Persistent atomic frequency comb based on Zeeman sub-levels of an erbium-doped crystal waveguide

Long-lived sub-levels of the electronic ground-state manifold of rare-earth ions in crystals can be used as atomic population reservoirs for photon echo-based quantum memories. We measure the dynamics of the Zeeman sub-levels of erbium ions that are doped into a lithium niobate waveguide, finding population lifetimes at cryogenic temperatures as long as seconds. Then, using these levels, we prepare and characterize atomic frequency combs, which can serve as a memory for quantum light at 1532 nm wavelength. The results allow predicting a 0.1\% memory efficiency, mainly limited by unwanted background absorption that we conjecture to be caused by the coupling between two-level systems (TLS) and erbium spins. Hence, while it should be possible to create an AFC-based quantum memory in Er$^{3+}$:Ti$^{3+}$:LiNbO$_3$, improved crystal growth together with optimized AFC preparation will be required to make it suitable for applications in quantum communication.