Approach to solving spin-boson dynamics via non-Markovian quantum trajectories

We develop a systematic and efficient approach for numerically solving the non-Markovian quantum state diffusion equation for an open quantum system that can be strongly coupled to an environment. As an important application, we consider a real-time simulation of a spin-boson model in a strong-coupling regime that is difficult to deal with using conventional methods. We show that the non-Markovian stochastic Schrödinger equation can be efficiently implemented as a real-time simulation for this model, so as to give an accurate description of spin-boson dynamics beyond the rotating-wave approximation.

Figure 1

Spin state $\langle {\sigma }_z\rangle$ for various memory parameters: $\gamma =0.2$, $0.4$, and $0.8$. Here $\omega =1$, $\Gamma \gamma =0.2$, and $\mathcal{N}=100$.

Figure 2

Spin state $\langle {\sigma }_z\rangle$ for $\mathcal{N}=100$, 70, 40, 10, and 0, $\overline{O}=0$, and RWA. Here $\gamma =0.2$ and $\Gamma \gamma =0.2$.

Figure 3

(a) Average $\langle \parallel Q_0^{\left(n\right)}\parallel \rangle$ of the trace norm of perturbative terms $Q_0^{\left(n\right)}$ from the simulation in Fig. 1 for $\gamma =0.2$. (b) The probability density $P\left(N_Q\right)$ of $N_Q$ at $t=12$ from the simulations in Fig. 1 for $\gamma =0.2$, $0.4$, and $0.8$. Solid lines show fits to exponential distributions for the tails of the distributions.