Spin Readout of a CMOS Quantum Dot by Gate Reflectometry and Spin-Dependent Tunneling

Silicon spin qubits are promising candidates for realizing large-scale quantum processors, benefitting from a magnetically quiet host material and the prospects of leveraging the mature silicon device fabrication industry. We report the measurement of an electron spin in a singly occupied gate-defined quantum dot, fabricated using CMOS-compatible processes at the 300-mm wafer scale. For readout, we employ spin-dependent tunneling combined with a low-footprint single-lead quantum-dot charge sensor, measured using rf gate reflectometry. We demonstrate spin readout in two devices using this technique, obtaining valley splittings in the range 0.5–0.7 meV using excited-state spectroscopy, and measure a maximum electron-spin relaxation time ($T_1$) of $9\pm 3$ s at 1 T. These long lifetimes indicate the silicon-nanowire geometry and fabrication processes employed here show a great deal of promise for qubit devices, while the spin-readout method demonstrated here is well suited to a variety of scalable architectures.

Popular Summary

The same silicon technology used in conventional integrated circuits can be exploited for a physical realization of a qubit, the unit cell of a quantum computer. In this approach, information is encoded in the spin degree of freedom of an electron confined in a nanoscale semiconductor device known as a quantum dot. The small size of the quantum dots enables a high qubit density similar to the density of transistors in current processors. To reach the full potential in qubit density, and thus in quantum-computer performance, qubits need to be manufactured using industrial mass fabrication techniques while the footprint of circuits fabricated alongside each qubit for readout or control needs to be minimized. Our work addresses both issues, evaluating whether CMOS-compatible manufacturing processes performed at the scale of 300-mm wafers can be used to make long-lived spin qubits combined with a reduced-footprint readout method.

The readout of an electron spin trapped in the dot is performed by conditioning its tunneling to an electric reservoir on its spin polarization. Such a tunneling event disturbs the potential of a neighbor “sensor” dot, which is constantly monitored. To do so, a small oscillating rf signal sent to the sensor gate electrode is continuously attempting to move an electron between the sensor dot and the reservoir. The breakdown of this dynamic equilibrium due to spin-dependent tunneling is measured as a change in the dot capacitance.

Our results show long relaxation times measured using a compact readout setup, positioning CMOS-compatible devices as potential high-quality qubits compatible with scalable manufacturing.

Figure 1

Device and measurement setup. (a) False-color transmission electron micrograph of a silicon nanowire with a pair of split gates. Quantum dots are formed under each gate, referred to as “sensor” and “qubit” dots, and controlled, respectively, by $V_S$ and $V_Q$. The sensor dot is connected to a lumped-element resonator for dispersive readout. Fast pulses, $V_{\mathrm{ac}}$, are applied to the qubit dot through a bias tee. To lift the spin degeneracy, a magnetic field is applied in the $[\overline{1}10]$ crystallographic direction, perpendicular to the nanowire. The magnetic field orientation can be rotated in the plane of the device, making an angle $\theta$ to $[\overline{1}10]$. (b) Magnitude of the reflection coefficient, $|\mathrm{\Gamma }|$, showing the resonator frequency at 0 T. Applying a magnetic field reduces the resonant frequency due to changes in the kinetic inductance of the superconducting inductor that forms the resonator [31], see Appendix pp2 for further details.

Figure 2

Spin readout. (a) Three-level pulse sequence applied to the qubit-dot gate: first emptying the dot (E), then loading an electron with a random spin orientation into the dot (L), and finally reading the spin state (R). (b) For spin readout, the qubit-dot potential is tuned so its spin-up and spin-down states straddle the reservoir Fermi energy. A spin-down electron remains in the qubit dot, whereas a spin-up electron tunnels out (1) followed by a spin-down electron entering the dot (2). Due to capacitive interdot coupling, changes in the qubit-dot charge state cause the sensor-dot electrochemical potential to shift into or out of alignment with the reservoir, leading to the appearance or suppression of a phase response signal $\mathrm{\Delta }\varphi$ in reflectometry. (c) Single-shot schematics and time-averaged measured phase response (1024 averages) for device A (red), and B (blue), where the spin-up signature is, respectively, a dip or a peak in the phase response. (d) Charge stability diagram of the double quantum dot near the $(n_q,n_s)=(1,N)\leftrightarrow (0,N+1)$ charge transition for device B (device A measurements use a nominally identical charge transition). Only the sensor-dot lead-to-dot transition is visible in reflectometry.

Figure 3

Spin-relaxation rates and their magnetic field dependence. (a) Relaxation rate measured with the magnetic field applied perpendicular to the nanowire, in the plane of the device, in the $[\overline{1}10]$ crystallographic direction. Curves are fits to a general model described in the text, and $E_V$ marks the field at which the Zeeman splitting matches the measured valley splitting in device B. (b) Dependence of $T_1^{-1}$ on magnetic field orientation at 1 T for device B, where $\theta$ is the angle between the magnetic field and the $[\overline{1}10]$ crystallographic direction for device B in the nanowire plane. The angular dependence expected from spin-valley mixing in an ideal corner dot (dashed gray curve) is insufficient to explain the observed trend. Spin-lattice relaxation mechanisms can, however, give rise to higher-order angular modulations [34] in quantum dots with high symmetry (see, for example, orange dashed curve and Appendix pp10).

