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arXiv:cond-mat/9807250 · Physical Review A

Vortex stabilization in Bose-Einstein condensate of alkali-metal atom gas

Tomoya Isoshima, Kazushige Machida

Published Mar 1, 1999• 68 citations
arXivHTMLPDF

Abstract

A quantized vortex in Bose-Einstein condensation (BEC) of an alkali-metal atom gas is known to be unstable intrinsically at zero temperature. We examine two stabilization mechanisms of a vortex theoretically. (i) The finite temperature effect is shown to stabilize a vortex. (ii) An additional pinning potential, which may be produced by a focused laser beam at the vortex center, is also shown to stabilize it even at zero temperature. The mean-field calculation for BEC confined by a harmonic potential is employed. The detailed properties of a stable vortex are given, such as the spatial profiles of the condensate and noncondensate, the particle current density around the core, the whole excitation spectrum, and their temperature dependence.

DOI
10.1103/physreva.59.2203

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A quantized vortex in Bose-Einstein condensation (BEC) of an alkali-metal atom gas is known to be unstable intrinsically at zero temperature. We examine two stabilization mechanisms of a vortex theoretically. (i) The finite temperature effect is shown to stabilize a vortex. (ii) An additional pinning potential, which may be produced by a focused laser beam at the vortex center, is also shown to stabilize it even at zero temperature. The mean-field calculation for BEC confined by a harmonic potential is employed. The detailed properties of a stable vortex are given, such as the spatial profiles of the condensate and noncondensate, the particle current density around the core, the whole excitation spectrum, and their temperature dependence.
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.
The stability of a quantized vortex state in Bose-Einstein condensation is examined within Bogoliubov theory for alkali atom gases confined in a harmonic potential under forced rotation. By solving the non-linear Bogoliubov equations coupled with the Gross-Pitavskii equation, the elementary excitations and the total energy of the systems are calculated as a function of rotation velocity. There are two distinct criteria of vortex stability; The position of the excitation energy levels relative to the condensate energy level yields the local stability criterion, and the total energy relative to that of the non-vortex state yields the global stability criterion. The vortex stability phase diagram in the rotation velocity vs the particle density of the system is obtained, allowing one to locate the appropriate region to observe the singly quantized vortex.
Bose-Einstein condensation, first predicted by Bose and Einstein in 1924, was finally realized in dilute, weakly interacting gases of alkali atoms in 1995. A few years later, quantized vortices - intimately related to the phenomenon of superfluidity - were created and observed in these novel quantum many-body systems.\n\nIn this Thesis, vortices in dilute atomic Bose-Einstein condensates are studied theoretically and computationally using microscopic mean-field theory formalisms. Special emphasis is on the structure and the stability of vortices at finite temperatures. The formation of quantized circulation in Bose-Einstein condensates is investigated, as well as multiply quantized vorticity and the adiabaticity of the precessing motion of a vortex.\n\nThis research strongly relies on numerically solving the Gross-Pitaevskii equation for the macroscopic condensate wavefunction and the coupled Bogoliubov equations and their variants for the collective quasiparticle excitation eigenmodes. The computed elementary excitation spectra are used, for instance, in determining the local stability of various condensate states. The vortex formation process is studied at finite temperatures in terms of the surface modes of the condensate providing the Landau critical velocities for the breakdown of superfluidity. Free energy calculations are used for determining the thermodynamic equilibrium states.\n\nSingly quantized, axisymmetric vortex states are found to be locally energetically stable even in the zero-temperature limit within the self-consistent finite-temperature approximations. This would imply for the vortex a precession direction opposite to that observed in the experiment. Adiabatic approximation of quantum mechanics is formulated for Bose-Einstein condensed systems and is applied to a case of a moving vortex line. The experimentally observed precessing motion of the vortex is found to be nonadiabatic. A method to create stable multiply quantized vortices using an additional pinning potential is presented. The computed critical trap rotation frequencies for vortex nucleation at finite temperatures are in agreement with experiments and the predictions of zero-temperature field theories.
Characteristic features in phases of Bose-Einstein condensations (BEC) for systems of two-components in gas phases of Alkali-metal atoms trapped by harmonic potentials are discussed on the basis of numerical calculations by the use of Gross-Pitaevskii equation. Condensations with and without vortices are considered in order to make clear spatial distributions. The shape of spatial distribution is essentially dependent on the ratio of interaction strengths between intra-components and inter-components. We emphasize the possibility of coexistence of vortex-free state (where the angular momentum ℓ is 0.) for the one component in BEC and vortex state (ℓ z =1) for another component whose shape is the donut-like spatial distribution. Furthermore, fluctuations of these states are discussed. In partiucular, we concentrate our attention to the appearance of the core modes with ℓ z =0 symmetry for the component with a vortex. In connection with the behavior of the core modes, the contribution of the component without a vortex to the stability of the above vortex is discussed on the basis of numerical calculation.
Since the first realizations of Bose-Einstein condensation in dilute alkali-atom vapours in 1995, these novel quantum gases have attracted wide interest. The main focus of the research has been on finding out the coherence and superfluidity properties of the condensates. From the theoretical point of view, these systems provide a rare possibility to model an interacting many-particle system exhaustively and quantitatively accurately from first-principles quantum field theories. However, the challenge of developing a correct and computationally feasible finite-temperature formalism still remains.\n\nThe coherence and superfluidity properties are intimately related to the existence and stability of quantized vortices. In this thesis, the structure and stability of vortex states in weakly interacting Bose-Einstein condensates is investigated within microscopic finite-temperature mean-field theories. An effective scheme for computationally solving the Bogoliubov-de Gennes quasiparticle eigenequations is developed, and applied to study the microscopic structure of vortex states in partially condensed vapours. In contrast to experimental observations and the predictions of the zero-temperature Bogoliubov approximation, stationary vortex states are found to be metastable within the self-consistent Popov approximation and its extensions even in the zero-temperature limit.\n\nThe reasons underlying this discrepancy are analysed in detail. A criterion for the validity of stationary mean-field approximations in modelling slowly time-dependent systems is derived, and applied to precessing off-axis vortex states. Under typical experimental conditions moving vortices are shown to be deformed due to the inability of the thermal cloud to follow the vortex core rigidly. Consequently, the validity of the commonly used stationary mean-field theories in describing such states is shown to be questionable. Finally, an analysis of uniformly precessing off-axis vortex states within a fully time-dependent Popov approximation is presented. Even dynamically deformed vortices are shown to become energetically metastable as the vortex core is partially filled with noncondensed gas in the course of thermalization. This self-stabilization mechanism of vortex states, shown to occur under very general circumstances, is an inherent property of all self-consistent formalisms having a structure similar to the Popov approximation. However, it is argued to be affected by the improper treatment of the noncondensate dynamics within these formalisms, and the need for a theory taking properly into account the coupled dynamics of the condensate and the noncondensate in modelling vortex states is emphasized. The computational scheme developed is also applied to investigate possibilities to energetically stabilize multiply quantized vortex states by piercing an externally rotated condensate with a blue-detuned laser beam.
We consider the intrinsic stability of the vortex states of a pure Bose-Einstein condensate confined in a harmonic potential under the effects of a coherent atom-atom interaction. We find that stable vortices can be supported and vortex stability can be controlled by changing the interparticle interaction strength. At unstable regimes, a vortex will spontaneously disintegrate into states with different angular momenta even without external perturbations, with the lifetime determined by its imaginary excitation frequencies.