Measuring electron spin flip-flops through nuclear spin echo decays

Abstract

We use the nuclear spin coherence of 31 P donors in 28 Si to determine flip-flop rates of donor electron spins. Isotopically purified 28 Si crystals minimize the number of 29 Si flip-flops, and measurements at 1.7 K suppress electron spin relaxation. The crystals have donor concentrations ranging from 1.2 × 10 14 to 3.3 × 10 15 P/cm 3 , allowing us to detect how electron flip-flop rates change with donor density. We also simulate how electron spin flip-flops can cause nuclear spin decoherence.We find that when these flip-flops are the primary cause of decoherence, Hahn echo decays have a stretched exponential form. For our two higher donor density crystals (> 10 15 P/cm 3 ), there is excellent agreement between simulations and experiments. In lower density crystals (< 10 15 P/cm 3 ), there is no longer agreement between simulations and experiments, suggesting a different, unknown mechanism is limiting nuclear spin coherence. The nuclear spin coherence in the lowest density crystal (1.2 × 10 14 P/cm 3 ) allows us to place upper bounds on the magnitude of noise sources in bulk crystals such as electric field fluctuations that may degrade silicon quantum devices. I. INTRODUCTIONQuantum devices utilizing spins, electron spin resonance (ESR) and nuclear magnetic resonance (NMR) in solids, and magnetic resonance imaging (MRI) can all be affected by electron spin flip-flops. This decoherence mechanism causes errors in spin-based quantum devices, 1 affects electron and nuclear coherence times in ESR and NMR, and can be utilized for dynamic nuclear polarization 2 to enhance signal strength in MRI. 3 A flip-flop occurs when two dipole-dipole coupled electron spins, one spin up and the other spin down, swap their spin states. This is possible so long as the combined energy of the spins does not change. The rates of flip-flops (spin diffusion) can be calculated in

Persistent atomic frequency comb based on Zeeman sub-levels of an erbium-doped crystal waveguide

“…However, as the spin flip-flop rate decreases with the sixth power of the distance between ER-ions, we estimate its contribution to be small. In fact, if we extrapolate results from [27] to an approximate Er-doping concentration of 3.6×10 19 cm −3 (or 0.2%), we find a flip-flop rate of a few Hz -by far to little to explain the AFC background.…”