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We investigate theoretically quantum entanglement of light with thecollective spin polarization of a cold atomic ensemble in cavity-assisted Ramanschemes. Previous works concentrated mostly on the bad cavity limit where thesignals are much longer than the cavity field lifetime. In view of atomicrelaxation and other imperfections, there may arise a need to speed-up thelight-atoms interface operation. By increasing the cavity field lifetime, onecan achieve better light-matter coupling and entanglement. In our work, weconsider the non-adiabatic effects that become important beyond the bad cavitylimit in both low-photon and continuous variables regime. We find classicalcontrol field time profiles that allow one to retrieve from the cavity anoutput quantized signal of a predefined time shape and duration, which isoptimal for the homodyne detection, optical mixing or further manipulation.This is done for a wide range of the signal duration as compared to the cavityfield lifetime. We discuss an optimal cavity-atomic ensemble matching in termsof the cavity field lifetime which allows one to apply less intense controlfield and to minimize a variety of non-linear effects, such as AC light shifts,four-wave mixing, etc, which may be potentially harmful to an experiment.

Cavity-assisted squeezing and entanglement: Non-adiabatic effects and optimal cavity-atomic ensemble matching