Coherent control of donor states in Si

The spin degrees of freedom of group V donors in Si satisfy many of the criteria required for qubits [1,2]. The orbital Rydberg states of group V donors can also be used to control these spins coherently [3,4]. Critical to such schemes are the population (T$_{1})$ and dephasing (T$_{2})$ lifetimes of these Rydberg states. We describe the use the free electron laser FELIX [5] to perform pump-probe experiments to measure T$_{1}$ [6] and photon echo experiments to measure T$_{2}$ [7]. The lifetimes we obtain from a theoretical analysis of the experiments are $\sim $ 200 ps, which is long enough for orbital excitation to be a practical control mechanism for 2-qubit quantum gates. The experimental and theoretical analysis of these gates is also described. \\[4pt] [1] DiVincenzo D P, ``The Physical Implementation of Quantum Computation,'' arXiv:quant-ph/0002077 \\[0pt] [2] Morley G W, \textit{et al}, ``Initializing, manipulating and storing quantum information with bismuth dopants in silicon'' \textit{ Nature Materials} \textbf{9} 725 -- 729 (2010) (doi:10.1038/nmat2828) \\[0pt] [3] Stoneham, A. M., Fisher, A. J. {\&} Greenland, P.T. ``Optically driven silicon-based quantum gates with potential for high-temperature operation'' \textit{ J Phys Condens Matter} \textbf{15}, L447-451 (2003). \\[0pt] [4] http://arxiv.org/find/cond-mat/1/au:+Wu\_W/0/1/0/all/0/1 Wu W, Greenland P T, Fisher A J, ``Exchange in multi-defect semiconductor clusters: assessment of `control-qubit' architectures'' http://arxiv.org/abs/0711.0084 \\[0pt] [5] Knippels G M H, \textit{et al}, ``Generation and Complete Electric-Field Characterization of Intense Ultrashort Tunable Far-Infrared Laser Pulses'' \textit{ Phys. Rev. Lett}. \textbf{83}, 1578-1581 (1999) \\[0pt] [6] N Q Vinh N Q et al, ``Silicon as a model ion trap: time domain measurements of donor Rydberg states'' \textit{PNAS} 105 10649-10653 (2008) \\[0pt] [7] Greenland P T et al \textit{Nature}, 465, 1057-1061 (2010) (doi:10.1038/nature09112)