Investigation of non-markovian dynamics of two dipole-dipole interacting Qubits based on numerical solution of the non-linear stochastic schrödinger equation
In this paper, we investigate non-markovian dynamics of a system of two interacting qubits. With the help of stochastic calculus we derive the non-Markovian non-linear stochastic Schrödinger equation. This equation is solved by the direct computer simulation. The simulation is used to obtain some dynamic properties of the system.
В работе исследуется динамика системы двух диполь-дипольно взаимодей- ствующих атомов в марковском и немарковском приближениях с помощью численного ре- шения стохастического уравнения Шредингера (СУШ). Показано существенное влияние немарковских шумов на динамику системы в виде осцилляций вероятностей обнаружить систему во втором и третьем энергетическом состоянии. Markovian and non-Markovian dynamics of two dipole-dipole interacting atoms is studied with the help of stochastic Schroedinger equation (SSE). It is shown that the non-Markovian effects are appeared in the form of oscillations of probabilities to find the systems in the entanglement states. Keywords: non-Markovian dynamics, stochastic Schrödinger equation, dipole-dipole interaction.
In this paper, dynamics of a qubit in an external laser field is investigated for the non-Markov environment described by an Ornstein-Uhlenbeck process. A non-linear non-Markovian stochastic Schrödinger equation is derived for the quantum system. The stochastic equation is preserved for a positive semi-definite of the density matrix and its trace. By the numerical solution of the equation, the probability of finding the system in the excited state and the influence of non-Markov noise parameters on this probability are studie.
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.
We investigate the non-Markovian quantum dynamics of a hybrid open system consisting of one qubit and one qutrit by employing a stochastic Schrödinger equation to generate diffusive quantum trajectories. We have established an exact quantum state diffusion (QSD) equation for the dissipative qubit-qutrit system coupled to a bosonic heat bath at zero temperature. As an important application, the non-Markovian QSD equation is employed to simulate the entanglement decay and generation measured by negativity. Finally, some steady-state properties of the hybrid system are also discussed.