We show that the dynamical instability of quantum vortices with more than a single quantum of angular momentum results from a superradiant bound state inside the vortex core. Our conclusion is supported by an analytic WKB calculation and numerical simulations of both linearised and fully non-linear equations of motion for a doubly-quantised vortex at the centre of a circular bucket trap. In the late stage of the instability, we reveal a striking novel behaviour of the system in the non-linear regime. Contrary to expectation, in the absence of dissipation the system never enters the regime of two well-separated phase defects described by Hamiltonian vortex dynamics. Instead, the separation between the two defects undergoes modulations which never exceed a few healing lengths, in which compressible kinetic energy and incompressible kinetic energy are exchanged. This suggests that, under the right conditions, pairs of vortices may be able to form meta-stable bound states.
We show that the dynamical instability of quantum vortices with more than a single unit of circulation results from a superradiant bound state inside the vortex core. We then reveal a striking behavior of the system in the nonlinear regime. Counter to the expectation that the instability should produce well-separated vortices, the system evolves into a bound state of corotating singularities orbiting within a few healing lengths of each other, undergoing modulations in separation. During these modulations, kinetic energy is traded back and forth between sound waves and vortical degrees of freedom.
Multiquantum vortices in dilute atomic Bose-Einstein condensates confined in long cigar-shaped traps are known to be both energetically and dynamically unstable. They tend to split into single-quantum vortices even in the ultralow temperature limit with vanishingly weak dissipation, which has also been confirmed in the recent experiments [Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004)] utilizing the so-called topological phase engineering method to create multiquantum vortices. We study the stability properties of multiquantum vortices in different trap geometries by solving the Bogoliubov excitation spectra for such states. We find that there are regions in the trap asymmetry and condensate interaction strength plane in which the splitting instability of multiquantum vortices is suppressed, and hence they are dynamically stable. For example, the doubly quantized vortex can be made dynamically stable even in spherical traps within a wide range of interaction strength values. We expect that this suppression of vortex-splitting instability can be experimentally verified.
The dynamical instabilities and ensuing dynamics of singly and doubly quantized vortex states of Bose-Einstein condensates with attractive interactions are investigated using full three-dimensional numerical simulations of the Gross-Pitaevskii equation. With increasing the strength of attractive interactions, a series of dynamical instabilities such as quadrupole, dipole, octupole, and monopole instabilities emerge. The most prominent instability depends on the strength of interactions, the geometry of the trapping potential, and deviations from the axisymmetry due to external perturbations. Singly quantized vortices split into two clusters and subsequently undergo split-merge cycles in a pancake-shaped trap, whereas the split fragments immediately collapse in a spherical trap. Doubly quantized vortices are always unstable to disintegration of the vortex core. If we suddenly change the strength of interaction to within a certain range, the vortex splits into three clusters, and one of the clusters collapses after a few split-merge cycles. The vortex split can be observed using a current experimental setup of Leanhardt et al. [Phys. Rev. Lett. 89, 190403 (2002)].
We study numerically the dynamical instabilities and splitting of singly and doubly quantized composite vortices in two-component Bose-Einstein condensates harmonically confined to quasi two dimensions. In this system, the vortices become pointlike composite defects that can be classified in terms of an integer pair $({\ensuremath{\kappa}}_{1},\phantom{\rule{0.16em}{0ex}}{\ensuremath{\kappa}}_{2})$ of phase winding numbers. Our simulations based on zero-temperature mean-field theory reveal several vortex splitting behaviors that stem from the multicomponent nature of the system and do not have direct counterparts in single-component condensates. By calculating the Bogoliubov excitations of stationary axisymmetric composite vortices, we find nonreal excitation frequencies (i.e., dynamical instabilities) for the singly quantized
(1,1) and $(1,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}1)$ vortices and for all variants of doubly quantized vortices, which we define by the condition ${max}_{j=1,2}|{\ensuremath{\kappa}}_{j}|=2$. While the short-time predictions of the linear Bogoliubov analysis are confirmed by direct time integration of the Gross-Pitaevskii equations of motion, the time integration also reveals intricate long-time decay behavior not captured by the linearized dynamics. First, the $(1,\phantom{\rule{0.16em}{0ex}}\ifmmode\pm\else\textpm\fi{}1)$ vortex is found to be unstable against splitting into a
(1,0) vortex and a $(0,\phantom{\rule{0.16em}{0ex}}\ifmmode\pm\else\textpm\fi{}1)$ vortex. Second, the
(2,1) vortex exhibits a two-step decay process in which its initial splitting into a
(2,0) vortex and a
(0,1) vortex is followed by the off-axis splitting of the
(2,0) vortex into two
(1,0) vortices. Third, the $(2,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}2)$ vortex is observed to split into a $(\ensuremath{-}1,\phantom{\rule{0.16em}{0ex}}1)$ vortex, three
(1,0) vortices, and three $(0,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}1)$ vortices. Each of these splitting processes is the dominant decay mechanism of the respective stationary composite vortex for a wide range of intercomponent interaction strengths and relative populations of the two condensate components and should be amenable to experimental detection. Our results contribute to a better understanding of vortex physics, hydrodynamic instabilities, and two-dimensional quantum turbulence in multicomponent superfluids.
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.
The existence of quantized vortices is a key feature of Bose-Einstein condensates. In equilibrium condensates only quantum vortices of unit topological charge are stable, due to the dynamical instabilities of multiply charged defects, unless supported by strong external rotation. In this Letter we elucidate the formation, stability, coalescence and interactions of bound vortex states in trapped nonequilibrium Bose condensates such as exciton-polariton condensates pumped in a ring geometry. These bound states consist of like-signed vortices which share a single core, but whose singularities are spatially separated within the core. We propose that they may form spontaneously during the condensate formation or externally imprinted and stabilized by the particle fluxes towards the condensate center, which is a stark contrast with instability of multiply charged vortices in equilibrium condensates. We show that the maximum topological charge of these states is limited by the Kelvin-Helmholtz instability, and, therefore, by the condensate radius and pumping intensity. We show that multiply charged vortices in trapped nonconservative condensates become promising testbeds for analog gravity and for studying the fundamental physics of multiply charged vortices in quantum fluids.