Parametrizations of a two-level quantum control system

M. Nihtila, P. Kokkonen, J. Lévine
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引用次数: 1

Abstract

A known two-level population transfer model of a quantum system is studied. Construction of the basic four-dimensional real-variable model is repeated first. By using a technique of underdetermined systems of ordinary differential equations (ODE) the two scalar control variables are represented then as functions of the state variables. This representation is used to obtain an underdetermined system of nonlinear ODEs, which does not include the control variables. Via a flatness-based idea two state variables are used to parametrize the remaining ones and the two controls. The coordinate system of the states is converted into polar form. Then another form of parametrization is obtained for the states and controls. A quadratic energy minimizing optimization is also studied. It is converted via the two parametrizations to two equivalent variational problems. A general solution to the polar-form variational problem is given. Simulation results to be presented in a companion paper will complete results of this study.
二能级量子控制系统的参数化
研究了已知量子系统的两能级种群迁移模型。首先重复基本四维实变量模型的构建。利用欠定常微分方程组技术,将两个标量控制变量表示为状态变量的函数。该表示用于得到不包含控制变量的非线性ode的欠定系统。通过基于平面的思想,使用两个状态变量来参数化剩余的状态变量和两个控件。将状态坐标系转换为极坐标形式。然后得到状态和控制参数化的另一种形式。研究了一种二次能量最小化优化方法。通过两个参数化将其转化为两个等价的变分问题。给出了极型变分问题的一般解。模拟结果将在一篇配套论文中提出,以完成本研究的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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