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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 work 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 ∼ 1 k/ns, and study the limitations to the achieved 70 ∼ 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 99% level when the atomic states are better prepared and by equipping a faster and more powerful pulse shaper. Our technique also enables a backgroundfree measurement of the superradiant emission to unveil the precise scaling of the emission intensity and decay rate with optical depth for the first time to our knowledge.

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