The methods of mathematical control theory are widely used in the modern physics, but still they are less popular in quantum science. We will discuss the aspects of control theory, which are the most useful in applications to the real problems of quantum optics. We apply this technique to control the behavior of the two-level quantum particles in the modulated external optical field in the frame of the so-called "semi classical model", where quantum two-level atomic system interacts with classical electromagnetic field. In chapter 1 we give some basic definitions, terminologies and preliminary results related to applied control theory. In chapter 2 we propose a simple model of feedforward control for the quantum particle system, which is a basement for further investigation of two-level quantum particle in the external one-dimensional optical field. In chapter 3 we demonstrate the possibility to stabilize the probability amplitudes of the upper level for a single quantum two-level atom in a classical optical field with feedback control scheme. In chapter 4 an effective quantum particle beam-splitter is realized in the frame of open- loop control scheme.
Saif Ullah is young Pakistani writer and poet. He has published two Urdu poetry books (Zindan e Alam and Talaash) and a beautiful Socio-religious book (Muhammad (PBUH) - The best ever institution of love and wisdom). His 4th book (World needs Muhammad (PBUH) will be published in August 2021 which covers reasons for Major problems in the world, their consequences and finally their solution. These books are available with Daastan Publishers, Guftugu Publishers, Awaaz Publisher and also on Amazon.