Gigahertz-Bandwidth Optical Memory in Pr${}^{3+}$:Y${}_2$SiO${}_5$

We experimentally study a broadband implementation of the atomic frequency comb (AFC) rephasing protocol with a cryogenically cooled Pr${}^{3+}$:Y${}_2$SiO${}_5$ crystal. To allow for storage of broadband pulses, we explore a novel regime where the input photonic bandwidth closely matches the inhomogeneous broadening of the material $(\sim 5\text{GHz})$, thereby significantly exceeding the hyperfine ground and excited state splitting $(\sim 10\text{MHz})$. Through an investigation of different AFC preparation parameters, we measure a maximum efficiency of $10\mathrm{\%}$ after a rephasing time of $12.5$ns. With a suboptimal AFC, we witness up to 12 rephased temporal modes.