Multi-frequency spin manipulation using rapidly tunable superconducting coplanar waveguide microresonators

In this work, we demonstrate the use of frequency-tunable superconducting NbTiN coplanar waveguide microresonators for multi-frequency pulsed electron spin resonance (ESR) experiments. By applying a bias current to the center pin, the resonance frequency (∼7.6 GHz) can be continuously tuned by as much as 95 MHz in 270 ns without a change in the quality factor of 3000 at 2 K. We demonstrate the ESR performance of our resonators by measuring donor spin ensembles in silicon and show that adiabatic pulses can be used to overcome magnetic field inhomogeneities and microwave power limitations due to the applied bias current. We take advantage of the rapid tunability of these resonators to manipulate both phosphorus and arsenic spins in a single pulse sequence, demonstrating pulsed double electron-electron resonance. Our NbTiN resonator design is useful for multi-frequency pulsed ESR and should also have applications in experiments where spin ensembles are used as quantum memories

All-electric control of donor nuclear spin qubits in silicon.

The electronic and nuclear spin degrees of freedom of donor impurities in silicon form ultra-coherent two-level systems that are potentially useful for applications in quantum information and are intrinsically compatible with industrial semiconductor processing. However, because of their smaller gyromagnetic ratios, nuclear spins are more difficult to manipulate than electron spins and are often considered too slow for quantum information processing. Moreover, although alternating current magnetic fields are the most natural choice to drive spin transitions and implement quantum gates, they are difficult to confine spatially to the level of a single donor, thus requiring alternative approaches. In recent years, schemes for all-electrical control of donor spin qubits have been proposed but no experimental demonstrations have been reported yet. Here, we demonstrate a scalable all-electric method for controlling neutral 31P and 75As donor nuclear spins in silicon. Using coplanar photonic bandgap resonators, we drive Rabi oscillations on nuclear spins exclusively using electric fields by employing the donor-bound electron as a quantum transducer, much in the spirit of recent works with single-molecule magnets. The electric field confinement leads to major advantages such as low power requirements, higher qubit densities and faster gate times. Additionally, this approach makes it possible to drive nuclear spin qubits either at their resonance frequency or at its first subharmonic, thus reducing device bandwidth requirements. Double quantum transitions can be driven as well, providing easy access to the full computational manifold of our system and making it convenient to implement nuclear spin-based qudits using 75As donors

Large Stark tuning of donor electron spin qubits in germanium

Donor electron spins in semiconductors make exceptional qubits 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 As75 and P31 donor electrons and compare them to the available theory. Our data reveal that P31 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

Large Stark tuning of donor electron spin qubits in germanium

Donor electron spins in semiconductors make exceptional qubits 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 As75 and P31 donor electrons and compare them to the available theory. Our data reveal that P31 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

Electron Spin Coherence of Shallow Donors in Natural and Isotopically Enriched Germanium.

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 nonmagnetic 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 wave function, high mobility, and highly anisotropic conduction band valleys which will all give rise to new physics. In this Letter, the first pulsed electron spin resonance measurements of T_{2} and the spin-lattice relaxation (T_{1}) times for ^{75}As and ^{31}P donors in natural and isotopically enriched germanium are presented. We compare samples with various levels of isotopic enrichment and find that spectral diffusion due to ^{73}Ge nuclear spins limits the coherence in samples with significant amounts of ^{73}Ge. For the most highly enriched samples, we find that T_{1} limits T_{2} to T_{2}=2T_{1}. We report an anisotropy in T_{1} and the ensemble linewidths for magnetic fields oriented along different crystal axes but do not resolve any angular dependence to the spectral-diffusion-limited T_{2} in samples with ^{73}Ge

Electron Spin Coherence of Shallow Donors in Natural and Isotopically Enriched Germanium.

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 nonmagnetic 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 wave function, high mobility, and highly anisotropic conduction band valleys which will all give rise to new physics. In this Letter, the first pulsed electron spin resonance measurements of T_{2} and the spin-lattice relaxation (T_{1}) times for ^{75}As and ^{31}P donors in natural and isotopically enriched germanium are presented. We compare samples with various levels of isotopic enrichment and find that spectral diffusion due to ^{73}Ge nuclear spins limits the coherence in samples with significant amounts of ^{73}Ge. For the most highly enriched samples, we find that T_{1} limits T_{2} to T_{2}=2T_{1}. We report an anisotropy in T_{1} and the ensemble linewidths for magnetic fields oriented along different crystal axes but do not resolve any angular dependence to the spectral-diffusion-limited T_{2} in samples with ^{73}Ge