We study the dynamics of vortex nucleation and lattice formation in a Bose--Einstein condensate in a rotating square optical lattice by numerical simulations of the Gross--Pitaevskii equation. Different dynamical regimes of vortex nucleation are found, depending on the depth and period of the optical lattice. We make an extensive comparison with the experiments by R. A. Williams et al. [Phys. Rev. Lett. 104, 050404 (2010)], especially focusing on the issues of the critical rotation frequency for the first vortex nucleation and the vortex number as a function of rotation frequency.We study the dynamics of vortex nucleation and lattice formation in a Bose--Einstein condensate in a rotating square optical lattice by numerical simulations of the Gross--Pitaevskii equation. Different dynamical regimes of vortex nucleation are found, depending on the depth and period of the optical lattice. We make an extensive comparison with the experiments by R. A. Williams et al. [Phys. Rev. Lett. 104, 050404 (2010)], especially focusing on the issues of the critical rotation frequency for the first vortex nucleation and the vortex number as a function of rotation frequency.

arXiv:1108.1857Physical Review ANov 18, 201126 citations

Vortex nucleation in rotating Bose-Einstein condensates with density-dependent gauge potential

Ishfaq Ahmad Bhat, Thudiyangal Mithun, Bishwajyoti Dey

We study numerically the vortex dynamics and vortex-lattice formation in a rotating density-dependent Bose-Einstein condensate (BEC), characterized by the presence of nonlinear rotation. By varying the strength of nonlinear rotation in density-dependent BECs, we calculate the critical frequency, ${\mathrm{\ensuremath{\Omega}}}_{\text{cr}}$, for vortex nucleation both in adiabatic and sudden external trap rotations. The nonlinear rotation modifies the extent of deformation experienced by the BEC due to the trap and shifts the ${\mathrm{\ensuremath{\Omega}}}_{\text{cr}}$ values for vortex nucleation. The critical frequencies, and thereby the transition to vortex-lattices in an adiabatic rotation ramp, depend on conventional $s$ -wave scattering lengths through the strength of nonlinear rotation, $\mathit{C}$ , such that ${\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}>0)<{\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}=0)<{\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}<0)$. In an analogous manner, the critical ellipticity (${\ensuremath{\epsilon}}_{\text{cr}}$) for vortex nucleation during an adiabatic introduction of trap ellipticity ($\ensuremath{\epsilon}$) depends on the nature of nonlinear rotation besides trap rotation frequency. The nonlinear rotation additionally affects the vortex-vortex interactions and the motion of the vortices through the condensate by altering the strength of Magnus force on them. The combined result of these nonlinear effects is the formation of the non-Abrikosov vortex-lattices and ring-vortex arrangements in the density-dependent BECs.We study numerically the vortex dynamics and vortex-lattice formation in a rotating density-dependent Bose-Einstein condensate (BEC), characterized by the presence of nonlinear rotation. By varying the strength of nonlinear rotation in density-dependent BECs, we calculate the critical frequency, ${\mathrm{\ensuremath{\Omega}}}_{\text{cr}}$, for vortex nucleation both in adiabatic and sudden external trap rotations. The nonlinear rotation modifies the extent of deformation experienced by the BEC due to the trap and shifts the ${\mathrm{\ensuremath{\Omega}}}_{\text{cr}}$ values for vortex nucleation. The critical frequencies, and thereby the transition to vortex-lattices in an adiabatic rotation ramp, depend on conventional $s$-wave scattering lengths through the strength of nonlinear rotation, $\mathit{C}$, such that ${\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}>0)<{\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}=0)<{\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}<0)$. In an analogous manner, the critical ellipticity (${\ensuremath{\epsilon}}_{\text{cr}}$) for vortex nucleation during an adiabatic introduction of trap ellipticity ($\ensuremath{\epsilon}$) depends on the nature of nonlinear rotation besides trap rotation frequency. The nonlinear rotation additionally affects the vortex-vortex interactions and the motion of the vortices through the condensate by altering the strength of Magnus force on them. The combined result of these nonlinear effects is the formation of the non-Abrikosov vortex-lattices and ring-vortex arrangements in the density-dependent BECs.

arXiv:2304.06208Physical review. EApr 21, 20239 citations

Nucleation of vortices in a rotating Bose-Einstein condensate

Subhasis Sinha, Yvan Castin

Laser SpectroscopyJun 1, 20020 citations

Dynamics of vortex lattice formation in a rotating Bose–Einstein condensate

Makoto Tsubota, Kenichi Kasamatsu, Masahito Ueda

Physica B Condensed MatterMay 1, 20034 citations

s

-wave scattering lengths through the strength of nonlinear rotation,

\mathit{C}

, such that ${\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}>0)<{\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}=0)<{\mathrm{\ensuremath{\Omega}}}_{\text{cr}}(\mathit{C}<0)$. In an analogous manner, the critical ellipticity (${\ensuremath{\epsilon}}_{\text{cr}}$) for vortex nucleation during an adiabatic introduction of trap ellipticity ($\ensuremath{\epsilon}$) depends on the nature of nonlinear rotation besides trap rotation frequency. The nonlinear rotation additionally affects the vortex-vortex interactions and the motion of the vortices through the condensate by altering the strength of Magnus force on them. The combined result of these nonlinear effects is the formation of the non-Abrikosov vortex-lattices and ring-vortex arrangements in the density-dependent BECs.