Analysing Bose-Einstein Condensates (BECs) Optimal Control. Magnetic Trap Parameters Control Model and Optical Lattice Parameters Control Model

Student: Zagorodnev Denis

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Applied Mathematics (Bachelor)

Year of Graduation: 2020

In the present paper, we consider the problem of optimal control of the properties of the Bose–Einstein condensate (BEC) held in a magnetic trap and exposed to laser radiation. Via the "hydrodynamic" approach to finding solutions of the Gross–Pitaevskii equation for the BEC wave function and the choice of various control quality criteria, we develop two models for optimal control of the parameters of the magnetic trap and optical lattice that minimize the phase change of the BEC wave function under laser radiation. We carried out the analytical and numerical study of the developed optimal control models, analyzed in detail the numerical results for each of the developed optimal control models and also, fulfilled the comparison of our numerical results with the real physical experiments data.

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