Analytical solutions for optimal photon absorption into inhomogeneous spin memories

We investigate for optimal photon absorption a quantum electrodynamical model of an inhomogeneously-broadened spin ensemble coupled to a single-mode cavity. Solutions to this problem under experimental assumptions are developed in the Schrödinger picture without using perturbation theory concerning the cavity-spin interactions. Furthermore, we exploit the possibility of modulating the frequency and coupling rate of the resonator. We consider a one-photon input pulse and show some optimal scenarios, where exact formulas and numerical results are obtained for the absorption probabilities and the optimal pulse shapes. In particular, if the external loss dominates the internal loss of the cavity, we find the optimal cooperativity for different parameters and identify cases where absorption with a success probability larger than 99% is achieved.