Magnetic monopoles, which are particle-like field configurations with which one can associate a topological charge, widely exist in various three-dimensional condensate systems. In this paper, by making use of Duan 's topological current theory, we obtain the charge density of magnetic monopoles and their bifurcation theory in a charged two-condensate Bose–Einstein system. The evolution of magnetic monopoles is studied from the topological properties of a three-dimensional vector field. The magnetic monopoles are found generating or annihilating at the limit points and encountering, splitting or merging at the bifurcation points.
Magnetic monopoles, which are particle-like field configurations with which one can associate a topological charge, widely exist in various three-dimensional condensate systems. In this paper, by making use of Duan 's topological current theory, we obtain the charge density of magnetic monopoles and their bifurcation theory in a charged two-condensate Bose–Einstein system. The evolution of magnetic monopoles is studied from the topological properties of a three-dimensional vector field. The magnetic monopoles are found generating or annihilating at the limit points and encountering, splitting or merging at the bifurcation points.
Bose–Einstein condensation is a quantum statistical phase transition that occurs in a system consisting of bosons when a single-particle quantum state becomes macroscopically occupied. This peculiar state of matter was first predicted in 1925 and finally realized seventy years later in vapours of weakly-interacting alkali-metal atoms. Since then, Bose–Einstein condensates have been one of the most fascinating research fields in modern physics. \n \nThe gaseous condensates offer a robust platform to accurately study interacting many-particle systems from the first principles. Experimentally, the possibility to precisely control a condensate with external fields and directly image its order parameter provides unforeseen opportunities to obtain deep insight into phenomena across different subfields of physics. In particular, gaseous condensates can emulate complicated models that arise in atomic, condensed-matter, and even particle physics, allowing realizations of exotic phenomena that are elusive in their original contexts. An outstanding example is the existence of various topological defects in ultacold quantum gases with internal degrees of freedom. \n \nIn this thesis, we investigate the creation, stability, and dynamical properties of various topological defects in spinor Bose–Einstein condensates. The majority of the theoretical results is obtained by numerically solving the dynamics using Gross–Pitaevskii equations for spin-1 condensates. Many theoretical predictions are confirmed by the very good agreement with experiments. \n \nThe first experimental observations of a topological point defect in an order parameter describing the quantum gas are presented. Such a point defect is reminiscent to the magnetic monopole particle appearing in grand unified theories. Therefore, the discovery of monopoles in quantum gases further encourages the quest for finding magnetic monopoles in natural electromagnetic fields, a search largely initiated by Paul Dirac almost a century ago. \n \nSubsequently, the fine structure and decay dynamics of the point defect are studied numerically and verified in experiments. The created monopole is gradually destroyed during the polar-to-ferromagnetic quantum phase transition, which results in the spontaneous emergence of a Dirac monopole in synthetic magnetic field. In addition to the singular point defect, the first experimental realization of a knot soliton in the context of quantum field is reported. This thesis lays the foundation for studies of the dynamics and stability of three-dimensional topological structures in quantum systems.
Recently, an effective non-Abelian magnetic field with a topology of a monopole was shown to emerge from the adiabatic motion of multilevel atoms in spatially varying laser fields [J. Ruseckas, Phys. Rev. Lett. 95, 010404 (2005)10.1103/PhysRevLett.95.010404]. We study this monopole in a Bose-Einstein condensate of degenerate dressed states and find that the topological charge of the pseudospin cancels the monopole charge resulting in a vanishing gauge invariant charge. As a function of the laser wavelength, different stationary states are classified in terms of their effect to the monopole part of the magnetic field and a crossover to vortex ground state is observed.
