  In this paper, we study the dynamical properties of two coupled quantum
harmonic oscillators coupled with bosonic non-Markovian environment both in
position and momentum. We deduce the exact analytical master equation using
Quantum State Diffusion method and give the quantum trajectory description when
the control is added to the system by applying interaction between two harmonic
oscillators. With numerical simulation, we compare the evolution of
entanglement under different controlling effects. At last, we use nonlinear
Quantum State Diffusion method to strengthen our above results by getting the
same evolution.
