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 counterpropagating, shaped subnanosecond pulses impart subwavelength 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 ${}^{87}\mathrm{Rb}$ 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 $\sim 1\hslash k$/ns, and study the limitations to the achieved $70\sim 75\%$ spin-wave control efficiency by jointly characterizing the spin-wave control and matter-wave 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.

• Received 26 April 2020
• Revised 1 December 2020
• Accepted 28 November 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.043418

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society