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arXiv:cond-mat/9903002 · Physical Review A

Instability of the nonvortex state toward a quantized vortex in a Bose-Einstein condensate under external rotation

Tomoya Isoshima, Kazushige Machida

Published Oct 1, 1999• 61 citations
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Abstract

The instability condition of the nonvortex state toward vortex formation is examined within the Bogoliubov theory when a Bose-Einstein condensate is under externally forced rotation. The obtained critical angular velocity combined with the previous stability conditions for a vortex yields a detailed phase diagram in the critical velocity vs the system parameter. This facilitates vortex formation experiments for alkali-metal-atom gases confined in a harmonic potential.

DOI
10.1103/physreva.60.3313

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•Jan 10, 2003•0 citations
The instability condition of the nonvortex state toward vortex formation is examined within the Bogoliubov theory when a Bose-Einstein condensate is under externally forced rotation. The obtained critical angular velocity combined with the previous stability conditions for a vortex yields a detailed phase diagram in the critical velocity vs the system parameter. This facilitates vortex formation experiments for alkali-metal-atom gases confined in a harmonic potential.
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.
The vortex phase diagram in the external rotation frequency versus temperature is calculated for dilute Bose-Einstein condensed gases. It is determined within the Bogoliubov-Popov theory for a finite temperature where the condensate and noncondensate fractions are treated on an equal footing. The temperature dependences of various thermodynamic instability lines for the vortex nucleation are computed to construct the phase diagram. Experiments are proposed to resolve a recent controversy on the vortex creation problem associated with the quantized vortex observation in 87Rb{}^{87}\mathrm{Rb}87Rb atom gases.
Multiply quantized vortices in trapped Bose-Einstein condensates are studied using the Bogoliubov theory. Suitable combinations of a localized pinning potential and an external rotation of the system are found to energetically stabilize, both locally and globally, vortices with multiple circulation quanta. We present a phase diagram for stable multiply quantized vortices in terms of the angular rotation frequency of the system and the width of the pinning potential. We argue that multiquantum vortices could be experimentally created using a suitable choice of these two parameters.
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.
The relative stability of various axisymmetric vortices in a spinor Bose-Einstein condensate with F=1F=1F=1 is examined within extended Bogoliubov theory. This yields the phase diagram in the plane of external rotation frequency vs magnetization. We compare antiferromagnetic, nonmagnetic, and ferromagnetic cases. The excitation spectrum is evaluated under rotation to investigate the local stability of the possible vortices and the vortex nucleation frequency.
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.