Toward high-fidelity coherent electron spin transport in a GaAs double quantum dot

In this paper, we investigate how to achieve high-fidelity electron spin transport in a GaAs double quantum dot. Our study examines spin transport from multiple perspectives. We first study how a double dot potential may affect/accelerate spin relaxation. We calculate spin relaxation rate in a wide range of experimental parameters and focus on the occurrence of spin hot spots. A safe parameter regime is identified in order to avoid these spin hot spots. We also study the non-adiabatic transitions in the Landau-Zener process of sweeping the interdot detuning, and propose a scheme to take advantage of possible Landau-Zener-St\"{u}kelburg interference to achieve high-fidelity spin transport at a higher speed. Finally, we calculate the double-dot correction on the effective $g$-factor for the tunneling electron, and estimate the resulting phase error between different spin states. Our results should provide a useful guidance for future experiments on coherent electron spin transport.Comment: 10 pages, 7 figure

Nutational resonances, transitional precession, and precession-averaged evolution in binary black-hole systems

In the post-Newtonian (PN) regime, the timescale on which the spins of binary black holes precess is much shorter than the radiation-reaction timescale on which the black holes inspiral to smaller separations. On the precession timescale, the angle between the total and orbital angular momenta oscillates with nutation period $\tau$, during which the orbital angular momentum precesses about the total angular momentum by an angle $\alpha$. This defines two distinct frequencies that vary on the radiation-reaction timescale: the nutation frequency $\omega \equiv 2\pi/\tau$ and the precession frequency $\Omega \equiv \alpha/\tau$. We use analytic solutions for generic spin precession at 2PN order to derive Fourier series for the total and orbital angular momenta in which each term is a sinusoid with frequency $\Omega - n\omega$ for integer $n$. As black holes inspiral, they can pass through nutational resonances ($\Omega = n\omega$) at which the total angular momentum tilts. We derive an approximate expression for this tilt angle and show that it is usually less than $10^{-3}$ radians for nutational resonances at binary separations $r > 10M$. The large tilts occurring during transitional precession (near zero total angular momentum) are a consequence of such states being approximate $n=0$ nutational resonances. Our new Fourier series for the total and orbital angular momenta converge rapidly with $n$ providing an intuitive and computationally efficient approach to understanding generic precession that may facilitate future calculations of gravitational waveforms in the PN regime.Comment: 18 pages, 9 figures, version published in PR