Spectral analysis for cascade-emission-based quantum communication in atomic ensembles

The ladder configuration of atomic levels provides a source for telecom photons (signal) from the upper atomic transition. \ For rubidium and cesium atoms, the signal field has the range around 1.3-1.5 $\mu$m that can be coupled to an optical fiber and transmitted to a remote location. \ Cascade emission may result in pairs of photons, the signal entangled with the subsequently emitted infrared photon (idler) from the lower atomic transition.\ This correlated two-photon source is potentially useful in the (Duan-Lukin-Cirac-Zoller) DLCZ protocol for the quantum repeater.\ We implement the cascade emission to construct a modified DLCZ quantum repeater and investigate the role of time-frequency entanglement in the protocol.\ The dependence of protocol on photon-number resolving and non-resolving detectors is also studied.\ We find that frequency entanglement deteriorates the performance but the harmful effect can be diminished by using shorter pump pulses to generate the cascade emission.\ An optimal cascade-emission-based DLCZ scheme is realized by applying a pure two-photon source in addition to using detectors of perfect quantum efficiency.