Systematic formulation of slow polaritons in atomic gases

We formulate a theory of slow polaritons in atomic gases and apply it to the slowing down, storing, and redirecting of laser pulses in an electromagnetically induced transparency (EIT) medium. The normal modes of the coupled matter and radiation are determined through a full diagonalization of the dissipationless Hamiltonian. Away from the EIT resonance, where the polaritons acquire an excited-state contribution, lifetimes are introduced as a secondary step. With detuning included various four-wave mixing possibilities are analyzed. We investigate specifically the possibility of reverting a stopped polariton by reversing the control beam.