SU(3) symmetry in theory of a weakly interacting gas of spin-1 atoms with Bose-Einstein condensate

Peletminskii, A. S.; Peletminskiǐ, S. V.; Slyusarenko, Yu. V.

doi:10.1016/j.physleta.2020.126798

Cited by 8 publications

(23 citation statements)

References 34 publications

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“…However, for non-local interaction, the mentioned form of the Hamiltonian is insufficient for a correct description of the system due to the fact that the scattering length approximation fails and the scattering of two atoms with total spin S = 1 is now possible. In this case, the interaction Hamiltonian should be constructed of the spin and quadrupole operators, which are introduced through the prism of the SU(3) algebra on an equal footing [16,22]. In particular, eight Gell-Mann generators λ a (a = 1, .…”

Section: Hamiltonian With Quadrupole Degrees Of Freedommentioning

confidence: 99%

“…where the unitary operator U (U U † = 1) mixes the creation and annihilation operators [16,35]. The quantity E 0 determines the ground-state thermodynamic potential in the Gibbs statistical operator including the contribution from the quadratic terms in creation and annihilation operators.…”

Section: Broken-axisymmetry Statementioning

confidence: 99%

“…In this paper, in contrast to the above studies of spinor condensates, we refuse the scattering-length approximation assuming the interatomic interaction to be of non-local nature. In this case, the corresponding many-body Hamiltonian of spin-1 atoms should be constructed of the spin and quadrupole operators, which are introduced in an elegant way through the prism of the SU(3) algebra on an equal footing [16]. In particular, three Gell-Mann generators are identified with three components of the spin operator and the remaining five ones, representing the quadrupole degrees of freedom, are organized into the quadrupole matrix.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Broken-axisymmetry state and magnetic state diagram of spin-1 condensate through the prism of quadrupole degrees of freedom

Bulakhov,

Peletminskii,

Peletminskii

et al. 2021

Preprint

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We theoretically study a weakly interacting gas of spin-1 atoms with Bose-Einstein condensate in external magnetic field within the Bogoliubov approach. To this end, in contrast to previous studies, we employ the general Hamiltonian, which includes both spin and quadrupole exchange interactions as well as the couplings of the spin and quadrupole moment with the external magnetic field (the linear and quadratic Zeeman terms). The latter is responsible for the emergence of the broken-axisymmetry state. We also re-examine ferromagnetic, quadrupolar, and paramagnetic states employing the proposed Hamiltonian. For all magnetic states, we find the relevant thermodynamic characteristics such as magnetization, quadrupole moment, thermodynamic potential, as well as excitation energies for broken-axisymmetry state. We show that the broken-axisymmetry state can be prepared at three different regimes of applied magnetic field. We also present the magnetic state diagrams for each regime of realizing the broken-axisymmetry state.

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Section: Hamiltonian With Quadrupole Degrees Of Freedommentioning

confidence: 99%

Section: Broken-axisymmetry Statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Broken-axisymmetry state and magnetic state diagram of spin-1 condensate through the prism of quadrupole degrees of freedom

Bulakhov,

Peletminskii,

Peletminskii

et al. 2021

Preprint

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show abstract

“…, so that the interaction Hamiltonian takes the form V = c0 + c2 (S 1 • S 2 ), where c0 = 1 3 (g 0 + 2g 2 ) and c2 = 1 3 (g 2 − g 0 ) [18,27]. The comparison of Eqs.…”

Section: Quadrupole Degrees Of Freedom In Quantum Gasesmentioning

confidence: 99%

“…However, even after applying this procedure, there remains some inconsistency in the description of a Bose gas with a condensate within the quadratic approximation based on the Bogoliubov model [26]. For spinor condensates, the scattering-length approximation does not allow taking into account the interaction effects associated with the quadrupole degrees of freedom and can lead to an incomplete structure of the single-particle excitation spectra [27] so that the non-local character of interaction can not be ignored in some problems. The role of non-local interaction has been recently discussed in context of both ultracold Bose [26,28] and Fermi [29][30][31] gases .…”

Section: Introductionmentioning

confidence: 99%

Magnetic phases and phase diagram of spin-1 condensate with quadrupole degrees of freedom

Bulakhov,

Peletminskii,

Peletminskii

et al. 2020

Preprint

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We obtain and justify a many-body Hamiltonian of pairwise interacting spin-1 atoms, which includes eight generators of the SU(3) group associated with spin and quadrupole degrees of freedom. It is shown that this Hamiltonian is valid for non-local interaction potential, whereas for local interaction specified by s-wave scattering length, the Hamiltonian should be bilinear in spin operators only (of the Heisenberg type). We apply the obtained Hamiltonian to study the ground-state properties and single-particle excitations in a weakly interacting gas of spin-1 with Bose-Einstein condensate taking into account the quadrupole degrees of freedom. It is shown that the system under consideration can be in ferromagnetic, quadrupole, and paramagnetic phases. The corresponding phase diagram is constructed. The main characteristics such as the density of the grand thermodynamic potential, condensate density, and single-particle excitation spectra modified by quadrupole degrees of freedom are determined in different phases.

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Multipole degrees of freedom in physics of high-spin quantum atomic gases

Bulakhov

Peletminskii

Slyusarenko

2021

Low Temperature Physics

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We provide the general arguments that quantum atomic gases of interacting high-spin atoms represent a physical system in which the multipole (hidden) degrees of freedom may be manifested. Their manifestation occurs when the interatomic interaction is of non-local type. For a local interaction described by the s-wave scattering length, the multipole degrees of freedom do not reveal themselves. To illustrate our findings, we theoretically examine the phenomenon of Bose–Einstein condensation in an interacting gas of spin-1 atoms in an external magnetic field. This study is based on the SU(2) invariant Hamiltonian, which has a bilinear structure in the spin and quadrupole operators along with the scalar term. It is shown that depending on the conditions imposed on the interaction amplitudes (stability conditions), the ground state of the system may exhibit three different phases: quadrupolar, ferromagnetic, and paramagnetic. The basic thermodynamic characteristics affected by hidden degrees of freedom are found for all phases.

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SU(3) symmetry in theory of a weakly interacting gas of spin-1 atoms with Bose-Einstein condensate

Cited by 8 publications

References 34 publications

Broken-axisymmetry state and magnetic state diagram of spin-1 condensate through the prism of quadrupole degrees of freedom

Broken-axisymmetry state and magnetic state diagram of spin-1 condensate through the prism of quadrupole degrees of freedom

Magnetic phases and phase diagram of spin-1 condensate with quadrupole degrees of freedom

Multipole degrees of freedom in physics of high-spin quantum atomic gases

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