## Introduction to BEC

Bose-Einstein condensation (BEC) is a manifestation of macroscopic occupation of a single quantum state. The idea of such phenomenon dates back to 1924-1925, when Albert Einstein extended the statistical arguments presented by Satyendra Nath Bose to systems consisting of a conserved number of bosonic particles. Einstein recognised that at sufficiently low temperatures the quantum statistical distribution of an ideal gas of bosons shows condensation of a macroscopic fraction of the material into the ground state of the system. This phenomenon, subsequently termed Bose-Einstein condensation, is a unique, purely quantum-mechanical phase transition in the sense that it occurs in principle even in noninteracting bosonic systems.

A breakthrough in realizing the original idea of BEC occurred in 1995, when research groups at University of Colorado, MIT, and Rice University observed convincing evidence of BEC in dilute alkali atom clouds. These pioneering experiments, from which the Nobel prize was awarded in 2001, launched an avalanche of theoretical and experimental research on the physics of weakly interacting atomic condensates. Due to weak interactions, these systems are rare examples of interacting quantum gases amenable to detailed quantitative analysis, and thus provide unique possibilities for testing the fundamental principles and theories of many-particle quantum physics and even simulating physical phenomena and devices.

## Overview of our BEC research

One of the most fundamental branches of research in QCD group is the studies on coherent matter fields, that is Bose-Einstein condensates (BECs) of dilute atomic gases. In BEC research community, we are best-known from the development of methods to create and creation of monopoles, quantum knots, skyrmions, and multi-quantum vortices into the condensate by control of the external magnetic fields.

Some time ago, we introduced a robust method to create Dirac monopoles into the condensate utilizing adiabatic control of the the external magnetic fields [Phys. Rev. Lett. 103, 030401 (2009) PRESS RELEASE]. Consequently, we reported the observations of Dirac monopoles in the synthetic magnetic field [Nature 505, 657 (2014) PRESS RELEASE] and isolated monopoles, i.e. quantum-mechanical point defects, in the quantum field [Science 348, 5644 (2015)]. All the experimental results have been achieved in collaboration with Prof. David S. Hall’s group at Amherst College, USA. We have also investigated the creation of non-Abelian monopoles in these systems, but thus far only theoretically [Phys. Rev. Lett. 102, 080403 (2009)].

Our studies of topology in spin-1 BECs also involve defects belonging to the third homotopy group, namely skyrmion and knot structures. In our experimental collaboration, we have observed quantum knots [Nat. Phys. 12, 478 (2016)] and Shankar skyrmions [Sci. Adv. 3, eaao3820 (2018)]. We have furthermore proposed methods to create quantum knots using the so-called counterdiabatic magnetic field [Phys. Rev. A 96, 063609 (2017)] and skyrmionic structures in spin-2 BECs using quadrupole magnetic field [New J. Phys. 20, 055011 (2018)].

Furthermore, we have introduced cyclic vortex creation procedure, which resulted in a so-called vortex pump, that is, a method to cyclically increase the vorticity of the system rendering it possible to create giant vortices [Phys. Rev. Lett. 99, 250406 (2007); J. Low Temp. Phys. 161, pp. 561 (2010)]. Also the dynamics of these giant vortices is of our interest [Phys. Rev. Lett. 97, 110406 (2006); Phys. Rev. Lett. 99, 200403 (2007); Phys. Rev. A 81, 033627 (2010)]. We have also studied so-called coreless vortices in spinor BECs [Phys. Rev. A 79, 023618 (2009)].

Our research interests also span rotating multi-component BECs [Phys. Rev. A 85, 043613 (2012)] as well as elementary excitations, both dipolar and spin-orbit coupled condensates [Phys. Rev. A 82, 053616 (2010);Phys. Rev. A 84, 043638 (2011); Phys. Rev. A, 86, 051607(R) (2012)] and vortex dipoles [Phys. Rev. A 83, 011603(R) (2011)].