those presented here are fiber memories that rely on nonlinear optical
interaction with strong laser light, which imparts added noise, and are not
representative of all fiber or delay-line memories. Citation numbers appear in
Ref. [257].

##  5 Conclusion

In this work we have comprehensively reviewed broadband quantum memory in
atomic ensembles, including its motivation, the challenge posed by linewidth-
bandwidth mismatch, the physical protocols applicable to atomic ensembles, the
underlying theory for homogeneous and inhomogeneous systems and application of
the theory for efficiency optimization and sensitivity analysis, and the
current state-of-the-art performance of broadband atomic ensembles relative to
delay-line and fiber memories. We hope this chapter serves as a useful guide
to and reference for broadband atomic ensemble quantum memory.

## Acknowledgements

This work was funded in part by NSF grant Nos. 1640968, 1806572, 1839177,
1936321, and 2207822; and NSF Award DMR1747426. This material is based upon
work supported by the U.S. Department of Energy Office of Science National
Quantum Information Science Research Centers. We thank J. Gary Eden, Benjamin
D. Hunt, Sehyun Park, Andrey Mironov, Thomas Reboli, Kathleen Oolman, Yujie
Zhang, Dongbeom Kim, Yunkai Wang, Colin Lualdi, Tegan Loveridge, and Ujaan
Purakayastha for helpful discussion, and Jim Brownfield and Ernest Northern
for expert assistance machining the barium heat pipe oven.

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