Non-Markovian trajectory approach of three-level quantum systems

Hao‐Sheng Zeng, Yu-Kun Ren, Xiaolan Wang +1 more

Z. Kanokov

Jun Jing, Ting Yu

The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum trajectory approach to a dissipative three-level model. We have established a convolutionless stochastic Schrödinger equation called the time-local quantum state diffusion (QSD) equation without any approximations, in particular, without Markov approximation. Our exact time-local QSD equation opens a new avenue for exploring quantum dynamics for a higher dimensional quantum system coupled to a non-Markovian environment.

Michael W. Jack, Matthew J. Collett, Daniel F. Walls

We present a formulation of non-Markovian quantum trajectories for open systems from a measurement theory perspective. In our treatment there are three distinct ways in which non-Markovian behavior can arise: a mode-dependent coupling between the bath (reservoir) and system, a dispersive bath, and spectral detection of the output into the bath. In the first two cases the non-Markovian behavior is intrinsic to the interaction; in the third case the non-Markovian behavior arises from the method of detection. We focus in detail on the trajectories that simulate real-time spectral detection of the light emitted from a localized system. In this case the non-Markovian behavior arises from the uncertainty in the time of emission of particles that are later detected. The results of computer simulations of the spectral detection of the spontaneous emission from a strongly driven two-level atom are presented.

Dariusz Chruściński, Andrzej Kossakowski

Kade Head-Marsden, David A. Mazziotti

Treatment of Markovian, many-electron dynamics from the solution of the Lindblad equation for the 1-electron reduced density matrix requires additional constraints on the bath operators to maintain fermion statistics. Recently, we generalized Lindblad's formalism to non-Markovian dynamics through an ensemble of Lindbladian trajectories. Here we show that the fermion statistics of non-Markovian dynamics can be enforced through analogous constraints on the bath operators of each Lindbladian trajectory in the ensemble. To illustrate, we apply the non-Markovian method to three distinct systems of two fermions in three levels. While the electrons violate the fermion statistics without the constraints, correct fermion behavior is recovered with the constraints.