathrm{\Omega }}_{\mathrm{Rabi}}/2\pi$ of a four-level system (blue dots) compared with the Rabi frequency of a two-level system (red line).

Figure 7

Different measurement methods for extraction of relaxation time $T_1$. (a) Readout and weak spectroscopy drive tone overlap. (b) The strong readout tone is applied after the spectroscopy drive tone. (c) A $\pi$ pulse is used to excite the qubit. This drive tone overlaps with the readout tone. (d) The readout tone is applied after the $\pi$ pulse. (e) Comparison of extracted $T_1$ values from datasets (a)–(d).

Figure 8

Spectroscopy data for estimation of dephasing time $T_2^{\ast }$. (a) Spectroscopy signal as a function of qubit drive $P_{\mathrm{drive},\mathrm{s}}$ and drive frequency $f_{\mathrm{drive}}$. (b) Line cut from (a) at $P_{\mathrm{drive},\mathrm{s}}=-116.7\mathrm{dBm}$ with fit to a Lorentzian line shape (purple line). (c) Qubit linewidth ${\delta }_{\mathrm{HWHM}}$ versus power $P_{\mathrm{drive},\mathrm{s}}$ with fit using $2\pi {\delta }_{\mathrm{HWHM}}=1/T_2^{\mathrm{\prime }}=(1/T_2^{\ast 2}+n_s{w}_{\mathrm{vac}}^2{T}_1/T_2^{\ast }{)}^{1/2}$. The decoherence time is estimated from the intersection of the fit with the $y$ axis.

Figure 9

Coherence times and $f_q$ as a function of $V_G$. (a) Spectroscopy signal. (b) The qubit frequency $f_q$ as a function of $V_G$ and $T_1$ for 20 different gate voltages. (c) Same as (b) but for $T_2^{\ast }$. (d) Coherence times $T_1$ and $T_2^{\ast }$ as a function of gate dispersion $d{f}_{\mathrm{q}}/d{V}_G$.

Figure 10

Schematic of the experimental setup used for the experiments. The readout resonator can be driven by a vector network analyzer (VNA) or by a signal from a rf source that is modulated by an arbitrary waveform generator (AWG) (blue line). The amplified output signal can be read out either by the VNA or undergo down-conversion by mixing with a reference signal. Microwave equipment is synchronized using a 10-MHz clock reference. To tune the chemical potential of the SAG nanowire junction, a dc line (purple) is connected to the sample. The dc signal merges with the (pink) rf signal used for driving the qubit in a bias tee channel.