Stored light in linear and nonlinear dielectrics

Summary form only given. We compare old experimental and theoretical results for the storage and retrieval of quantum information in atomic dielectrics done on the ²³Na D₁ lines and based on nonlinear degenerate self-induced transparency (SIT) with more recent experiments and theory based on linearised electromagnetically induced transparency (EIT) done on the ⁸⁷Rb D₁ lines. Although the nonlinear SIT theory is very different from the recent linearised EIT theory there are remarkable conceptual similarities at the level of quantum expectation values between the two theories of quantum memory in their modes of storage and retrieval of quantum information. However it has been argued that the linearised theories have the merit of recording information on the atomic dielectric accurate to all (countable) orders of normally ordered correlation functions while this is not true for the nonlinear theories. By working from the closely related theoretical case of the quantum nonlinear dielectric formed from the condensed repulsive Bose gases we bring strong evidence to show that the quantum nonlinear SIT theories can in fact show similar levels of accuracy namely beyond expectation and to all (countable) orders of correlation functions. Up to neglect of incoherence effects the exact quantum theory of EIT is exactly solvable by methods such as the quantum inverse method or Bethe ansatz, and the 3-level Λ atom model of EIT induces dark quantum solitons. We explore the whole set of quantum dielectrics formed by the nonlinear and linearised EIT dielectrics interpreted as quantum memories. We explore how far it is possible in principle to store quantum information accurately for continuous wave optical inputs via a merely countable infinity of correlation functions. We hope to have evaluated quantum correlation functions of arbitrary countable order for the quantum nonlinear EIT system by exact quantum inverse methods and results for quantum memory purposes will be reported. We can already explore the complete Hilbert space for strictly (non-degenerate) resonant SIT at the level of the quantum sine-Gordon equation and quantised breathers here provide generalised qubits for quantum information purposes in which the number of breather states- is in general greater than two and is bounded by an adjustable constant coupling in the nonlinearity.