Large Stark tuning of donor electron spin qubits in germanium

Abstract

Donor electron spins in semiconductors make exceptional quantum bits because of their long coherence times and compatibility with industrial fabrication techniques. Despite many advances in donor-based qubit technology, it remains difficult to selectively manipulate single donor electron spins. Here, we show that by replacing the prevailing semiconductor host material (silicon) with germanium, donor electron spin qubits can be electrically tuned by more than an ensemble linewidth, making them compatible with gate addressable quantum computing architectures. Using X-band pulsed electron spin resonance, we measured the Stark effect for donor electron spins in germanium. We resolved both spin-orbit and hyperfine Stark shifts and found that at 0.4 T, the spin-orbit Stark shift dominates. The spin-orbit Stark shift is highly anisotropic, depending on the electric field orientation relative to the crystal axes and external magnetic field. When the Stark shift is maximized, the spin-orbit Stark parameter is four orders of magnitude larger than in silicon. At select orientations a hyperfine Stark effect was also resolved and is an order of magnitude larger than in silicon. We report the Stark parameters for 75 As and 31 P donor electrons and compare them to the available theory. Our data reveal that 31 P donors in germanium can be tuned by at least four times the ensemble linewidth making germanium an appealing new host material for spin qubits that offers major advantages over silicon.

Quantum gates with donors in germanium

“…Close agreement with recent experiments in Ref. 21 validates our predictions and insight into the underlying physical mechanisms.…”

“…(21) also clearly shows that ∆ g > 0, since we find that the donor is more bound with increasing magnitude of the applied electric field, but g < g ⊥ -this is indeed confirmed by recent measurements of Ge:As in Ref. 21. More remarkably, the agreement between this work and our theory is very good, as shown by Table VI: this validates our theory and builds our confidence in all the results and the predictions presented in this paper.…”

“…Close agreement with the contemporary experimental measurements of Ge:As by Sigillito et al in Ref. 21 validates our estimates of the electrical tuning of donor spin splitting. We predict that single qubit gates with Ge:P donors could be performed with nanosecond timescales under realistic assumptions, a huge improvement to the Si framework.…”

“…In the regime of low electric fields relevant to the recent experiments (|E| ∼kV/m) of Ref. 21, the intervalley couplings ∆ are shifted much less than the diagonal valley energies Λ, as they involve higher Fourier components of the linear electric-field term in the Hamiltonian. While all terms will be retained in the numerical calculations that follow, it is instructive to set ∆ m ≈ ∆ a ≈ ∆ 0 (∆ 0 being the zero-field intervalley coupling), and acknowledge that owing to the large anisotropy described above |Λ a − Λ 0 | |Λ m − Λ 0 | (where Λ 0 the zero field intravalley coupling).…”

Strong confinement-induced engineering of the g factor and lifetime of conduction electron spins in Ge quantum wells

“…Inspired by a recent experimental report on donor-bound electrons68, we can foresee that the demonstrated strong dependence of the electron Landé g factor upon confinement can be utilized in conjunction with externally applied electric fields to provide an exceptional tunability . With this respect, the anisotropy may be additionally fine-tuned by a Rashba field induced by asymmetric doping and subsequently modulated via an external gate27.…”