Scientific journal
Advances in current natural sciences
ISSN 1681-7494
"Перечень" ВАК
ИФ РИНЦ = 0,775

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Here we present the application of control methods to nanotechnology. This special technology is used in mastering of real objects with the space sizes of few nanometers. It allows operate with such objects for the purposes of the modern technology, for example, in the field of nanolithography, then the beam of cooled atoms passing through standing laser wave(s) to be concentrated on the so-called "mask". In this sense the method itself is very similar to ordinary lithography but with the opportunity to get nano-scale of the objects (microchips etc.).

Every atomic beam in nanolithography consists of many quantum particles, and for every atom from the beam we have the second order ODE based on the Schroedinger equation. The coefficients of this equation depend on the laser field (consisted actually of two fields: basic and additional modulated). Because of the field modulation they are changed and they are time-dependent, it influences on the atomic dynamics, and we get the opportunity to realize a feedback, i.e. to express the process in the terms of control theory and to apply control methods to the dynamical differential equations. Here the input is the beam characteristics and the output is the space distributions of the particles on the mask.

Standard speed gradient method, however, is not very productive in nanotechnology. From one side, it allows achieve the selected level of energy (the eigenfunction of Hamiltonian for dynamical differential equation). But for the practical purposes of nanolithography we need to prepare an atomic beam with the very narrow spatial distribution. Thus, it is logical to include the parameters of the desired distribution in the goal function of the control process. For this purpose we have to re-formulate the mathematical task and introduce the new type of controlled systems. We demand the achievement of the narrow spatial distribution of the dynamical particles as the main goal of the control. Additionally we investigate the statistical properties of the particle dynamics but not the behavior of the single particle. Statistical approach is very natural if we discuss the dynamical properties of a quantum system, but this problem was not formulated in the frame of classical control theory of real systems. At present only separate cases of atomic beam dynamics are investigated.

Let´s sum up our main results:

  1. The statistical description of the system (the ensemble of N particles) is realized.
  2. The closed control equation for proportional speed gradient feedback is presented.
  3. The possibility of statistical control application to the purposes of quantum beam focusing is demonstrated.

Thus, the statistical scheme can be successfully applied in the models of quantum beam control.