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arXiv:1910.04381

Spin-textures of the Bose-Einstein condensates with three kinds of spin-1 atoms

Y. Z. He, Y. M. Liu, Bao Cheng-guang

Published Oct 10, 2019• 0 citations
arXivHTMLPDF

Abstract

We have performed a quantum mechanic calculation (including solving the coupled Gross-Pitaevskii equations to obtain the spatial wave functions, and diagonalizing the spin-dependent Hamiltonian in the spin-space to obtain the total spin state) together with an analytical analysis based on a classical model. Then, according to the relative orientations of the spins $S_A$, $S_B$ and $S_C$ of the three species, the spin-textures of the ground state can be classified into two types. In Type-I the three spins are either parallel or anti-parallel to each others, while in Type-II they point to different directions but remain to be coplanar. Moreover, according to the magnitudes of $S_A$, $S_B$ and $S_C$ the spin-textures can be further classified into four kinds, namely, $p$+$p$+$p$ (all atoms of each species are in singlet-pairs), one species in $f$ (fully polarized) and two species in $q$ (a mixture of polarized atoms and singlet-pairs), two in $f$ and one in $q$, and $f$+$f$+$f$. Other combinations are not allowed. The scopes of the parameters that supports a specific spin-texture have been specified. A number of spin-texture-transitions have been found. For Type-I, the critical values at which a transition takes place are given by simple analytical formulae, therefore these values can be predicted.

