Non-Markovian quantum state diffusion

Walter T. Strunz, Lajos Diósi, Nicolas Gisin

Xinyu Zhao, Ting Yu

Walter T. Strunz

Mi Chen, J. Q. You

Non-Markovian quantum state diffusion (NMQSD) provides a powerful approach to the dynamics of an open quantum system in bosonic environments. Here we develop a NMQSD method to study the open quantum system in fermionic environments. This problem involves anticommutative noise functions (i.e., Grassmann variables) that are intrinsically different from the noise functions of bosonic baths. We obtain the NMQSD equation for quantum states of the system and the non-Markovian master equation. Moreover, we apply this NMQSD method to single- and double-quantum-dot systems.

Timothy P. Spiller

Kimmo Luoma, Walter T. Strunz, Jyrki Piilo

We solve two long-standing problems for stochastic descriptions of open quantum system dynamics. First, we find the classical stochastic processes corresponding to non-Markovian quantum state diffusion and non-Markovian quantum jumps in projective Hilbert space. Second, we show that the diffusive limit of non-Markovian quantum jumps can be taken on the projective Hilbert space in such a way that it coincides with non-Markovian quantum state diffusion. However, the very same limit taken on the Hilbert space leads to a completely new diffusive unraveling, which we call non-Markovian quantum diffusion. Further, we expand the applicability of non-Markovian quantum jumps and non-Markovian quantum diffusion by using a kernel smoothing technique allowing a significant simplification in their use. Lastly, we demonstrate the applicability of our results by studying a driven dissipative two level atom in a non-Markovian regime using all of the three methods.