Stochastic Schrodinger Equation for a Quantum Oscillator with Dissipation

I. Semina, Vitalii Semin, Francesco Petruccione +1 more

Firstly, the Markovian stochastic Schrödinger equations are presented, together with their connections with the theory of measurements in continuous time. Moreover, the stochastic evolution equations are translated into a simulation algorithm, which is illustrated by two concrete examples — the damped harmonic oscillator and a two-level atom with homodyne photodetection. We then consider how to introduce memory effects in the stochastic Schrödinger equation via coloured noise. Specifically, the approach by using the Ornstein-Uhlenbeck process is illustrated and a simulation for the non-Markovian process proposed. Finally, an analytical approximation technique is tested with the help of the stochastic simulation in a model of a dissipative qubit.

Julian Schwinger

A. Ya. Bekshaev, R. A. Volkov

Dmitrii E. Makarov, Horia I. Metiu

The behavior of a quantum system coupled to a reservoir is usually described by an equation for the reduced density matrix. If the dephasing and the change of population in these equations can be described phenomenologically, then it is possible to develop a stochastic Schrödinger equation to describe quantum dynamics with dissipation. In this article, we propose a method for treating dephasing, within the stochastic Schrödinger equation, for many-level systems.

Xinyu Zhao, Wufu Shi, Lian-Ao Wu +1 more

This paper considers the extension of the non-Markovian stochastic approach for quantum open systems strongly coupled to a fermionic bath to the models in which the system operators commute with the fermionic bath. This technique can also be a useful tool for studying open quantum systems coupled to a spin-chain environment, which can be further transformed into an effective fermionic bath. We derive an exact stochastic Schr\"odinger equation (SSE), called the fermionic quantum state diffusion (QSD) equation, from the first principle by using the fermionic coherent state representation. The reduced density operator for the open system can be recovered from the stochastic average of the solutions to the QSD equation over the Grassmann-type noise. By employing the exact fermionic QSD equation, we can derive the corresponding exact master equation. The power of our approach is illustrated by the applications of our stochastic approach to several models of interest including the one-qubit dissipative model, the coupled two-qubit dissipative model, the quantum Brownian motion model, and the $N$-fermion model coupled to a fermionic bath. Different effects caused by the fermionic and bosonic baths on the dynamics of open systems are also discussed.

Vinay Ambegaokar