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Acta Physica Sinica

Noncanonical vortex states and dynamics in Bose-Einstein condensates

Jian-Chong Xing, Wen-Jing Zhang, Tao Yang

Published Jan 1, 2023• 1 citation
Publisher

Abstract

Vortex excitations triggered by nonlinear interactions in Bose-Einstein condensates have attracted interest in the study of ultracold atoms. However, most studies focus on canonical vortex states with integer topological charges. In this paper, we study the dynamic properties of noncanonical vortex condensates with three phase distributions: power-exponent, new type power-exponent and oscillation type. The results show that the noncanonical vortices are dynamic unstable and their density distributions obviously depend on the phase parameters of the initial optical phase masks. Different noncanonical vortices decay into canonical clusters with diverse configurations showing rich topological excitation patterns. In particular, a new power exponential noncanonical vortex state decays into a stable canonical polygonal vortex cluster structure. Because the phase structures of the noncanonical optical vortices destroy the rotational symmetry of the condensate, the angular momentum of the condensate is no longer quantized, and its value changes with the power of the azimuthal angle of the optical field or the oscillation frequency, which is obviously different from the evolution of the corresponding noncanonical vortex optical field itself. In the dynamical process, the center-of-mass trajectory of noncanonical vortex condensates with the new type of power exponent phase is always a point, while for the noncanonical vortex condensates with power exponent and oscillating phase, the center-of-mass trajectories are ellipses centering at the origin of coordinates.

DOI
10.7498/aps.72.20222289

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Vortex excitations triggered by nonlinear interactions in Bose-Einstein condensates have attracted interest in the study of ultracold atoms. However, most studies focus on canonical vortex states with integer topological charges. In this paper, we study the dynamic properties of noncanonical vortex condensates with three phase distributions: power-exponent, new type power-exponent and oscillation type. The results show that the noncanonical vortices are dynamic unstable and their density distributions obviously depend on the phase parameters of the initial optical phase masks. Different noncanonical vortices decay into canonical clusters with diverse configurations showing rich topological excitation patterns. In particular, a new power exponential noncanonical vortex state decays into a stable canonical polygonal vortex cluster structure. Because the phase structures of the noncanonical optical vortices destroy the rotational symmetry of the condensate, the angular momentum of the condensate is no longer quantized, and its value changes with the power of the azimuthal angle of the optical field or the oscillation frequency, which is obviously different from the evolution of the corresponding noncanonical vortex optical field itself. In the dynamical process, the center-of-mass trajectory of noncanonical vortex condensates with the new type of power exponent phase is always a point, while for the noncanonical vortex condensates with power exponent and oscillating phase, the center-of-mass trajectories are ellipses centering at the origin of coordinates.
We study stationary clusters of vortices and antivortices in dilute pancake-shaped Bose-Einstein condensates confined in nonrotating harmonic traps. Previous theoretical results on the stability properties of these topologically nontrivial excited states are seemingly contradicting. We clarify this situation by a systematic stability analysis. The energetic and dynamic stability of the clusters is determined from the corresponding elementary excitation spectra obtained by solving the Bogoliubov equations. Furthermore, we study the temporal evolution of the dynamically unstable clusters. The stability of the clusters and the characteristics of their destabilizing modes only depend on the effective strength of the interactions between particles and the trap anisotropy. For certain values of these parameters, there exist several dynamical instabilities, but we show that there are also regions in which some of the clusters are dynamically stable. Moreover, we observe that the dynamical instability of the clusters does not always imply their structural instability, and that for some dynamically unstable states annihilation of the vortices is followed by their regeneration, and revival of the cluster.
We review the topic of quantized vortices in multicomponent Bose–Einstein condensates of dilute atomic gases, with an emphasis on the two-component condensates. First, we review the fundamental structure, stability and dynamics of a single vortex state in a slowly rotating two-component condensates. To understand recent experimental results, we use the coupled Gross–Pitaevskii equations and the generalized nonlinear sigma model. An axisymmetric vortex state, which was observed by the JILA group, can be regarded as a topologically trivial skyrmion in the pseudospin representation. The internal, coherent coupling between the two components breaks the axisymmetry of the vortex state, resulting in a stable vortex molecule (a meron pair). We also mention unconventional vortex states and monopole excitations in a spin-1 Bose–Einstein condensate. Next, we discuss a rich variety of vortex states realized in rapidly rotating two-component Bose–Einstein condensates. We introduce a phase diagram with axes of rotation frequency and the intercomponent coupling strength. This phase diagram reveals unconventional vortex states such as a square lattice, a double-core lattice, vortex stripes and vortex sheets, all of which are in an experimentally accessible parameter regime. The coherent coupling leads to an effective attractive interaction between two components, providing not only a promising candidate to tune the intercomponent interaction to study the rich vortex phases but also a new regime to explore vortex states consisting of vortex molecules characterized by anisotropic vorticity. A recent experiment by the JILA group vindicated the formation of a square vortex lattice in this system.
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.
It has been demonstrated experimentally that non-axisymmetric vortices precess around the center of a Bose-Einstein condensate. Two types of single vortex states have been observed, usually referred to as the S vortex and the U vortex. We study theoretically the single vortex excitations in spherical and elongated condensates as a function of the interaction strength. We solve numerically the Gross-Pitaevskii equation and calculate the angular momentum as a function of precession frequency. The existence of two types of vortices means that we have two different precession frequencies for each angular momentum value. As the interaction strength increases the vortex lines bend and the precession frequencies shift to lower values. We establish that for given angular momentum the S vortex has higher energy than the U vortex in a rotating elongated condensate. We show that the S vortex is related to the solitonic vortex, which is a nonlinear excitation in the nonrotating system. For small interaction strengths the S vortex is related to the dark soliton. In the dilute limit a lowest Landau level calculation provides an analytic description of these vortex modes in terms of the harmonic oscillator states.
We study the energetic and dynamic stability of coreless vortices in nonrotated spin-1 Bose-Einstein condensates, trapped with a three-dimensional optical potential and a Ioffe-Pritchard field. The stability of stationary vortex states is investigated by solving the corresponding Bogoliubov equations. We show that the quasiparticle excitations corresponding to axisymmetric stationary states can be taken to be eigenstates of angular momentum in the axial direction. Our results show that coreless vortex states can occur as local or global minima of the condensate energy or become energetically or dynamically unstable depending on the parameters of the Ioffe-Pritchard field. The experimentally most relevant coreless vortex state containing a doubly quantized vortex in one of the hyperfine spin components turned out to have very nontrivial stability regions, and especially a quasiperiodic dynamic instability region which corresponds to splitting of the doubly quantized vortex.
In this review, we give an overview of the experimental and theoretical advances in the physics of quantized vortices in dilute atomic-gas Bose--Einstein condensates in a trapping potential, especially focusing on experimental research activities and their theoretical interpretations. Making good use of the atom optical technique, the experiments have revealed many novel structural and dynamic properties of quantized vortices by directly visualizing vortex cores from an image of the density profiles. These results lead to a deep understanding of superfluid hydrodynamics of such systems. Typically, vortices are stabilized by a rotating potential created by a laser beam, magnetic field, and thermal gas. Finite size effects and inhomogeneity of the system, originating from the confinement by the trapping potential, yield unique vortex dynamics coupled with the collective excitations of the condensate. Measuring the frequencies of the collective modes is an accurate tool for clarifying the character of the vortex state. The topics included in this review are the mechanism of vortex formation, equilibrium properties, and dynamics of a single vortex and those of a vortex lattice in a rapidly rotating condensate.