Non-Markovian Quantum Jumps

Open quantum systems that interact with structured reservoirs exhibit non-Markovian dynamics. We present a quantum jump method for treating the dynamics of such systems. This approach is a generalization of the standard Monte Carlo wave function (MCWF) method for Markovian dynamics. The MCWF method identifies decay rates with jump probabilities and fails for non-Markovian systems where the time-dependent rates become temporarily negative. Our non-Markovian quantum jump approach circumvents this problem and provides an efficient unraveling of the ensemble dynamics.

Figure 1

(a) The decay rate for a two-level atom in photonic band gap as a function of time. (b) NMQJ and exact results. In (a) the decay rate displays oscillatory behavior with temporary negative values. In (b) we plot the excited state probability of the atom, and the results show the match between the exact and simulation results. The initial pure states in examples 1 and 2 are $|e⟩$ and $(|g⟩+|e⟩)/\sqrt{2}$, respectively.

Figure 2

An example realization with a jump—reverse jump cycle. The ground and excited state probabilities are given as function of time. The first jump at time $t\simeq 0.8$ occurs at the positive decay rate region and destroys the superposition state. The second jump at $t\simeq 5.0$ occurs at the negative decay region and recreates the superposition. The dotted lines show the evolution without any jumps.