Figure 4

Excited-state spectroscopy. (a) Measured spin-up fraction for different load levels obtained using energy-selective loading in a four-level pulse scheme as shown in the inset and fit. (b) Illustration of different loading level regimes. (I) When the load level is too low, no electrons are loaded, and an electron with random spin tunnels in during the plunge stage. (II) If the reservoir $E_F$ is placed between the spin-up and -down state, only spin-down electrons tunnel in. (III) At higher load levels, a random spin tunnels in during the load stage. (IV) When $E_F$ lies between the spin-up and -down levels of the excited state, an electron can occupy any spin state of the ground state and the spin-down excited state. Assuming fast spin-conserving relaxation from the excited to the ground state, most of the electrons are found with spin down. (V) For even higher load levels, the electron tunnels into any possible state. (c) Zeeman splitting $E_Z$ and excited-state energy $E_V$ obtained by fitting (a) to Eq. (3) at different magnetic fields for devices A and B.

Figure 5

(a) $Q$ factor and resonant frequency of the resonator at different magnetic fields applied in the $[\overline{1},1,0]$ crystallographic direction. The error bars are smaller than the scatter dots. (b) $Q$ factor and inductance when $B=1\mathrm{T}$ is applied in different directions. $\theta$ is the angle of the magnetic field with respect to $[\overline{1},1,0]$ in the plane of the device, as in Fig. 1.

Figure 6

(a) Left: normalized phase response of the resonator over time in the readout stage at different $V_Q$ offsets for device A. The pulse sequence is depicted in the inset. Right: simulation for an applied magnetic field of 1.4 T. The simulation takes into account the mismatch between the bias-tee cutoff frequency and the compensated pulse. (b) Same for device B at $B=3$ T. (b)–(d) Diagrams of the qubit-dot electrochemical potential with respect to the lead Fermi energy at three different offsets. At offset (b) the electron remains in the dot. In (c) only spin-up electrons can tunnel out from the dot and, shortly afterwards, an electron with spin down comes back to the dot. In (d) the electron always tunnels out. (f) Dot occupation number along line 1 comparing measurement (dotted) with simulation (line). (g) Dot occupation number as a function of time at low offsets along line 2. The phase rise time due to the resonator bandwidth corresponds to the first microsecond of the graph. (e),(h),(i) Corresponding data and simulation for device B.

Figure 7

Two-level pulse sequence based on “load” and “read.” (a) Demodulated phase over time in the readout stage normalized at each $V_Q$ offset for device A (left) and its simulation (right) for an applied magnetic field of 1.4 T. The pulse sequence is depicted in the inset. (b)–(d) Diagrams of the qubit-dot electrochemical potential with respect to the lead Fermi energy at three different pulse offsets, $V_Q$. (e) The same as (a), but for device B at $B=3$ T.

Figure 8

Lever-arm and device characterization. (a) Device A stability diagram. A solid square indicates the readout area corresponding to the first electronic transition of the qubit dot since no other shifts are visible for a large range of smaller $V_Q$. The dashed square indicates dot-donor transitions. The donor is presumed to be bismuth since the sample is bismuth doped. (b) As above for device B. The black dashed line helps the eye to follow one of the qubit-dot electronic transitions. (c) Coulomb diamond of the sensor dot in device B from the sensor dot-to-lead transition used in the readout. The slopes used for calculating ${\alpha }_{SS}$ (see text) are marked with dashed black lines.

Figure 9

Qubit-dot lever arm from temperature measurements. (a) Homodyne $I/Q$ voltage as a function of $\mathrm{\Delta }{V}_Q$, at fridge temperatures of 200 and 800 mK for device B. (b) Width of the Fermi-Dirac distribution measured in (a) as a function of the fridge temperature and fit. (c) Zeeman energy obtained as $\mathrm{\Delta }{E}_z=e{\alpha }_{QQ}{V}_Q$ from Fig. 6, where $QQ$ is the lever arm calculated in (b). Dashed line shows the Zeeman energy for $g=2$.

Figure 10

Perturbation of the qubit-dot electrochemical potential, given in Tesla, due to the rf-carrier power, $P_c$. (a) Blue: electronic transition half width maximum, ${ϵ}_{1/2}$ of the sensor dot, converted to a qubit-dot potential using the cross lever arm ${\alpha }_{QS}$. Error bars are smaller than the dot size. Green: a direct measurement of broadening obtained by sweeping the qubit-dot voltage [see Fig. 9]. (b) Spin-up fraction at different readout offsets, $V_Q$, and powers at 1 T.

Figure 11

(a),(b) The normalized spin-up fraction with respect to the waiting time for devices A and B, respectively, fitted to an exponential decay for different magnetic fields. (c) Comparison between the relaxation time measured with the rf-readout tone continuously on, or switched off during the waiting time.