Vortex core structure and global properties of rapidly rotating Bose-Einstein condensates
Vortex core structure and global properties of rapidly rotating Bose-Einstein condensates
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DOI：
10.1103/physreva.69.043619
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发表时间：
2003-08
影响因子：
2.9
通讯作者：
G. Baym;C. Pethick
中科院分区：
文献类型：
--
作者：
G. Baym;C. Pethick
We develop an approach for calculating stationary states of rotating Bose-Einstein condensates in harmonic traps which is applicable for arbitrary ratios of the rotation frequency to the transverse frequency of the trap ${\ensuremath{\omega}}_{\ensuremath{\perp}}$. Assuming the number of vortices to be large, we write the condensate wave function as the product of a function that describes the structure of individual vortices times an envelope function varying slowly on the scale of the vortex spacing. By minimizing the energy, we derive Gross-Pitaevskii equations that determine the properties of individual vortices and the global structure of the cloud. For low rotation rates, the structure of a vortex is that of an isolated vortex in a uniform medium, while for rotation rates approaching the frequency of the trap (the mean-field lowest-Landau-level regime), the structure is that of the lowest $p$-wave state of a particle in a harmonic trap with frequency ${\ensuremath{\omega}}_{\ensuremath{\perp}}$. The global structure of the cloud is determined by minimizing the energy with respect to variations of the envelope function; for conditions appropriate to most experimental investigations to date, we predict that the transverse density profile of the cloud will be of the Thomas-Fermi form, rather than the Gaussian structure predicted on the assumption that the wave function consists only of components in the lowest Landau level for a regular array of vortices.
We develop an approach for calculating stationary states of rotating Bose-Einstein condensates in harmonic traps which is applicable for arbitrary ratios of the rotation frequency to the transverse frequency of the trap ${\ensuremath{\omega}}_{\ensuremath{\perp}}$. Assuming the number of vortices to be large, we write the condensate wave function as the product of a function that describes the structure of individual vortices times an envelope function varying slowly on the scale of the vortex spacing. By minimizing the energy, we derive Gross-Pitaevskii equations that determine the properties of individual vortices and the global structure of the cloud. For low rotation rates, the structure of a vortex is that of an isolated vortex in a uniform medium, while for rotation rates approaching the frequency of the trap (the mean-field lowest-Landau-level regime), the structure is that of the lowest $p$-wave state of a particle in a harmonic trap with frequency ${\ensuremath{\omega}}_{\ensuremath{\perp}}$. The global structure of the cloud is determined by minimizing the energy with respect to variations of the envelope function; for conditions appropriate to most experimental investigations to date, we predict that the transverse density profile of the cloud will be of the Thomas-Fermi form, rather than the Gaussian structure predicted on the assumption that the wave function consists only of components in the lowest Landau level for a regular array of vortices.