Charge Dynamics and Spin Blockade in a Hybrid Double Quantum Dot in Silicon

Electron spin qubits in silicon, whether in quantum dots or in donor atoms, have long been considered attractive qubits for the implementation of a quantum computer because of silicon’s “semiconductor vacuum” character and its compatibility with the microelectronics industry. While donor electron spins in silicon provide extremely long coherence times and access to the nuclear spin via the hyperfine interaction, quantum dots have the complementary advantages of fast electrical operations, tunability, and scalability. Here, we present an approach to a novel hybrid double quantum dot by coupling a donor to a lithographically patterned artificial atom. Using gate-based rf reflectometry, we probe the charge stability of this double quantum-dot system and the variation of quantum capacitance at the interdot charge transition. Using microwave spectroscopy, we find a tunnel coupling of 2.7 GHz and characterize the charge dynamics, which reveals a charge $T_2^{*}$ of 200 ps and a relaxation time $T_1$ of 100 ns. Additionally, we demonstrate a spin blockade at the inderdot transition, opening up the possibility to operate this coupled system as a singlet-triplet qubit or to transfer a coherent spin state between the quantum dot and the donor electron and nucleus.

Popular Summary

Quantum physics applied to computing is predicted to lead to revolutionary enhancements in computational speed and power. However, the building blocks of such a “quantum” computer, called qubits, have to be resistant to environmental disturbance; they need to hold information encoded in them for long periods of time. One of the most promising ways to build such qubits consists of exploiting the spin degree of freedom of natural atoms implanted in silicon, which is a material used extensively in the electronics industry. Moreover, in order to transfer coherent information between distant qubits, it is possible to create spin buses in silicon out of artificial atoms called “quantum dots” that are controlled with electrostatic gates. Here, we demonstrate the coupling between such a quantum dot and a natural atom in silicon.

We show the coupling between a quantum dot located at the corner of a silicon nanowire transistor and a phosphorous atom implanted in the transistor channel. We additionally present the hybridization between these two systems as a function of the electrostatic environment. Our work focuses on the charge dynamics in the double-dot regime—which we measure using microwave spectroscopy—to characterize the charge relaxation and dephasing times at 30 mK. We also demonstrate spin blockade in the system by highlighting the formation of singlet and triplet states in the hybrid double dot. Such a qubit can take advantage of the enhanced spin lifetime of the donor as well as provide a way to transfer information into the even longer-lived quantum memory offered by the donor nucleus. In addition, we engineer the sample in an industrial microfabrication-compatible facility, thereby providing a rich perspective on the scalability of these devices.

Our work on this novel hybrid qubit demonstrates a viable way to harness the complementary advantages of excellent coherence times and fast control offered by our two systems for a large-scale quantum computing architecture. Its scientific value also lies in the previously unexplored physics of the coupling between a natural atom (the phosphorus donor) and an artificial atom (the quantum dot). We expect that our results will open up new perspectives for more interesting spin physics in the future.

Figure 1

(a) A sketch of the device, showing a cross section of the nanowire channel and wraparound gate, with quantum dots localized in the top corners of the nanowire and a dopant located deeper in the channel. For clarity, the source and drain are not represented on this sketch. (b) In our rf reflectometry measurements, an rf signal is sent through a directional coupler to a resonator made from the device capacitance, parasitic capacitance, and surface-mounted inductor. The reflected signal is amplified at low temperatures and demodulated using a reference signal to give $V_{\text{rf}}$. (c) The derivative of the demodulated resonator response as a function of $V_{\mathrm{tg}}$ and $V_{\mathrm{bg}}$ gives the charge stability diagram. Transitions with weak $V_{\mathrm{bg}}$ dependence are attributed to changes in the charge occupancies of the two distinct (and uncoupled) corner dots. The charge transition indicated with a black arrow is attributed to a phosphorus atom in the bulk of the nanowire.

Figure 2

(a) A close-up of the charge stability diagram showing the charge transition between a corner dot and a donor, with charge occupancies labeled as (corner dot, donor). The “asterisk” indicates the avoided level crossing sketched in (b) the energy levels of the hybrid double quantum dot, where the quantum dot and the P atom form bonding $|g⟩$ and antibonding $|e⟩$ states when the detuning $\epsilon$ is near zero. For simplicity, spin effects are omitted here and will be discussed later. For $|\epsilon |\gg 0$, the double dot has ionic-type wave functions, where the charges are localized on the dot or donor. (c) States $|g⟩$ and $|e⟩$ have opposite values of quantum capacitance, and hence, monitoring [panel (d)] the interdot charge transition (asterisk), as a function of applied microwave frequency, shows a reduction in signal amplitude upon resonance with the $|g⟩$:$|e⟩$ transition (see S4 for more details).

Figure 3

(a) Interdot charge transitions measured under continuous resonant MW (light blue), and chopped MW at 10 MHz (dark blue) and at 10 kHz (purple). (b) Renormalized average charge-state population difference as a function of the chopping period $\tau$. The data are fitted using Eq. (2) to give the charge relaxation time $T_1$.

Figure 4

(a) The quantum capacitance signature of the interdot charge transition (ICT) becomes strongly suppressed with increasing magnetic field, as the $T_{-}$ triplet state becomes the ground state, as shown in the energy-level diagram [panel (b)] near the (1,1) to (0,2) transition in the presence of a magnetic field. ${\epsilon }_{\mathrm{ST}}$ denotes the value at which the singlet and $T_{-}$ states intersect, and is responsible for the shift and asymmetry observed in (c), the ICT measured at 0 mT, 100 mT and 200 mT.