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.
The possibility of quantum computing with spins in germanium nanoscale transistors has recently attracted interest since it promises highly tuneable qubits that have encouraging coherence times. We here present the first complete theory of the orbital states of Ge donor electrons, and use it to show that Ge could have significant advantages over silicon in the implementation of a donor-based quantum processor architecture. We show that the stronger spin-orbit interaction and the larger electron donor wave functions for Ge donors allow for greater tuning of the single qubit energy than for thos…
Germanium has emerged as an exceptionally promising material for spintronics and quantum information applications, with significant fundamental advantages over silicon. However, efforts to create atomic-scale devices using donor atoms as qubits have largely focussed on phosphorus in silicon. Positioning phosphorus in silicon with atomic-scale precision requires a thermal incorporation anneal, but the low success rate for this step has been shown to be a fundamental limitation prohibiting the scale-up to large-scale devices. Here, we present a comprehensive study of arsine (AsH$_3$) on the germ…
Electric fields can be used to tune donor spins in silicon using the Stark shift, whereby the donor electron wave function is displaced by an electric field, modifying the hyperfine coupling between the electron spin and the donor nuclear spin. We present a technique based on dynamic decoupling of the electron spin to accurately determine the Stark shift, and illustrate this using antimony donors in isotopically purified silicon-28. We then demonstrate two different methods to use a DC electric field combined with an applied resonant radio-frequency (RF) field to conditionally control donor nu…
Photon Echo in Uniaxially Stressed Germanium with Antimony Donors
Institute for Physics of Microstructures, Russian Academy of Sciences（俄罗斯科学院微观物理研究所）；Budker Institute of Nuclear Physics, Siberian Branch of the Russian Academy of Sciences（俄罗斯科学院西伯利亚分校布德克核物理研究所）；Novosibirsk National Research State University（新西伯利亚国立研究大学）；FELIX Laboratory, Radboud University（拉德堡德大学FELIX实验室）；Leibniz-Institut für Kristallzüchtung（莱布尼茨晶体生长研究所）
We present a complete theoretical treatment of Stark effects in doped silicon, whose predictions are supported by experimental measurements. A multi-valley effective mass theory, dealing non-perturbatively with valley-orbit interactions induced by a donor-dependent central cell potential, allows us to obtain a very reliable picture of the donor wave function within a relatively simple framework. Variational optimization of the 1s donor binding energies calculated with a new trial wave function, in a pseudopotential with two fitting parameters, allows an accurate match of the experimentally det…
Germanium is a widely used material for electronic and optoelectronic devices and recently it has become an important material for spintronics and quantum computing applications. Donor spins in silicon have been shown to support very long coherence times ($T_{2}$) when the host material is isotopically enriched to remove any magnetic nuclei. Germanium also has non-magnetic isotopes so it is expected to support long $T_{2}$s while offering some new properties. Compared to Si, Ge has a strong spin-orbit coupling, large electron wavefunction, high mobility, and highly anisotropic conduction band …
We report the use of novel, capacitively terminated coplanar waveguide (CPW) resonators to measure the quadratic Stark shift of phosphorus donor qubits in Si. We confirm that valley repopulation leads to an anisotropic spin-orbit Stark shift depending on electric and magnetic field orientations relative to the Si crystal. By measuring the linear Stark effect, we estimate the effective electric field due to strain in our samples. We show that in the presence of this strain, electric-field sources of decoherence can be non-negligible. Using our measured values for the Stark shift, we predict mag…
Atomistic tight-binding (TB) simulations are performed to calculate the Stark shift of the hyperfine coupling for a single Arsenic (As) donor in Silicon (Si). The role of the central-cell correction is studied by implementing both the static and the non-static dielectric screenings of the donor potential, and by including the effect of the lattice strain close to the donor site. The dielectric screening of the donor potential tunes the value of the quadratic Stark shift parameter ($η_2$) from -1.3 $\times$ 10$^{-3} μ$m$^2$/V$^2$ for the static dielectric screening to -1.72 $\times$ 10$^{-3} μ$…
