Study of Electron Spin Dynamics of Phosphorus-Doped Silicon

Abstract

Quantum information stored in a quantum bit (qubit), basic element of quantum computation, is fragile to interaction with environments, and disappears with time. To overcome this, quantum error correction technique has been studied and it is known that, if a given requirement is satisfied, it is possible to perform fault-tolerant quantum computation. The requirement is that the number of physical qubits should be able to increase arbitrarily and the error probability per each gate operation should be smaller than a certain level (10^-4-10^-6). Kanes silicon-based quantum computer, suggested to satisfy the severe requirement of quantum error correction, has attracted particular attention as a promising candidate for practical quantum computer. Regarding this, relatively short coherence time of electron spins in silicon, compared to that of 31P nuclear spins, is a key factor for reliable quantum computation. Previous researches focused on decreasing density of impurities (donor and 29Si) in silicon to increase coherence time of electron spins. However, considering that the speed of two-qubit operation is proportional to exchange constant (J) between electron spins, research for a sample with high donor density is necessary. In this study, electron spin resonance experiments were performed for dielectric Si:P with the donor density of 6.52E16 /cc and 1.1E17 /cc to investigate electron spin dynamics in silicon. Based on the measured relaxation times for electron spins, their relevant mechanisms were elucidated. Furthermore, it was verified if electron spin coherence can be preserved long enough, to satisfy the requirement for fault-tolerant quantum computation, by dynamical decoupling technique. To obtain information for dynamics of single electron spin from measurements on bulk sample, the effect of field inhomogeneity due to 29Si nuclei in silicon was dealt with by spin echo technique, which utilizes refocusing (π) pulse. For the given experimental condition, the dominant mechanisms for decoherence of electron spins are estimated to be instantaneous diffusion and (29Si) nuclear-induced spectral diffusion. The measured time constants for each mechanism are 0.9 ms (TID) and 0.26 ms (TSD), respectively. Instantaneous diffusion arises when dipolar-coupled electron spins are simultaneously flipped by an applied microwave pulse. The theoretical formula for TID agrees with previous experimental results obtained for low donor densities, but shows large discrepancy with our result (TID,theory~0.02 ms). This can be explained qualitatively by the fact that as donor density increases, the number of exchange-coupled spin pairs, which have exchange constant (J) larger than hyperfine interaction (A) between 31P and electron, also increases. Meanwhile, spectral diffusion arises when local magnetic field at a resonant spin fluctuates due to lattice-related flips of nearby spins or dipolar flip-flops of nearby spins. By comparing our results of TSD with previous results, it is shown that inhomogeneous field due to the presence of 29Si nuclei suppresses electron-induced spectral diffusion so that (29Si) nuclear-induced spectral diffusion becomes dominant. In our results of dynamical decoupling experiment to suppress spectral diffusion, the theoretically driven optimal DD sequence (UDD) outperforms the conventional equidistant sequence (PDD) especially at short times, often called high-fidelity regime. This regime is important in quantum error correction and thus these results show that dynamical decoupling can take an important role in quantum computation. From the measured echo decay using UDD with four refocusing pulses, the time taken for error probability to be 10-6 is estimated to be about 0.13 ms and this value is comparable to the limit of gate operation time due to the limit of current pulse generation technology.