Stochastic Schrödinger equations for optical fields based on atom detection

We derive stochastic Schrödinger equations describing the evolution of an optical linear amplifier conditioned on the state-selective detection of the source atoms. By applying a classical pulse to each atom immediately before the detection process we generate different stochastic Schrödinger equations including that of the quantum-jump method and quantum-state diffusion. We also study the transition from the distinct jumps of the quantum-jump method to the diffusive behavior of quantum-state diffusion and trace the effect of the information gained by the detection of the state of the atom on the state of the field.