Non-Markovian Fermionic Quantum State Diffusion Approach

Jürgen T. Stockburger, Hermann Grabert

Walter T. Strunz, Lajos Diósi, Nicolas Gisin

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.

Evgeny Polyakov, Alexey N. Rubtsov

We present a stochastic approach for the description of the quantum dynamics of open system in a fermionic environment (bath). The full quantum evolution as provided by the Schrodinger equation is reformulated exactly as a probabilistic average over the so-called dressed quantum trajectories. The latter are defined as follows. The fermionic environment can be represented as a fermi sea whose "surface" is covered by the ripples of quantum fluctuations. If we consider these fluctuations in the basis of the particle-hole coherent states, then these fluctuations produce a classical particle-hole noise.The probability distribution of this noise is provided by the generalized particle-hole Husimi function of the vacuum. Then we define the dressed quantum trajectory as the evolution of the open system and the bath which is conditioned on a particular particle-hole noise sample. The resulting description resembles the non-Markovian quantum state diffusion for the bosonic bath. Therefore, we expect that our fermionic approach will share its favourable propeties like the possibility to carry out Monte-Carlo simulations of non-Markovian quantum dynamics on long times.

Wei Wu, Maoxin Liu

We investigate the effect of counter-rotating-wave terms on the non-Markovianity in quantum open systems by employing the hierarchical equations of motion in the framework of the non-Markovian quantum state diffusion approach. As illustrative examples, the non-Markovian memory effect of a qubit embedded in a bosonic or a fermionic environment with a detuned Lorentz spectrum at zero temperature is analyzed. It is found that the counter-rotating-wave terms are able to enhance the observed non-Markovianity whether the environment is composed of bosons or fermions. This result suggests that the rotating-wave approximation may reduce the non-Markovianity in quantum open systems. Moreover, we find that the modification of the non-Markovianity due to the different statistical properties of environmental modes becomes larger with the increase of the system-environment coupling strength.