Entanglement generation and verification are essential steps to achieve long-distance quantum communication with atomic ensembles according to some protocols. In this dissertation, new schemes for generating quantum state entanglement between two atomic ensembles by stimulated Raman scattering are proposed and analyzed under various practical factors such as linear dispersion, readout losses, and detector noise. In the photon-number-state entanglement scheme, new regimes of discrete-variable entanglement are found to be achievable at microscopic and mesoscopic excitation levels. In the field-quadrature-amplitude entanglement scheme, the inequality of quadrature variance satisfies the entanglement criteria for bipartite Gaussian state entanglement, even at low readout efficiency.

Significant progress towards the experimental generation of such entanglement is reported. Population transfer between the atomic ground states is a prerequisite step to prepare the gain medium for stimulated Raman scattering. The high transfer efficiency is achieved through broadband optical pumping. The Stokes and time-delayed anti-Stokes scattering are observed, which is a primary step to verify the quantum memory effect in the atomic vapor. The photon statistics of the Stokes field is measured with a photon-number detection system operating at below the shot-noise level. The pulse energy dependence of Stokes fields on several practical factors is explored. Some new features and phenomena of stimulated Raman scattering in rubidium vapor are observed and analyzed. The simultaneous generation of Stokes and anti-Stokes scattering is observed in the cooperative Raman scattering process, in which only a single strong pump field is present. An enhanced Raman scattering process is also observed, in which the Stokes signal generated by the time-delayed second pump is enhanced by the presence of the first pump when the two pumps are in the Stokes pump frequency range. In addition, we observe very large pulse delay during propagation through ⁸⁵Rb cell, and we explain it with a theoretical linear dispersion model.