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arXiv:cond-mat/0511160 · Physical Review A

Critical frequency for vortex nucleation in Bose-Fermi mixtures in optical lattices

M. Guilleumas, M. Centelles, M. Barranco, R. Mayol, Martí Pi

Published Nov 3, 2005• 3 citations
arXivHTMLPDF

Abstract

We investigate within mean-field theory the influence of a one-dimensional optical lattice and of trapped degenerate fermions on the critical rotational frequency for vortex line creation in a Bose-Einstein condensate. We consider laser intensities of the lattice such that quantum coherence across the condensate is ensured. We find a sizable decrease of the thermodynamic critical frequency for vortex nucleation with increasing applied laser strength and suggest suitable parameters for experimental observation. Since $^{87}\mathrm{Rb}\ensuremath{-}^{40}\mathrm{K}$ mixtures may undergo collapse, we analyze the related question of how the optical lattice affects the mechanical stability of the system.

DOI
10.1103/physreva.72.053602

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We investigate within mean-field theory the influence of a one-dimensional optical lattice and of trapped degenerate fermions on the critical rotational frequency for vortex line creation in a Bose-Einstein condensate. We consider laser intensities of the lattice such that quantum coherence across the condensate is ensured. We find a sizable decrease of the thermodynamic critical frequency for vortex nucleation with increasing applied laser strength and suggest suitable parameters for experimental observation. Since 87Rb\ensuremath−40K^{87}\mathrm{Rb}\ensuremath{-}^{40}\mathrm{K}87Rb\ensuremath−40K mixtures may undergo collapse, we analyze the related question of how the optical lattice affects the mechanical stability of the system.
Using mean field theory, we have studied Bose-Fermi mixtures in a one-dimensional optical lattice in the case of an attractive boson-fermion interaction. We consider that the fermions are in the degenerate regime and that the laser intensities are such that quantum coherence across the condensate is ensured. We discuss the effect of the optical lattice on the critical rotational frequency for vortex line creation in the Bose-Einstein condensate, as well as how it affects the stability of the boson-fermion mixture. A reduction of the critical frequency for nucleating a vortex is observed as the strength of the applied laser is increased. The onset of instability of the mixture occurs for a sizably lower number of fermions in the presence of a deep optical lattice.
We report the observation of vortex nucleation in a rotating optical lattice. A 87Rb Bose-Einstein condensate was loaded into a static two-dimensional lattice and the rotation frequency of the lattice was then increased from zero. We studied how vortex nucleation depended on optical lattice depth and rotation frequency. For deep lattices above the chemical potential of the condensate we observed a linear dependence of the number of vortices created with the rotation frequency, even below the thermodynamic critical frequency required for vortex nucleation. At these lattice depths the system formed an array of Josephson-coupled condensates. The effective magnetic field produced by rotation introduced characteristic relative phases between neighboring condensates, such that vortices were observed upon ramping down the lattice depth and recombining the condensates.
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.
In this paper we suggest a convenient quantum statistical approach to calculate the critical rotation frequency for vortex nucleation in a rotating condensate boson atoms. We extende the quantum mecanices approach for achieving the critical rotation rate to enclode the effect of finite temperature. Dependence of the critical rotation on the interatomic interaction, atoms number and temperature is considered. A simple semiclassical approach is suggested. The calculated results showed that the critical rotation rate α depending crucially on the above mensioned parameters, its change very rapidly at very low temperature. Which means that the vortical configuration is achieved for an accurate rotation rate value α, depends on temperature, interatomic interaction and number of condensate atoms. The obtained results provide useful qualitative theoretical results for future Bose Einstein condensation experiments in rotating traps. Motivated by our work, it will be interesting to study the critical rotation for vortex nucleation of rotating condensate boson atoms in optical lattice.
We give an overview on our current experiments with Bose-Fermi degenerate mixtures in a one dimensional (ID) optical lattice. Our system consists of a Fermi gas of 40 K atoms and a Bose-Einstein condensate of 87 Rb. The two species are simultaneously trapped in a combined magnetic and optical lattice potential. We have investigated the thermodynamical properties of the mixture in a tight lattice and observed a change in the density of states. This is a signature of a quasi two dimensional confinement of the atoms in the lattice sites. We also discuss the mechanical stability of the mixture in presence of the 1D lattice.
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 sss-wave scattering lengths through the strength of nonlinear rotation, C\mathit{C}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.