DOI
10.48550/arxiv.1910.04381

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We have performed a quantum mechanic calculation (including solving the coupled Gross-Pitaevskii equations to obtain the spatial wave functions, and diagonalizing the spin-dependent Hamiltonian in the spin-space to obtain the total spin state) together with an analytical analysis based on a classical model. Then, according to the relative orientations of the spins SAS_ASA​, SBS_BSB​ and SCS_CSC​ of the three species, the spin-textures of the ground state can be classified into two types. In Type-I the three spins are either parallel or anti-parallel to each others, while in Type-II they point to different directions but remain to be coplanar. Moreover, according to the magnitudes of SAS_ASA​, SBS_BSB​ and SCS_CSC​ the spin-textures can be further classified into four kinds, namely, ppp+ppp+ppp (all atoms of each species are in singlet-pairs), one species in fff (fully polarized) and two species in qqq (a mixture of polarized atoms and singlet-pairs), two in fff and one in qqq, and fff+fff+fff. Other combinations are not allowed. The scopes of the parameters that supports a specific spin-texture have been specified. A number of spin-texture-transitions have been found. For Type-I, the critical values at which a transition takes place are given by simple analytical formulae, therefore these values can be predicted.
Abstract We have performed a quantum mechanic calculation (including solving the coupled Gross-Pitaevskii equations to obtain the spatial wave functions, and diagonalizing the spin-dependent Hamiltonian in the spin-space to obtain the total spin state) together with an analytical analysis based on a classical model. Then, according to the relative orientations of the spins SA, SB and SC of the three species, the spin-structures of the ground state can be classified into two types. In Type-I the three spins are either parallel or anti-parallel to each other, while in Type-II they point to different directions but remain to be coplanar. Moreover, according to the magnitudes of SA, SB and SC, the spin-structures can be further classified into four kinds, namely, p + p + p (all atoms of each species are in singlet-pairs), one species in f (fully polarized) and two species in q (a mixture of polarized atoms and singlet-pairs), two in f and one in q, and f + f + f. Other combinations are not allowed. The scopes of the parameters that supports a specific spin-structure have been specified. A number of spin-structure-transitions have been found. For Type-I, the critical values at which a transition takes place are given by simple analytical formulae, therefore these values can be predict.
Abstract Based on the numerical solutions of the coupled Gross–Pitaevskii equations, the spin-textures of the ground state of a Bose–Einstein condensate with two kinds of spin-1 atoms have been studied. Besides, making use of the fractional parentage coefficients, the probabilities of an atom in spin component μ and of two correlated atoms one in μ and one in ν have been calculated. The previous results under the single spatial mode approximation (SMA) are found to be qualitatively consistent with the present results beyond the SMA. The variation of the probabilities against the input parameters is found to match the corresponding variation of the spin-textures excellently. In particular, once a spin-texture transition occurs, the associated probabilities will change suddenly. Since the probabilities are observable, the observation provides a way for the experimental identification of the spin-textures. Besides, sine the critical points (where a transition occurs) can be accurately identified, information on the input parameters (say, the very weak spin-dependent forces) can be extracted.
The interaction between two species of atoms in the condensate has been deduced and the trial wave functions that conserve the total spin have been constructed for the states of the ground band. A couple of generalized Gross-Pitaevskii equations have been derived for the spatial wave functions and the energies. The mixture of 23Na^{23}\mathrm{Na}23Na and 87Rb^{87}\mathrm{Rb}87Rb has been calculated as an example. The density of states is found to exhibit a ladder shape.
We consider a mixture of two distinct species of atoms of pseudospin 12\frac{1}{2}21​ with both intraspecies and interspecies spin-exchange interactions and find all the ground states in a general case of the parameters in the effective Hamiltonian. In general, corresponding to the two-species and two-pseudospin states, there are four orbital wave functions into which the atoms condense. We find that in certain parameter regimes, the ground state is the so-called polarized entangled Bose-Einstein condensation; that is, in addition to condensation of interspecies singlet pairs, there are unpaired atoms with spins polarized in the same direction. The interspecies entanglement and polarization significantly affect the generalized Gross-Pitaevskii equations governing the four orbital wave functions into which the atoms condense, as an interesting interplay between spin and orbital degrees of freedom.
We present an overview of our recent theoretical studies on the quantum phenomena of the spin-1 Bose-Einstein condensates, including the phase diagram, soliton solutions and the formation of the topological spin textures. A brief exploration of the effects of spin-orbit coupling on the ground-state properties is given. We put forward proposals by using the transmission spectra of an optical cavity to probe the quantum ground states: the ferromagnetic and polar phases. Quasi-one-dimension solitons and ring dark solitons are studied. It is predicted that characteristics of the magnetic solitons in optical lattice can be tuned by controlling the long-range light-induced and static magnetic dipoledipole interactions; solutions of single-component magnetic and single-, two-, three-components polar solitons are found; ring dark solitons in spin-1 condensates are predicted to live longer lifetimes than that in their scalar counterparts. In the formation of spin textures, we have considered the theoretical model of a rapidly quenched and fast rotating trapped spin-1 Bose-Einstein condensate, whose dynamics can be studied by solving the stochastic projected Gross-Pitaevskii equations. Spontaneous generation of nontrivial topological defects, such as the hexagonal lattice skyrmions and square lattice of half-quantized vortices was predicted. In particular, crystallization of merons (half skyrmions) can be generated in the presence of spin-orbit coupling.
We investigate the ground state of rotating two-component Bose-Einstein condensates in the combined potential well of one-dimensional spin-dependent optical lattice potential and harmonic potential. The density distribution of the condensate is striped. By defining the generalized momentum operator, we derive the velocity distribution of the condensate. The velocity contours are concentric circles for each stripe, with different centers for different stripes. This velocity distribution corresponds to a specific spin texture structure. In this texture, the azimuthal angle of the magnetic moments varies along the y-direction, while the z-component of the magnetic moments varies along the x-direction. When the lattice period [Formula: see text], the texture is divided into two regions. The magnetic moments reverse in a counterclockwise direction and in a clockwise direction as y increases in regions I and II, respectively. Furthermore, when the lattice period [Formula: see text], the texture is divided into three regions. The magnetic moments reverse in a counterclockwise direction, do not reverse, and reverse in a clockwise direction as y increases in regions I, II, and III, respectively. Accurate manipulation of the texture can be achieved by adjusting the optical lattice periods [Formula: see text] and [Formula: see text], the relative phase φ, and the rotational angular frequency Ω.