The Stark shift of the hyperfine coupling constant is investigated for a P donor in Si far below the ionization regime in the presence of interfaces using Tight-binding and Band Minima Basis approaches and compared to the recent precision measurements. The TB electronic structure calculations included over 3 million atoms. In contrast to previous effective mass based results, the quadratic Stark coefficient obtained from both theories agrees closely with the experiments. This work represents the most sensitive and precise comparison between theory and experiment for single donor spin control. …
The dependence of the g-factors of semiconductor donors on applied electric and magnetic fields is of immense importance in spin based quantum computation and in semiconductor spintronics. The donor g-factor Stark shift is sensitive to the orientation of the electric and magnetic fields and strongly influenced by the band-structure and spin-orbit interactions of the host. Using a multimillion atom tight-binding framework the spin-orbit Stark parameters are computed for donors in multi-valley semiconductors, silicon and germanium. Comparison with limited experimental data shows good agreement f…
We present an analysis of electron transport through two weakly coupled precision placed phosphorus donors in silicon. In particular, we examine the (1,1) to (0,2) charge transition where we predict a new type of current blockade driven entirely by the nuclear spin dynamics. Using this nuclear spin blockade mechanism we devise a protocol to readout the state of single nuclear spins using electron transport measurements only. We extend our model to include realistic effects such as Stark shifted hyperfine interactions and multi-donor clusters. In the case of multi-donor clusters we show how nuc…
The silicon-based quantum computer proposal has been one of the intensely pursued ideas during the past three years. Here we calculate the donor electron exchange in silicon and germanium, and demonstrate an atomic-scale challenge for quantum computing in Si (and Ge), as the six (four) conduction band minima in Si (Ge) lead to inter-valley electronic interferences, generating strong oscillations in the exchange splitting of two-donor two-electron states. Donor positioning with atomic scale precision within the unit cell thus becomes a decisive factor in determining the strength of the exchange…
We present a strategy for producing multi-qubit gates that promise high fidelity with minimal tuning requirements. Our strategy combines gap protection from the adiabatic theorem with dynamical decoupling in a complementary manner. To avoid degenerate states and maximize the benefit of the gap protection, the scheme is best suited when there are two different kinds of qubits (not mutually resonant). Furthermore, we require a robust operating point in control space where the qubits interact with little sensitivity to noise. This allows us to circumvent a No-Go theorem that prevents block-box dy…
We apply the full power of modern electronic band structure engineering and epitaxial heterostructures to design a transistor that can sense and control a single donor electron spin. Spin resonance transistors may form the technological basis for quantum information processing. One and two qubit operations are performed by applying a gate bias. The bias electric field pulls the electron wave function away from the dopant ion into layers of different alloy composition. Owing to the variation of the g-factor (Si:g=1.995, Ge:g=1.563), this displacement changes the spin Zeeman energy, allowing sin…
Preserving coherence long enough to perform meaningful calculations is one of the major challenges on the pathway to large scale quantum computer implementations. Noise coupled from the environment is the main contributing factor to decoherence but can be mitigated via engineering design and control solutions. However, this is only possible after acquiring a thorough understanding of the dominant noise sources and their spectrum. In this paper, we employ a silicon quantum dot spin qubit as a metrological device to study the noise environment experienced by the qubit. We compare the sensitivity…
Spin qubits in semiconductor quantum dots represent a prominent family of solid-state qubits in the effort to build a quantum computer. They are formed when electrons or holes are confined in a static potential well in a semiconductor, giving them a quantized energy spectrum. The simplest spin qubit is a single electron spin located in a quantum dot, but many additional varieties have been developed, some containing multiple spins in multiple quantum dots, each of which has different benefits and drawbacks. While these spins act as simple quantum systems in many ways, they also experience comp…
