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Dynamic evolution of spin-1 and spin-2 dipolar BECs

Konstantinos Tsekouras

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

This study investigates the dynamical evolution of spin-1 and spin-2 Bose-Einstein Condensates (BECs) when the dipolar interaction is taken into consideration. Using the Single-Mode Approximation (SMA) equations of motion are derived for each condensate component which are then numerically solved. The results convincingly show that the dipolar interaction has a significant effect despite being much weaker than the collision or spin-exchange interaction and that if included magnetic effects are easy to treat. Further, an analytical Mean-Field Theory formulation is used to derive and simplify equations of motion for a spin-1 BEC in 2D (pancake) configuration. Moving to a reference frame that rotates at the Larmor frequency greatly simplifies the equations and removes first-order Zeeman terms, rendering the effects of the dipolar interaction much clearer to observe in the condensate evolution.

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This study investigates the dynamical evolution of spin-1 and spin-2 Bose-Einstein Condensates (BECs) when the dipolar interaction is taken into consideration. Using the Single-Mode Approximation (SMA) equations of motion are derived for each condensate component which are then numerically solved. The results convincingly show that the dipolar interaction has a significant effect despite being much weaker than the collision or spin-exchange interaction and that if included magnetic effects are easy to treat. Further, an analytical Mean-Field Theory formulation is used to derive and simplify equations of motion for a spin-1 BEC in 2D (pancake) configuration. Moving to a reference frame that rotates at the Larmor frequency greatly simplifies the equations and removes first-order Zeeman terms, rendering the effects of the dipolar interaction much clearer to observe in the condensate evolution.
With current magnetic-field shielding and high-precision detection in dipolar spinor Bose-Einstein condensates, it is possible to experimentally detect the low- or zero-field nonsecular dipolar dynamics. Here we analytically investigate the zero-field nonsecular magnetic dipolar interaction effect, with an emphasis on magnetization dynamics in a spin-1 Bose-Einstein condensate under the single spatial mode approximation within the mean-field theory. Due to the biaxial nature of the dipolar interaction, a novel resonance occurs in the condensate magnetization oscillation, in contrast to the previous assumption of a conserved magnetization in strong magnetic fields. Furthermore, we propose a dynamical-decoupling detection method for such a resonance, which cancels the stray magnetic fields in experiment but restores the magnetization dynamics. Our results shed light on the dipolar systems and may find potential applications beyond cold atoms.
In order to uncover the effects of dipolar interaction on the magnetic properties of cold atom system,the ground state properties of dipolar spin-1,spin-2and binary mixed spin-1Bose-Einstein condensates(BEC)were studied.By treating field operator with mean field method and single model approximation,and minimizing the energy functional,the ground state phase diagrams were got.Then the diagrams with and without dipolar interaction were compared.The calculations show that under the dipole interaction,the degeneracy for ferromagnetic phases of spinor BEC is released and the boundaries between ferromagnetic and other phases are moved.The influence of dipole interaction on the spin-2alkali atoms is smaller than for spin-1alkali atoms in quantity and is analogous with binary mixed spin-1BEC qualitatively.The calculated quantities for every phase boundary provide reference for the related experiments.
The symmetry-breaking magnetization dynamics of a spin-1 Bose-Einstein condensate (BEC) due to the dipole-dipole interaction are investigated using the mean-field and Bogoliubov theories. When a magnetic field is applied along the symmetry axis of a pancake-shaped BEC in the m=0m=0m=0 hyperfine sublevel, transverse magnetization develops breaking the chiral or axial symmetry. A variety of magnetization patterns are formed depending on the strength of the applied magnetic field. The proposed phenomena can be observed in 87Rb^{87}\mathrm{Rb}87Rb and 23Na^{23}\mathrm{Na}23Na condensates.
We have numerically solved the low-energy excitation spectra of ferromagnetic Bose-Einstein condensates subject to dipolar interparticle interactions. The system is assumed to be harmonically confined by purely optical means, thereby maintaining the spin degree of freedom of the condensate order parameter. Using a zero-temperature spin-1 model, we solve the Bogoliubov excitations for different spin textures, including a spin-vortex state in the absence of external magnetic fields and a rapidly rotating polarized spin texture in a finite homogeneous field. In particular, we consider the effect of dipolar interactions on excitations characteristic of ferromagnetic condensates. The energies of spin waves and magnetic quadrupole modes are found to increase rapidly with the dipolar coupling strength, whereas the energies of density oscillations change only slightly.
In this paper, we study the dynamics of a single vortex and a corotating vortex pair in dipolar Bose-Einstein condensates under rotation.The results are obtained by numerically solving the nonlinear Gross-Pitaevskii equation.It is displayed that the dynamics behaviour is strongly dependent on the polarization angle and the rotation frequency.For a single vortex, the clockwise rotation occurs with an increasing rotation frequency, and the rotation direction is constant.The x coordinate and y coordinate as a function of time show that the single vortex is accelerated.The oscillation frequency is larger in the case of the totally repulsive dipolar interaction than for the anisotropic dipolar interaction.For a corotating vortex pair, the dynamic is different than in the case of a single vortex.When the rotation frequency is gradually increased, the corotating vortex pair spins from anti-clockwise to clockwise direction and the anisotropic dipolar interaction is fully embodied.In this process, the system has a critical rotation frequency to accomplish such transition.In addition, the vortex motion is confined to a small extent at this critical rotation frequency.These results reflect a competition between rotation and dipolar interaction.
In this paper, we study the dynamics properties of three-component antiferromagnetic dipolar Bose–Einstein condensates with external magnetic field. Our results are obtained by numerical simulations of the spinor Gross–Pitaevskii equation. We find that the population of the spin components is seriously influenced by magnetic field. The dynamical evolution process is accelerated in the presence of magnetic field. As a result, the periodic oscillation of spin exchange dynamics emerges and the components [Formula: see text] have the same amplitude. In addition, the density profile displays that the influences of dipolar interaction are masked by magnetic field. Moreover, we introduce an order parameter to characterize the disorder-order crossover, where it is seen that the system develops toward the disordered state with strong dipole strength when magnetic field is included.