Citation: Mardonov, S.N.; Ahmedov, B.J. Rabi Frequency Management of Collapsing Quasi-Two-Dimensional Bose-Einstein Condensates with Pseudospin-1/2. Particles 2022, 5, 135–145. https://doi.org/ 10.3390/particles5020012 Academic Editor: Armen Sedrakian Received: 31 March 2022 Accepted: 26 April 2022 Published: 28 April 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Article Rabi Frequency Management of Collapsing Quasi-Two-Dimensional Bose-Einstein Condensates with Pseudospin-1/2 Shukhrat N. Mardonov 1,2,3, * ,† and Bobomurat J. Ahmedov 1,2,4, * ,† 1 Ulugh Beg Astronomical Institute, Astronomy St. 33, Tashkent 100052, Uzbekistan 2 Tashkent Institute of Irrigation and Agricultural Mechanization Engineering, Kori Niyozi 39, Tashkent 100000, Uzbekistan 3 Department of Economics, Sustainable Agriculture and Digital Technology, Samarkand Branch of Tashkent State Agrarian University, A.Temur 7, Okdaryo, Samarkand 191200, Uzbekistan 4 Physics Faculty, National University of Uzbekistan, Tashkent 100174, Uzbekistan * Correspondence: mshuxrat@gmail.com (S.N.M.); ahmedov@astrin.uz (B.J.A.) † These authors contributed equally to this work. Abstract: The collapse of quasi-two-dimensional pseudospin-1/2 Bose-Einstein condensate of attract- ing atoms with intra- and cross-spin interaction is studied in the presence of the Rabi coupling. The condensate dynamics is presented as a function of the self-interaction and Rabi frequency. The evolu- tion of two components of the condensate by using the Gross-Pitaevskii equations is investigated. The initial Gaussian ansatz for two-component wave functions is selected for the better interpretation of the numerical results. The intra-spin-coupling modifies the critical number of atoms causing the collapse while the collapse is observed only in a single pseudospin component. It is demonstrated that for cross-spin-coupling only double spin-components collapse can occur. Keywords: collapse; Bose-Einstein condensate; Gross-Pitaevskii equation; synthetic magnetic field; Rabi frequency; pseudospin 1. Introduction Understanding of behavior of nonlinear quantum systems, including solitons and in- stantons, is critically important for understanding of quantum field and particles physics [1]. Thus, studies of experimentally available nonlinear quantum condensed matter systems can shed light on variety of processes occuring on much smaller spatial scales and involv- ing much higher energies. One of those nonlinear quantum condensed matter systems is Bose-Einstein condensate (BEC) of interacting atoms [2]. The BECs open new research avenues in low-energy quantum physics as well as in astrophysics and cosmology, where they are actively studied for the understanding of the nature of mysterious Dark Matter [3] and possible alternatives of the relativistic neutron stars as boson stars. The nonlinear self-interaction that can be “repulsive” or “attractive” due to the Feshbach resonance [4] or dipolar interactions [5,6] is critically important for the BECs properties. The attractive inter- action in the BEC can produce solitons [7], quantum droplets [8,9], collapse processes [10], and many other phenomena. The BEC collapse is a dynamical process, corresponding to the squeezing of the char- acteristic size of the condensate into a point and sequentially an explosion as occurs in the experiments [11–14]. The collapse process depends on the dimension of the system and interatomic interaction. For instance, in a one-dimensional system, a cubic inter- atomic attraction in the condensate characterizes soliton dynamics [15] rather than the collapse. However, in the presence of the stronger quintic nonlinearity, the condensate can collapse [16]. In three dimensional systems with cubic nonlinearity attractive interaction always leads to the BEC collapse while in two dimensions a critical number of atoms is Particles 2022, 5, 135–145. https://doi.org/10.3390/particles5020012 https://www.mdpi.com/journal/particles