The primary aims of the present proposed project is to study entanglement decoherence of many-body qubits or multilevel quantum systems and to develop a quantum trajectory approach in several important AMO physics domains. Two examples are: entanglement dynamics of multilevel atomic systems coupled to a quantized field and non-Markovian trajectories for quantum systems coupled to a fermionic environment. Our primary interest of application is quantum decoherence of quantum open systems in AMO and condensed matter systems and the simulation of quantum entanglement dynamics of many-body systems.