Non-Markovian quantum jump method for driven-dissipative two-level systems

We propose a modified non-Markovian quantum jump method to overcome the obstacle of dramatically increased trajectory number in conventional quantum trajectory simulations. In our method the trajectories are classified into the trajectory classes characterized by the number of quantum jumps. We derive the expression of the existence probability of each trajectory (class), which is essential to construct the density matrix of the open quantum system. This modified method costs less computational resources and is more efficient than the conventional quantum trajectory approach. As applications we investigate the dynamics of spin-$\frac{1}{2}$ systems subject to Lorentzian reservoirs with considering only the no-jump and one-jump trajectories. The revival of coherence and entanglement induced by the memory effect is observed.