Controlling Spin-Orbit Interactions in Silicon Quantum Dots Using Magnetic Field Direction

Abstract

Silicon quantum dots are considered an excellent platform for spin qubits, partly due to their weak spin-orbit interaction. However, the sharp interfaces in the heterostructures induce a small but significant spin-orbit interaction which degrade the performance of the qubits or, when understood and controlled, could be used as a powerful resource. To understand how to control this interaction we build a detailed profile of the spin-orbit interaction of a silicon metal-oxide-semiconductor double quantum dot system. We probe the derivative of the Stark shift, g-factor and g-factor difference for two single-electron quantum dot qubits as a function of external magnetic field and find that they are dominated by spin-orbit interactions originating from the vector potential, consistent with recent theoretical predictions. Conversely, by populating the double dot with two electrons we probe the mixing of singlet and spin-polarized triplet states during electron tunneling, which we conclude is dominated by momentum-term spin-orbit interactions that varies from 1.85 MHz up to 27.5 MHz depending on the magnetic field orientation. Finally, we exploit the tunability of the derivative of the Stark shift of one of the dots to reduce its sensitivity to electric noise and observe an 80 % increase in T * 2 . We conclude that the tuning of the spin-orbit interaction will be crucial for scalable quantum computing in silicon and that the optimal setting will depend on the exact mode of qubit operations used.Silicon-based spin qubits have attracted attention as candidates for large scale quantum computing thanks to their long coherence times, excellent controllability and fabrication techniques that are well established in the semiconductor industry [1][2][3][4][5][6][7][8][9][10][11][12][13]. Even though being weak compared, for instance, to GaAs, the spin-orbit interaction (SOI) significantly affects the behaviour of silicon spin qubits, especially through the dependency of the SOI on the valley state [12,14,15]. SOI is responsible for effects such as the Stark shift of the electron spin resonance (ESR) frequency, variation of Lande gfactors, and mixing between singlet (S) and polarized triplet (T − ) states [15][16][17][18]. These effects can be harnessed, for instance, to drive the ESR transition electrically via Stark shift or by exploiting the variation in the g-factors to address qubits individually with a global microwave (MW) field [14,[19][20][21]. In contrast, spin-orbit effects such as spin-flip tunneling and strong Stark shift can cause state leakage or increased sensitivity to electric noise [14,16,22]. Hence, understanding and controlling the SOI will be important for spin qubit control in larger arrays of dots in the future [23][24][25].Here, we fully characterize the SOI and demonstrate how we can tune it in a silicon metal-oxide-semiconductor * current address: Microsoft Quantum, (SiMOS) double quantum dot (QD) structure. The structure studied here is shown in Fig. 1b and described in Ref. [24]. We vary the directio...

Adiabatic electron charge transfer between two quantum dots in presence of 1/f noise

“…As shown in Fig. 3, for t = 0.1 µeV, measured recently in Si/SiO 2 quantum dots [51,52], the probability of transfer is lowered to ≈ 0.95 at v ≈ 1 µeV/ns when the oscillations caused by interference of two transfer paths are dephased. While in Sec.…”

“…2, in which the transfer probability for the excited state is seen to oscillate very rapidly, with amplitude larger than 0.01 for v ≈ 10 µeV/ns. For value of t = 0.1 recently reported for Si MOS quantum dots [51,52], the lower envelope of these oscillations reaches 0.9 for v ≈ 1 µeV/ns, showing that path-interference effects can have strong influence on transfer of higher-energy spin state in such dots. In presence of phase noise, coherence between two paths can easily be lost, which eventually prevents any interference from happening.…”

“…In presence of quasistatic noise (due to fluctuations of Overhauser splittings in the two dots), or the slowest components of 1/f noise that still lead to finite fluctuation of detuning during the transfer process, these oscillations become dephased, but the transfer probability is lowered compared to t = 0 case. This could make the window of v allowing for highfidelity electron transfer quite narrow in SiMOS devices, where such values of t were measured [51,52], unless one chooses the magnetic field direction and geometry of the structure that makes t smaller.…”

Hyperfine-assisted decoherence of a phosphorus nuclear-spin qubit in silicon

“…23 suggests that electrical control of the nuclear-spin qubit should be possible either by relying on an inhomogeneous magnetic field (artificial spin-orbit interaction), or by relying on intrinsic spin-orbit interaction. In a simple phenomenological picture, spin-orbit interaction can influence the dot-donor system in two ways; both effects have been observed in silicon double quantum dots [37][38][39][40] . On the one hand, it renormalizes the g-factor (with few percents), potentially making it anisotropic and different at the donor and in the dot.…”

A Silicon Surface Code Architecture Resilient Against Leakage Errors

“…However, single-qubit gates achieved by ESR have relatively slow speed (∼ 1 MHz), limited by the magnitude of the oscillating magnetic field. An alternative method to implement single-qubit gates is EDSR [61], which can be achieved in a uniform magnetic field [62] by exploiting the spinorbit coupling in silicon [63,64]. More commonly, EDSR is achieved using a magnetic field gradient created at the quantum dot, usually by placing a micromagnet in proximity.…”