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arXiv:1010.1643 · Physical Review A

Ground states of trapped spin-1 condensates in magnetic field

Michał Matuszewski

Published Nov 24, 2010• 23 citations
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Abstract

We consider a spin-1 Bose-Einstein condensate trapped in a harmonic potential under the influence of a homogeneous magnetic field. We investigate spatial and spin structure of the mean-field ground states under constraints on the number of atoms and the total magnetization. We show that the trapping potential can make the antiferromagnetic condensate separate into three distinct phases and ferromagnetic condensate into two distinct phases. In the ferromagnetic case, the magnetization is located in the center of the harmonic trap, while in the antiferromagnetic case magnetized phases appear in the outer regions. We describe how the transition from the Thomas-Fermi regime to the single-mode approximation regime with decreasing number of atoms results in the disappearance of the domains. We suggest that the ground states can be created in experiment by adiabatically changing the magnetic-field strength.

DOI
10.1103/physreva.82.053630

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We consider a spin-1 Bose-Einstein condensate trapped in a harmonic potential under the influence of a homogeneous magnetic field. We investigate spatial and spin structure of the mean-field ground states under constraints on the number of atoms and the total magnetization. We show that the trapping potential can make the antiferromagnetic condensate separate into three distinct phases and ferromagnetic condensate into two distinct phases. In the ferromagnetic case, the magnetization is located in the center of the harmonic trap, while in the antiferromagnetic case magnetized phases appear in the outer regions. We describe how the transition from the Thomas-Fermi regime to the single-mode approximation regime with decreasing number of atoms results in the disappearance of the domains. We suggest that the ground states can be created in experiment by adiabatically changing the magnetic-field strength.
We discuss the structure of spin-1 Bose-Einstein condensates in the presence of a homogenous magnetic field. We demonstrate that phase separation can occur in the ground state of antiferromagnetic (polar) condensates, while the spin components of ferromagnetic condensates are always miscible, so that no phase separation occurs in them. Our analysis predicts that this phenomenon takes place when the energy of the lowest homogenous state is a concave function of the magnetization. We propose a method for creating spin domains by adiabatic switching-on of a magnetic field. We also discuss the phenomena of dynamical instability and spin domain formation.
We analyze the structure of spin-one Bose-Einstein condensates in the presence of a homogeneous magnetic field. We classify the homogeneous stationary states and study their existence, bifurcations, and energy spectra. We reveal that phase separation can occur in the ground state of antiferromagnetic (polar) condensates while the spin components of the ferromagnetic condensates are always miscible and no phase separation occurs. Our theoretical model, confirmed by numerical simulations, explains that this phenomenon takes place when the energy of the lowest homogeneous state is a concave function of the magnetization. In particular, we predict that phase separation can be observed in a 23Na^{23}\text{N}\text{a}23Na condensate confined in a highly elongated harmonic trap. Finally, we discuss the phenomena of dynamical instability and spin domain formation.
In the presence of a magnetic field, multicomponent ground states appear in trapped spin-1 Bose-Einstein condensates for both ferromagnetic and antiferromagnetic types of spin-spin interaction. We aim to produce an accurate analytical description of the multicomponent states which is of fundamental importance. Despite being in the so-called regime of the Thomas-Fermi approximation (condensates with large particle number), the scenario of multicomponent states is problematic under this approximation due to the large variation in densities of the subcomponents. We generalize the variational method that we have introduced [P. K. Kanjilal and A. Bhattacharyay, Eur. Phys. J. Plus 137, 547 (2022)] to overcome the limitations of the Thomas-Fermi approximation. We demonstrate that the variational method is crucial in identifying multicomponent ground states. A comparison of the results of the variational method, which is multimodal by construction, with that of the single-mode approximation is also presented in this paper to demonstrate a marked improvement in accuracy over the single-mode approximation. We have also looked into the phase transition between phase-matched and polar states in a trapped condensate using the variational method and have identified substantial change in the phase boundary. The correspondence of the phase diagram of the trapped case with the homogeneous one identifies other limitations of the Thomas-Fermi approximation as opposed to the more accurate variational method.
Abstract Investigation of ground state structures and phase separation under confinement is of great interest in spinor Bose–Einstein condensates. In this paper we show that, in general, within the Thomas–Fermi approximation, the phase separation scenario of stationary states can be obtained including all the mixed states on an equal footing for a spin-1 condensate under any confinement. According to the process used here, the density of each and every stationary states can be determined exactly in terms of the system parameters. This allows to write the expression for energy density of all states in a form which are not an explicit function of densities of those states. An energy density comparison therefore, among all the allowed stationary states can be done which will reveal domain structures depending on the system parameters. We study here, in details, a particular case of spherically symmetric harmonic confinement as an example and show a wide range of potential phase separation scenario for anti-ferromagnetic and ferromagnetic interactions.
We have calculated the F=1 ground state of a spinor Bose-Einstein condensate trapped harmonic potential with an applied Ioffe-Pitchard magnetic field. The vortex phase diagram is found in the plane spanned by perpendicular and longitudinal magnetic fields. The ferromagnetic condensate has two vortex phases which differ by winding number in the spinor components. The two vortices for the F(z)=-1 antiferromagnetic condensate are separated in space. Moreover, we considered an average local spin |<S-->>| to testify to what extent it is parallel to magnetic field (the nonadiabatic effects). We have shown that the effects are important at vortex cores.
A hydrodynamic description is used to study the zero-temperature properties of a trapped spinor Bose-Einstein condensate in the presence of a uniform magnetic field. We show that, in the case of antiferromagnetic spin-spin interaction, the polar and ferromagnetic configurations of the ground state can coexist in the trap. These two phases are spatially segregated in such a way that the polar state occupies the inner part while the ferromagnetic state occupies the outer part of the atomic cloud. We also derive a set of coupled hydrodynamic equations for the number density and spin density excitations of the system. It is shown that these equations can be analytically solved for the system in an isotropic harmonic trap and a constant magnetic field. Remarkably, the related low lying excitation spectra are completely determined by the solutions in the region occupied by the polar state. We find that, within the Thomas-Fermi approximation, the presence of a constant magnetic field does not change the excitation spectra which still possess the similar form of that obtained by Stringari.