Ground-state phases of a mixture of spin-1 and spin-2 Bose-Einstein condensates

Irikura, Naoki; Eto, Yujiro; Hirano, Takuya; Saito, Hiroki

doi:10.1103/physreva.97.023622

Cited by 13 publications

(15 citation statements)

References 40 publications

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“…whereR TF is the mean Thomas-Fermi radius and M the atomic mass. We follow the notation in [27] and write s-wave scattering lengths as a…”

Section: Mean-field Descriptionmentioning

confidence: 99%

“…For 87 Rb, the full set of inter-hyperfine spin interaction parameters has recently been measured [26] with intriguing results. The current best values indicate that in an equal f = 1, f = 2 ground-state mixture, the f = 1 component manifests a polar ground state at zero magnetic field [27] even though the f = 1 component alone is ferromagnetic [6].…”

Section: Introductionmentioning

confidence: 99%

“…The method is interferometric: the scattering of interest induces a phase shift among the Zeeman levels, which is detected via the precession angle. The observed dynamics are compared to mean-field simulations under the single-mode approximation (SMA) [30,31], yielding the two spin-dependent inter-hypefine interaction parameters [27].…”

Section: Introductionmentioning

confidence: 99%

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Interferometric measurement of interhyperfine scattering lengths in Rb87

et al. 2019

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We present interferometeric measurements of the f = 1 to f = 2 inter-hyperfine scattering lengths in a single-domain spinor Bose-Einstein condensate of 87 Rb. The inter-hyperfine interaction leads to a strong and state-dependent modification of the spin-mixing dynamics with respect to a non-interacting description. We employ hyperfine-specific Faraday-rotation probing to reveal the evolution of the transverse magnetization in each hyperfine manifold for different state preparations, and a comagnetometer strategy to cancel laboratory magnetic noise. The method allows precise determination of inter-hyperfine scattering length differences, calibrated to intra-hyperfine scattering length differences. We report (a (12) 3 −a (12) 2 )/(a (1) 2 −a (1) 0 ) = −1.27(15) and (a (12) 1 −a (12) 2 )/(a (1) 2 −a (1) 0 ) = −1.31(13), limited by atom number uncertainty. With achievable control of atom number, we estimate precisions of ≈0.3 % should be possible with this technique.

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“…whereR TF is the mean Thomas-Fermi radius and M the atomic mass. We follow the notation in [27] and write s-wave scattering lengths as a…”

Section: Mean-field Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Interferometric measurement of interhyperfine scattering lengths in Rb87

et al. 2019

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“…In the p-phase the spins of atom are two-by-two coupled to zero to form the singlet pairs (s-pair), and the total spin of the condensate S = 0. In the f -phase all the spins are fully polarized, i.e., lying along a common direction, and S = N. For 2-species BEC it was found in [7][8][9][10][11][12][13][14][15][16][17] that there are three types of spin-textures, namely, (i) the p+p texture where both species are in p-phase; (ii) the f // f texture where both species are in f -phase, and the two total spins (each for a species) are lying either parallel or antiparallel to each other; and (iii) the f //q texture where one in f -phase and one in quasi-ferromagnetic phase (q-phase, a mixture of aligned spins and s-pairs).…”

Section: Introductionmentioning

confidence: 99%

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

Liu

Bao

2020

Sci Rep

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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 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.• From the experience of 2-species BEC, the spin-textures are seriously affected by the compactness of the spatial wave functions (i.e., ϕ 4 A dr and ϕ 4 B dr) and the overlap (i.e., ϕ 2 A ϕ 2 B dr). For 3-species BEC, ϕ 4 J dr (J = A, B,C) and ϕ 2 J ϕ 2 J ′ dr are believed to be also important. Therefore, we solve the coupled Gross-Pitaevskii equations (CGP) under the Thomas-Fermi approximation (TFA) to obtain the spatial wave functions. It is well known that the TFA cannot correctly describe the tails of the wave functions. However, when the particle numbers are huge, the gross feature given by the TFA is good. Since only the gross feature is concerned, the TFA is acceptable.• Let S J be the total spin of the J-species. When the singlet-pairing force has been neglected, the three {S J } together with the total spin S of the mixture are good quantum numbers is the total spin-states Ξ. Ξ is obtained via a diagonalization of the Hamiltonian in the spin-space. In order to extract physical features from Ξ, in addition to the good quantum numbers, the averaged anglesθ JJ ′ between S J and S J ′ have also been calculated. Thereby various types of spin-textures specified by {S J } and {θ JJ ′ } can be identified. and the transitions among them are found.• In addition to the above quantum mechanic (QM) calculation, a corresponding classical model has been proposed and solved analytically. The results from the model are checked via a comparison with those from QM calculation. This model helps greatly to understand the complicated 3-species spin-textures Hamiltonian and the ground stateWe consider that the condensate is a mixture of three kinds of spin-1 atoms with particle numbers N J (J = A, B or C), and they are trapped by isotropic and harmonic potenti...

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“…The ferromagnetic (antiferromagnetic) spin interaction in f = 1 (f = 2) [34,38], which lowers (raises) the energy of stretched states relative to other states, opposes the orientation-to-alignment conversion and can reestablish long f = 2 lifetimes.…”

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confidence: 99%

Bose-Einstein Condensate Comagnetometer

et al. 2020

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We describe a comagnetometer employing the f = 1 and f = 2 ground state hyperfine manifolds of a 87 Rb spinor Bose-Einstein condensate as co-located magnetometers. The hyperfine manifolds feature nearly opposite gyromagnetic ratios and thus the sum of their precession angles is only weakly coupled to external magnetic fields, while being highly sensitive to any effect that rotates both manifolds in the same way. The f = 1 and f = 2 transverse magnetizations and azimuth angles are independently measured by non-destructive Faraday rotation probing, and we demonstrate a 44.0(8) dB common-mode rejection in good agreement with theory. We show how spin-dependent interactions can be used to inhibit 2 → 1 hyperfine relaxing collisions, extending to ∼ 1 s the transverse spin lifetime of the f = 1, 2 mixtures. The technique could be used in high sensitivity searches for new physics on sub-millimeter length scales, precision studies of ultra-cold collision physics, and angle-resolved studies of quantum spin dynamics.

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Ground-state phases of a mixture of spin-1 and spin-2 Bose-Einstein condensates

Cited by 13 publications

References 40 publications

Interferometric measurement of interhyperfine scattering lengths in Rb87

Interferometric measurement of interhyperfine scattering lengths in Rb87

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

Bose-Einstein Condensate Comagnetometer

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