reSeArCH Letter
MEthodS
Device fabrication and choice of quantum dot size. The device is fabricated on
a p-type natural Si substrate (1–10 Ω cm). The substrate is subjected to a series
of high-temperature annealing processes up to 1,100 °C followed by a controlled
cool-down to 330 °C, at which point the surface is terminated with mono-atomic
hydrogen via thermal cracking. The result is a fully terminated H:Si (2 × 1) recon-
structed surface from which the hydrogen can be selectively removed with the
STM tip. Using the STM tip a lithographic mask representing the device and donor
qubits is created on the Si surface. Subsequent adsorption and incorporation (at
350 °C) of gaseous PH 3 precursor metallizes the exposed area with ~1/4 monolayer
of phosphorus. Then, 45 nm of natural Si is grown on the device using molecular
beam epitaxy.
The charging energy of the quantum dots, EcD, can be used to determine the
number of donors in each qubit^14 ,^19. In Extended Data Fig. 1 we show the defini-
tions of the parameters used for this calculation. The first is the RF-SET charging
energy, EcS, which is measured from the Coulomb diamonds in Extended Data
Fig. 1a. The mutual charging energy between the RF-SET and the donor qubit gives
a voltage shift on the RF-SET transition in the gate map that is defined as δVgS; see
Extended Data Fig. 1b. Its counterpart, the donor transition shift, is defined as δVgD.
Similarly, the voltage shift on donor transitions caused by the mutual charging
energy between the donors is defined as δVgD. The voltage differences between the
two charge transitions of the RF-SET (donor) is defined as ΔVgS ()ΔVgD, shown
in Extended Data Fig. 1b (Extended Data Fig. 1c). Finally, the number of charge
transitions of the SET between the two donor quantum dot charging events, ns,
can be determined by counting the number of current peaks in the charge stability
maps. After measuring all of these values in the charge stability map, we can cal-
culate the donor charging energy EcD, which is given by
=δΔ
Δ−δδ−
EEVVVVVcD n (1)cS
gSgSgD
gDDgDSBy comparing the calculated charging energies of the L dot,
EcD(L)7=. 09 ±.14 7meV, and the R dot, EcD(R)9=. 02 ±.18 5meV, with previous
results and theoretical calculations^14 , we estimate that the L dot contains 2P and
the R dot contains 3P. We also check the donor numbers by measuring the spin
relaxation time T 1 on both quantum dots. On L we find T 1 = 0.483 ± 0.083 s and
on R we determine T 1 = 0.107 ± 0.032 s at B = 2.5 T and an electron temperature
of 330 mK. These values are comparable to previous results on 2P1e (one electron
bound to two phosphorus donors) and consistent with theoretical predictions for
the 3P3e case at comparable magnetic fields^20.
Experimental measurement set-up. The device is measured at low temperatures
(50 mK) inside a dilution refrigerator; a diagram of our complete set-up is dis-
played in Extended Data Fig. 2. The gate electrodes (left, middle, right and SET)
of the device are connected to a room-temperature voltage source (SIM 928) to
control the electrostatic environment of the quantum dots, via 1:5 voltage dividers
and a two-stage RC low-pass filter (~300 kHz) at the 50-mK stage. An additional
voltage source (NI6363) with 1:50 voltage dividers is connected to the left and right
gates to supply the voltage pulses required for initializing the qubits. Faster pulsing
is required for the nanosecond detuning pulses that are needed to create coher-
ent state rotations, so two room-temperature, synchronized waveform generators
(AWG70001A) are also connected to the left and right gates through bias tees and
triggered by the NI6363. The bias tees each contain a 2-kΩ resistor and a 1.2-nF
capacitor, and the fast lines each have attenuators of − 18 dB between the 4-K and
50-mK stages for noise reduction and thermalization.
The spin readout of the quantum dots is performed with an SET used as a charge
detector comprising a quantum dot, source and drain leads. We perform readout
with the SET in combination with a lumped-element LC circuit (RF-SET) in the
megahertz regime using reflectometry techniques^34. The LC circuit consists of a
1-μH inductor and the parasitic capacitance of the device (< 1 pF) with a resonance
frequency of 258.3 MHz, and is used to impedance-match the SET with the rest of
the 50-Ω electronics. The input carrier wave (258.3 MHz) for the RF-SET readout
is supplied by a room-temperature RF signal generator and is passed through a var-
iable attenuator and d.c. block before reaching the dilution unit. The carrier wave is
further attenuated between the 4-K and 50-mK stages (− 40 dB) and travels through
a directional coupler before being reflected by the RF-SET, amplified at both 50 mK
(CMT CITLF-3) and room temperature, and then demodulated with the original
carrier wave at room temperature to measure the in-phase and quadrature signals.Data availability
The data pertaining to this study are available from the corresponding author
upon reasonable request.- Gorman, S. K. et al. Tunneling statistics for analysis of spin-readout fidelity. Phys.
Rev. Appl. 8 , 034019 (2017).