A group of researchers from Russia, Germany and Iran develops computational methods for creating a theory describing the behavior of cold atoms and ions in optical and electromagnetic traps. There is a high demand for these works due to the possibility of modeling with such completely controlled quantum systems of complex processes, from solid-state physics to high-energy physics. The projects on designing elements of a quantum computer and ultra-precise atomic clock based on trapped ultracold atoms and ions are being discussed. The results of the latest studies of the group were presented at the conference Grid, Cloud and High-Performance Computing in Science (Sinaia, Romania). The work was published in *Physical Review E*.

At ultralow temperatures (for alkali metal atoms they reach values of several nK), atoms move at a very low speed, which allows conducting high-precision experiments. However, to interpret and plan the experiments, theoretical calculations are required. Vladimir Melezhik, Doctor of Physical and Mathematical Sciences from RUDN University, is engaged in calculations of resonant phenomena and collision processes in ultracold quantum gases. Quantum gas is retained at ultralow temperatures in an optical trap formed by a specially tuned laser beams. The developed experimental technique makes it possible to control and tune the parameters of such quantum systems: the number of particles, their spin composition, temperature, and, last but not least, the effective interaction between atoms. However, the task of quantitative description of the processes occurring is significantly complicated by the fact that in such systems the atoms interact not only with each other but also with the trap.

Vladimir Melezhik and his co-authors focus on atomic and ion traps, which have the shape of highly elongated cigars and are similar to waveguides used for transmission of electromagnetic waves. The researchers have been studying the propagation of electromagnetic radiation in waveguides for a long time, and effective methods of calculation have been developed. However, a quantitative theory that could describe ultracold processes in atomic and ion waveguides is still under development.

"The trap adds a complexity to the problem. In free space, there are no preferred directions. This circumstance makes it possible to reduce the six-dimensional quantum two-body problem of two colliding atoms to a one-dimensional one. This is the key problem of quantum mechanics, described in textbooks. However, in the atomic trap, due to appearance of a preferred direction, the symmetry is violated which makes it impossible to reduce the problem to one-dimensional one. In certain cases the problem can be reduced to the two-dimensional Schrödinger equation. However, in most interesting cases it becomes necessary to integrate the Schrödinger equation in higher dimensions. To solve this class of problems, one needs to develop special computational methods and use powerful computers. We managed to make significant progress on this pass", the author of the report Vladimir Melezhik said.

By changing the parameters of the trap, one can control the intensity of effective interatomic interactions, from superstrong attraction to superstrong repulsion of atoms. This fact makes it possible to simulate various critical quantum phenomena using ultracold trapped atoms.

"One of the areas of our work is a numerical study of ultracold quantum systems using hybrid atomic-ion traps, offering new possibilities for modeling some actual processes of solid state physics, elements of quantum computing and precision physics research", the scientist concluded.

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The work was carried out in cooperation with scientists from the University of Hamburg (Germany), the Institute for Advanced Studies in Basic Sciences (IASBS) in Zanjan, Iran and the Joint Institute for Nuclear Research (Dubna).