Anisotropic Stark Effect and Electric-Field Noise Suppression for Phosphorus Donor Qubits in Silicon

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 magnetic fields for which the spin-orbit Stark effect cancels the hyperfine Stark effect, suppressing decoherence from electric-field noise. We discuss the limitations of these noise-suppression points due to random distributions of strain and propose a method for overcoming them

Spin relaxation and coherence times for electrons at the Si/SiO2 interface

While electron spins in silicon heterostructures make attractive qubits, little is known about the coherence of electrons at the Si/SiO2 interface. We report spin relaxation (T1) and coherence (T2) times for mobile electrons and natural quantum dots at a 28Si/SiO2 interface. Mobile electrons have short T1 and T2 of 0.3 us at 5 K. In line with predictions, confining electrons and cooling increases T1 to 0.8 ms at 350 mK. In contrast, T2 for quantum dots is around 10 us at 350 mK, increasing to 30 us when the dot density is reduced by a factor of two. The quantum dot T2 is shorter than T1, indicating that T2 is not controlled by T1 at 350 mK but is instead limited by an extrinsic mechanism. The evidence suggests that this extrinsic mechanism is an exchange interaction between electrons in neighboring dots.Comment: Extended with more experiments and rewritten. 6 pages, 5 figures, to be submitted to Phys. Rev.

Electron Spin Resonance at the Level of 10000 Spins Using Low Impedance Superconducting Resonators

We report on electron spin resonance (ESR) measurements of phosphorus donors localized in a 200 square micron area below the inductive wire of a lumped element superconducting resonator. By combining quantum limited parametric amplification with a low impedance microwave resonator design we are able to detect around 20000 spins with a signal-to-noise ratio (SNR) of 1 in a single shot. The 150 Hz coupling strength between the resonator field and individual spins is significantly larger than the 1 - 10 Hz coupling rates obtained with typical coplanar waveguide resonator designs. Due to the larger coupling rate, we find that spin relaxation is dominated by radiative decay into the resonator and dependent upon the spin-resonator detuning, as predicted by Purcell

Exchange coupling between silicon donors: the crucial role of the central cell and mass anisotropy

Donors in silicon are now demonstrated as one of the leading candidates for implementing qubits and quantum information processing. Single qubit operations, measurements and long coherence times are firmly established, but progress on controlling two qubit interactions has been slower. One reason for this is that the inter donor exchange coupling has been predicted to oscillate with separation, making it hard to estimate in device designs. We present a multivalley effective mass theory of a donor pair in silicon, including both a central cell potential and the effective mass anisotropy intrinsic in the Si conduction band. We are able to accurately describe the single donor properties of valley-orbit coupling and the spatial extent of donor wave functions, highlighting the importance of fitting measured values of hyperfine coupling and the orbital energy of the $1s$ levels. Ours is a simple framework that can be applied flexibly to a range of experimental scenarios, but it is nonetheless able to provide fast and reliable predictions. We use it to estimate the exchange coupling between two donor electrons and we find a smoothing of its expected oscillations, and predict a monotonic dependence on separation if two donors are spaced precisely along the [100] direction.Comment: Published version. Corrected b and B values from previous versio

Addressing spin transitions on 209Bi donors in silicon using circularly-polarized microwaves

Over the past decade donor spin qubits in isotopically enriched $^{28}$Si have been intensely studied due to their exceptionally long coherence times. More recently bismuth donor electron spins have become popular because Bi has a large nuclear spin which gives rise to clock transitions (first-order insensitive to magnetic field noise). At every clock transition there are two nearly degenerate transitions between four distinct states which can be used as a pair of qubits. Here it is experimentally demonstrated that these transitions are excited by microwaves of opposite helicity such that they can be selectively driven by varying microwave polarization. This work uses a combination of a superconducting coplanar waveguide (CPW) microresonator and a dielectric resonator to flexibly generate arbitrary elliptical polarizations while retaining the high sensitivity of the CPW

Developments in electromagnetic tomography instrumentation.

A new EMT sensor and instrumentation is described which combines the best features of previous systems and has a modular structure to allow for future system expansion and development