We consider the excitation spectrum and stability of quantized vortices in a weakly-interacting Bose gas trapped in a toroidal container, and discuss the driven rotation of such a condensate.
Bose-Einstein condensation is a quantum statistical phase transition which was theoretically predicted almost a hundred years ago. After years of seminal research, physicists realized the first almost ideal Bose-Einstein condensates in ultracold dilute atomic gases in 1995. Since then, the theoretical and experimental methods concerning such systems have been developing rapidly, and many fascinating phenomena have been found in these novel quantum systems.\n\nBose-Einstein condensation occurs in a system consisting of massive bosons when a single quantum state becomes macroscopically occupied as the temperature is lowered below the transition temperature. In general, condensates consisting of repulsively interacting bosons exhibit superfluidity: Particle currents can flow in the system without dissipation and viscosity. Moreover, the velocity fields of condensates have to be irrotational, which severely restricts the rotational characteristics of these systems. Apart from the center of mass motion, the system may carry angular momentum in the form of elementary excitations or so-called quantized vortices.\n\nThis Thesis is a theoretical study of subjects related to stability and dynamics of quantized vortices in dilute atomic Bose-Einstein condensates. The precession and instability of off-centered vortices in trapped condensates is investigated both in the zero-temperature limit and at finite temperatures. Dynamical stability of multiply quantized vortices and vortex clusters is studied in axisymmetric trap geometries. Splitting of energetically and dynamically unstable multiply quantized vortices into singly quantized vortices is also studied. Finally, as a separate subject, tunneling of a condensate through a potential barrier is investigated. Majority of this work relies on numerical methods for solving the Gross-Pitaevskii and Bogoliubov equations, which are of central importance in the study of dilute atomic Bose-Einstein condensates.
Abstract This chapter is devoted to discussing some key superfluid properties exhibited by dilute Bose gases confined in external traps. Key issues concern the behaviour of the critical velocity and the applicability of Landau’s criterion for superfluidity, the moment of inertia and its quenching caused by the irrotationality of the superfluid motion, the scissors mode, and the expansion of a rotating superfluid cloud. Rotational effects at high angular velocities, with the appearance of quantized vortices and vortex lattices, are also considered. The chapter also discusses the consequences for vortices on the collective oscillations of the trapped gas, the stability and the precession of vortex lines, and the nature of the superfluid flow in toroidal traps.