Analytically solvable pulses for spin qubit rotations

The hyperbolic secant pulse is a well known pulse shape for which the time dependent Schrodinger equation of a two-level system is analytically solvable. It has in the past been proposed [1] for optical spin rotations in quantum dots, and used experimentally to that end [2]. In this talk, a family of pulses will be introduced which can be viewed as the generalization of the sech pulse. These pulses may have skewed temporal profiles and frequency modulation (``chirping''). I will present results for the fidelity of spin rotations using some of these pulses and show that in the case of ``Raman-type'' control, where an auxiliary excited state is used, it can be advantageous to replace the usual 2$\pi$ sech pulse. \\[4pt] [1] Economou et al., Phys. Rev. B \textbf{74}, 205415 (2006), Economou and Reinecke, Phys. Rev. Lett. \textbf{99}, 217401 (2007) \\[0pt] [2] Greilich et al., Nature Physics \textbf{5}, 262 (2009)