Applications of coherent population transfer to quantum information processing

Abstract

We develop a theoretical framework for the exploration of quantum mechanical coherent population transfer phenomena, with the ultimate goal of constructing faithful models of devices for classical and quantum information processing applications. We begin by outlining a general formalism for weak-field quantum optics in the Schrödinger picture, and we include a general phenomenological representation of Lindblad decoherence mechanisms. We use this formalism to describe the interaction of a single stationary multilevel atom with one or more propagating classical or quantum laser fields, and we describe in detail several manifestations and applications of electromagnetically induced transparency. In addition to providing a clear description of the nonlinear optical characteristics of electromagnetically transparent systems that lead to "ultraslow light," we verify that -in principle -a multi-particle atomic or molecular system could be used as either a low power optical switch or a quantum phase shifter. However, we demonstrate that the presence of significant dephasing effects on the metastable levels destroys the induced transparency. Finally, a detailed calculation of the relative quantum phase induced by a system of atoms on a superposition of spatially distinct Fock states predicts that a significant quasi-Kerr nonlinearity and a low entropy cannot be simultaneously achieved in the presence of arbitrary spontaneous emission rates. Within our model, we identify the constraints that need to be met for this system to act as a one-qubit and a two-qubit conditional phase gate.

Cross-Kerr interaction in a four-level atomic system

“…This enables us to decompose the entire space into fourdimensional subspaces that are invariant under the unitary evolution. That is, given a system in a particular state, the evolution will remain in the subspace corresponding to absorption and creation of single photons due to transitions between the four atomic states [14].…”