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Computer Optics

Investigation of non-markovian dynamics of two dipole-dipole interacting Qubits based on numerical solution of the non-linear stochastic schrödinger equation

Andrei Pavelev, Vitalii Semin

Published Apr 1, 2019• 6 citations
Publisher

Abstract

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.
DOI
10.18287/2412-6179-2019-43-2-168-173

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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.
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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.