Atomic spin-wave control and spin-dependent kicks with shaped subnanosecond pulses

The absorption of traveling photons resonant with electric dipole transitions of an atomic gas naturally leads to electric dipole spin wave excitations. For a number of applications, it would be highly desirable to shape and coherently control the spatial waveform of the spin waves before spontaneous emission can occur. This paper details a recently developed optical control technique to achieve this goal, where counter-propagating, shaped sub-nanosecond pulses impart sub-wavelength geometric phases to the spin waves by cyclically driving an auxiliary transition. In particular, we apply this technique to reversibly shift the wave vector of a spin wave on the $D2$ line of laser-cooled $^{87}$Rb atoms, by driving an auxiliary $D1$ transition with shape-optimized pulses, so as to shut off and recall superradiance on demand. We investigate a spin-dependent momentum transfer during the spin-wave control process, which leads to a transient optical force as large as $\sim 1\hbar k$/ns, and study the limitations to the achieved $70\sim 75\%$ spin wave control efficiency by jointly characterizing the spin-wave control and matterwave acceleration. Aided by numerical modeling, we project potential future improvements of the control fidelity to the $99\%$ level when the atomic states are better prepared and by equipping a faster and more powerful pulse shaper. Our technique also enables a background-free measurement of the superradiant emission to unveil the precise scaling of the emission intensity and decay rate with optical depth.