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arXiv:0904.0086 · Physical Review A

Excited spin states and phase separation in spinor Bose-Einstein condensates

Michał Matuszewski, Tristram J. Alexander, Yuri S. Kivshar

Published Aug 5, 2009• 42 citations
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Abstract

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 $^{23}\text{N}\text{a}$ condensate confined in a highly elongated harmonic trap. Finally, we discuss the phenomena of dynamical instability and spin domain formation.

DOI
10.1103/physreva.80.023602

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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.
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.
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.
Antiferromagnetic condensates are generally believed not to display modulational instability and subsequent spin-domain formation. Here we demonstrate that in the presence of a homogeneous magnetic field antiferromagnetic spin-1 Bose-Einstein condensates can undergo spatial modulational instability followed by the subsequent generation of spin domains. Employing numerical simulations for realistic conditions, we show how this effect can be observed in sodium condensates confined in an optical trap. Finally, we link this instability and spin-domain formation with stationary modes of the condensate.
We interpret the recently observed spatial domain formation in spin-1 atomic condensates as a result of dynamical instability. Within the mean field theory, a homogeneous condensate is dynamically unstable (stable) for ferromagnetic (antiferromagnetic) atomic interactions. We find that this dynamical instability naturally leads to spontaneous domain formation as observed in several recent experiments for condensates with rather small numbers of atoms. For trapped condensates, our numerical simulations compare quantitatively to the experimental results, thus largely confirming the physical insight from our analysis of the homogeneous case.
It is investigated theoretically that magnetized Bose-Einstein condensation (BEC) with the internal (spin) degrees of freedom exhibits a rich variety of phase transitions, depending on the sign of the interaction in the spin channel. In the antiferromagnetic interaction case there exist always double BEC transitions from single component BEC to multiple component BEC. In the ferromagnetic case BEC becomes always unstable at a lower temperature, leading to a phase separation. The detailed phase diagram for the temperature vs the polarization, the spatial spin structure, the distribution of non-condensates and the excitation spectrum are examined for the harmonically trapped systems.
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.