Since their experimental discovery in 1995, dilute Bose–Einstein condensates have proven to be excellent platforms for studying interacting many-body quantum systems. The gaseous condensates can be conveniently controlled in space and time with lasers and magnetic fields. Theoretically, these low-temperature systems can be described starting from first principles, and their dynamics is accurately captured by the mean-field approach. Dilute condensates with internal spin degrees of freedom may host various topological defects including vortices, monopoles, and skyrmions. Precise external control fields can be used to engineer and study these topological states. \n \nIn this thesis, we investigate the creation, stability, and dynamics of various topological defects in spinor Bose–Einstein condensates. A combination of numerical and analytical methods is used and a part of the research is carried out in collaboration with an experimental research group. The majority of the research involves numerically solving the mean-field Gross–Pitaevskii equation for a spin-1 condensate. The computations are accelerated with graphics processing units. \n \nWe find that the ground state of a ferromagnetic spin-1 condensate supports a Dirac monopole in its synthetic magnetic field in the presence of a quadrupole magnetic field. The energetics of various stationary states of spin-orbit coupled condensates are analyzed and a robust method to observe these exotic states in experiments is proposed. The creation of topological skyrmions is simulated and a very good quantitative agreement with a recent experiment is obtained. Importantly, the first experimental observations of both, Dirac monopoles and topological point defects in a system governed by a quantum field are presented. Subsequently, the decay dynamics of the point defect is studied, revealing the decay into a ferromagnetic state supporting the Dirac monopole. \n \nThe impact of the research conducted in this thesis is not limited to gaseous Bose–Einstein condensates, but due to the universality of quantum mechanics and topological defects, our work provides knowledge, ideas, and inspiration across research fields.
Based on the three-dimensional spinor Gross-Pitaevskii (GP) equation, the dynamic behavior of the Bose-Einstein condensate under the action of a time-dependent periodic external magnetic field is studied. The results show that the Bose-Einstein condensate with spin-1 in a ferromagnetic state will undergo topological deformation under the action of an external magnetic field periodically varying with time. When the two zero points of the magnetic field enter into the condensate, the density pattern of the spin-up state forms small convexities protruding upward and downward on the z-axis, respectively. As the two zero points of the magnetic field gradually coincide in the condensate, the upward and downward protruding convexities are elongated. Finally, the spin-up state in the shape of a line is distributed on the z-axis, which is consistent with the scenario of the isolated Dirac string predicted by theoretical analysis. As far as we know, magnetic monopole can be divided into positive monopole and negative monopole. The positive magnetic monopole means that all magnetic induction lines are emitted from the center of the circle. And only the Dirac string points to the center of the circle. The negative monopole is that all the magnetic induction lines point from the outside to the center of the circle, and only the Dirac string emits from the center of the circle. Magnetic monopole is a topological defect in vector field, which accords with both quantum mechanics and gauge invariance of electromagnetic field. Single magnetic monopole has been studied a lot in theory, and its analogues have been observed in experiment. But multiple monopoles and the interaction between them are still rarely studied. In this paper, multiple monopoles are produced based on the fact that the periodic magnetic field has multiple zeros. We use a new periodic magnetic field to generate a positive and negative magnetic monopole. Due to the strong external magnetic field, the vorticity in the condensate is consistent with the magnetic field of the monopole. Finally, by calculating the superfluid vorticity of the condensate, the characteristic diagram of the magnetic monopole is obtained. The results show that the condensate forms a pair of positive and negative magnetic monopoles at the two zero points of the magnetic field, corresponding to the two small convexities protruding upward and downward on the z-axis of the spin-up state, respectively. As the two zero points of the magnetic field coincide, the two Dirac strings in the positive and negative magnetic monopole gradually approach to each other, and after about 5 ms, they are completely connected, finally forming an isolated Dirac string. This result provides a new idea for further studying the isolated Dirac strings.
We discuss the occurrence of Bose-Einstein condensation in systems of noninteracting charged particles in three and one dimensions and in presence of an external magnetic field. In the one dimensional, as well as in the magnetic field cases, although not a critical temperature, a characteristic temperature can be found, corresponding to the case in which the ground state density becomes a macroscopic fraction of the total density. The case of relativistic charged scalar and vector particles is studied. The results give support to the existence of superconductivity in extremely strong magnetic fields, and lead to the prediction of superconductive-ferromagnetic behavior in the vector field case, which might be of interest in condensed matter as well as in cosmology. Some features of the magnetization in the early universe are conjectured.