  We discuss a general model of a quantum memory for a single light mode in a
collective mode of atomic oscillators. The model includes interaction
Hamiltonians that are of second order in the canonical position and momentum
operators of the light- and atomic oscillator modes. We also consider the
possibility of measurement and feedback. We identify an interaction Hamiltonian
that leads to an ideal mapping by pure unitary evolution and compare several
schemes which realize this mapping using a common continuous-variable
description. In particular we discuss schemes based on the off-resonant Faraday
effect supplemented by measurement and feedback and proper preparation of the
atoms in a squeezed state and schemes based on off-resonant Raman coupling as
well as electromagnetically induced transparency (EIT).

Quantum Physics