Spin Quintet in a Silicon Double Quantum Dot: Spin Blockade and Relaxation

Abstract

Spins in gate-defined silicon quantum dots are promising candidates for implementing large-scale quantum computing. To read the spin state of these qubits, the mechanism that has provided the highest fidelity is spin-to-charge conversion via singlet-triplet spin blockade, which can be detected in situ using gate-based dispersive sensing. In systems with a complex energy spectrum, like silicon quantum dots, accurately identifying when singlet-triplet blockade occurs is hence of major importance for scalable qubit readout. In this work, we present a description of spin-blockade physics in a tunnel-coupled silicon double quantum dot defined in the corners of a split-gate transistor. Using gate-based magnetospectroscopy, we report successive steps of spin blockade and spin-blockade lifting involving spin states with total spin angular momentum up to S ¼ 3. More particularly, we report the formation of a hybridized spin-quintet state and show triplet-quintet and quintet-septet spin blockade, enabling studies of the quintet relaxation dynamics from which we find T 1 ∼ 4 μs. Finally, we develop a quantum capacitance model that can be applied generally to reconstruct the energy spectrum of a double quantum dot, including the spin-dependent tunnel couplings and the energy splitting between different spin manifolds. Our results allow for the possibility of using Si complementary metal-oxide-semiconductor quantum dots as a tunable platform for studying high-spin systems.

Non-reciprocal Pauli Spin Blockade in a Silicon Double Quantum Dot

“…Additionally, spin, valley, and orbital degrees of freedom may all be mixed on a wide energy range by spin-orbit and valley-orbit couplings, which together with Coulomb interactions provide efficient paths for decoherence. In particular, it has been shown in [49] that anisotropic QDs such as the ones characterised in this work are prone to Wigner-like localization: The electrons split apart in the charged dots due to Coulomb repulsion, which results in a significant compression of the energy spectrum [29] and mixing of the different degrees of freedom in the presence of spin-orbit and valley-orbit coupling mechanisms [50][51][52]. Although the observed γ Dq at the anti-crossing is large, one may expect a reduction away from the anticrossing where the energy difference of intradot transitions is ε-independent, thus encouraging coherent EDSR experiments for electron spins in silicon corner dots.…”

“…The number of electrons accumulated in the DQD is governed by the gate voltages V B1 and V T1 and changes in the DQD electron occupancy are detected dispersively by probing the resonator via the transmission line MW in with a frequency f close to f 0 and monitoring the phase shift of the reflected signal φ. Non-zero phase shifts occur as a result of cyclical interdot or dot-to-reservoir tunneling events happening under the influence of the microwave probe resulting in a finite DQD-resonator coherent coupling rate g 0 [32,35]. [29] (see Appendix D in Ref. [35] for the charge population data of the device also used in this work).…”

“…To probe the spin physics of the DQD and in particular of the (6,9)-(7,8) and (5,10)-(6,9) ICTs, we measure V T1 line traces that intersect the centre of each ICT while increasing B from 0 to 0.9 T. B is applied in-plane with the device and perpendicular to the nanowire, and the probe frequency f is continuously adjusted to account for the changing kinetic inductance of the NbN inductor and remain close to resonance f 0 (B) [29]. The resulting dispersive magnetospectroscopy measurements shown in Figs.…”

“…Pauli spin blockade, however, may be lifted thus compromising readout. Lifting of PSB may occur due to direct tunneling between triplets [24] or due to fast tunneling to low-energy high-spin states, such as the fourelectron quintet, which may result from small valley-orbit splittings and generally dense QD energy spectra [29][30][31]. Additionally, theory predicts that fast relaxation processes happening at rates similar or faster than the readout probe frequency can lift dispersively-detected PSB [32], and work on a charge-sensed GaAs double quantum dot (DQD) has observed spin blockade lifting due to dephasing arising from hyperfine and spin-orbit interactions [33].…”

Quantum Dot-Based Parametric Amplifiers

“…1(d)) we use separate silicon and superconducting chips for the QD device and resonator respectively [35]. The QD is formed in a split-gate, fully-depleted nanowire field-effect transistor [36] with a 70 nm channel width, 60 nm gate length and a 40 nm split-gate separation, fabricated in a complementary metal-oxide-semiconductor (CMOS) siliconon-insulator (SOI) process with an SOI thickness of 7 nm and buried oxide (BOX) thickness of 145 nm. For applied potentials V R above a certain threshold, electrons accumulate in the corner of the square nanowire cross-section directly under G R (see the red dashed line on the scanning electron micrograph and associated cross sectional sketch).…”