A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional trap can be described with the lowest Landau-level set of states. In this case, the condensate wave function $\ensuremath{\psi}(x,y)$ is a Gaussian function of ${r}^{2}={x}^{2}+{y}^{2}$ , multiplied by an analytic function $P(z)$ of the single complex variable $z=x+iy$ ; the zeros of $P(z)$ denote the positions of the vortices. Here, a similar description is used for a rapidly rotating anisotropic two-dimensional trap with arbitrary anisotropy $({\ensuremath{\omega}}_{x}∕{\ensuremath{\omega}}_{y}\ensuremath{\leqslant}1)$. The corresponding condensate wave function $\ensuremath{\psi}(x,y)$ has the form of a complex anisotropic Gaussian with a phase proportional to $xy$ , multiplied by an analytic function $P(\ensuremath{\zeta})$, where $\ensuremath{\zeta}\ensuremath{\propto}x+i{\ensuremath{\beta}}_{\ensuremath{-}}y$ and $0\ensuremath{\leqslant}{\ensuremath{\beta}}_{\ensuremath{-}}\ensuremath{\leqslant}1$ is a real parameter that depends on the trap anisotropy and the rotation frequency. The zeros of $P(\ensuremath{\zeta})$ again fix the locations of the vortices. Within the set of lowest Landau-level states at zero temperature, an anisotropic parabolic density profile provides an absolute minimum for the energy, with the vortex density decreasing slowly and anisotropically away from the trap center.A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional trap can be described with the lowest Landau-level set of states. In this case, the condensate wave function $\ensuremath{\psi}(x,y)$ is a Gaussian function of ${r}^{2}={x}^{2}+{y}^{2}$, multiplied by an analytic function $P(z)$ of the single complex variable $z=x+iy$; the zeros of $P(z)$ denote the positions of the vortices. Here, a similar description is used for a rapidly rotating anisotropic two-dimensional trap with arbitrary anisotropy $({\ensuremath{\omega}}_{x}∕{\ensuremath{\omega}}_{y}\ensuremath{\leqslant}1)$. The corresponding condensate wave function $\ensuremath{\psi}(x,y)$ has the form of a complex anisotropic Gaussian with a phase proportional to $xy$, multiplied by an analytic function $P(\ensuremath{\zeta})$, where $\ensuremath{\zeta}\ensuremath{\propto}x+i{\ensuremath{\beta}}_{\ensuremath{-}}y$ and $0\ensuremath{\leqslant}{\ensuremath{\beta}}_{\ensuremath{-}}\ensuremath{\leqslant}1$ is a real parameter that depends on the trap anisotropy and the rotation frequency. The zeros of $P(\ensuremath{\zeta})$ again fix the locations of the vortices. Within the set of lowest Landau-level states at zero temperature, an anisotropic parabolic density profile provides an absolute minimum for the energy, with the vortex density decreasing slowly and anisotropically away from the trap center.

arXiv:cond-mat/0609484Physical Review AJan 18, 200745 citations

Rotating Fermi gases in an anharmonic trap

Kiel Howe, Aristeu R. P. Lima, Axel Pelster

arXiv:0810.4983The European Physical Journal DJun 17, 200915 citations

Optical centrifuge for nanoparticles

Peiyao Xiong, Ka Kit Kelvin Ho, Jonathan M. H. Gosling +2 more

We study theoretically the creation of an optical centrifuge for the controlled rotation of levitated nanorotors within an optical tweezer. The optical centrifuge's motion is simulated by rapidly rotating the linear polarization of the tightly focused optical field used to form an optical trap. We show that nanorotors, formed by anisotropic nanoparticles levitated within a trap, can be accelerated to well-defined rotational rates in excess of 100 MHz over durations of hundreds of microseconds. The initial conditions required for stable acceleration, based on optical trap properties and the anisotropic susceptibility of the nanorotor are established and confirmed by numerical simulations. We also present initial experiments that have developed tools for the rapid angular acceleration of the polarization vector of the linearly polarized beam that is required to create the centrifuge. We show that over acceleration durations in the 100 μ s range, high rotational speeds could be achieved in modest vacuum.We study theoretically the creation of an optical centrifuge for the controlled rotation of levitated nanorotors within an optical tweezer. The optical centrifuge's motion is simulated by rapidly rotating the linear polarization of the tightly focused optical field used to form an optical trap. We show that nanorotors, formed by anisotropic nanoparticles levitated within a trap, can be accelerated to well-defined rotational rates in excess of 100 MHz over durations of hundreds of microseconds. The initial conditions required for stable acceleration, based on optical trap properties and the anisotropic susceptibility of the nanorotor are established and confirmed by numerical simulations. We also present initial experiments that have developed tools for the rapid angular acceleration of the polarization vector of the linearly polarized beam that is required to create the centrifuge. We show that over acceleration durations in the 100 μ s range, high rotational speeds could be achieved in modest vacuum.

arXiv:2506.16134Physical Review ResearchNov 21, 20251 citation

Vortex structures of rotating Bose-Einstein condensates in an anisotropic harmonic potential

Sergey I. Matveenko

We found an analytical solution for the vortex structure in a rapidly rotating trapped Bose-Einstein condensate in the lowest Landau level approximation. This solution is exact in the limit of a large number of vortices and is obtained for the case of a condensate in a anisotropic harmonic potential. The solution describes as limiting cases both a triangle vortex lattice in the symmetric potential trap and a quasi-one-dimensional structure of vortex rows in an asymmetric case, when the rotation frequency is very close to the lower trapping potential frequency. The shape of the density profile is found to be close to the Thomas-Fermi inverted paraboloid form, except in the vicinity of edges of a condensate cloud.We found an analytical solution for the vortex structure in a rapidly rotating trapped Bose-Einstein condensate in the lowest Landau level approximation. This solution is exact in the limit of a large number of vortices and is obtained for the case of a condensate in a anisotropic harmonic potential. The solution describes as limiting cases both a triangle vortex lattice in the symmetric potential trap and a quasi-one-dimensional structure of vortex rows in an asymmetric case, when the rotation frequency is very close to the lower trapping potential frequency. The shape of the density profile is found to be close to the Thomas-Fermi inverted paraboloid form, except in the vicinity of edges of a condensate cloud.

arXiv:1004.3896Physical Review ASep 30, 20105 citations

{r}^{2}={x}^{2}+{y}^{2}

, multiplied by an analytic function

P(z)

of the single complex variable

z=x+iy

; the zeros of

P(z)

denote the positions of the vortices. Here, a similar description is used for a rapidly rotating anisotropic two-dimensional trap with arbitrary anisotropy $({\ensuremath{\omega}}_{x}∕{\ensuremath{\omega}}_{y}\ensuremath{\leqslant}1)$. The corresponding condensate wave function $\ensuremath{\psi}(x,y)$ has the form of a complex anisotropic Gaussian with a phase proportional to

xy

, multiplied by an analytic function $P(\ensuremath{\zeta})$, where $\ensuremath{\zeta}\ensuremath{\propto}x+i{\ensuremath{\beta}}_{\ensuremath{-}}y$ and $0\ensuremath{\leqslant}{\ensuremath{\beta}}_{\ensuremath{-}}\ensuremath{\leqslant}1$ is a real parameter that depends on the trap anisotropy and the rotation frequency. The zeros of $P(\ensuremath{\zeta})$ again fix the locations of the vortices. Within the set of lowest Landau-level states at zero temperature, an anisotropic parabolic density profile provides an absolute minimum for the energy, with the vortex density decreasing slowly and anisotropically away from the trap center.