Metastable spin textures and Nambu-Goldstone modes of a ferromagnetic spin-1 Bose-Einstein condensate confined in a ring trap

Kunimi, Masaya

doi:10.1103/physreva.90.063632

Cited by 5 publications

(7 citation statements)

References 67 publications

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“…Modulation instability of spinor BECs in a ring geometry has been studied theoretically in Ref. [36]. Let us substitute the cw trial function (7) into the dynamical equations (2).…”

Section: A Continuous Wave Solutionsmentioning

confidence: 99%

“…[40][41][42][43][44]. In the context of mean field theory, sound waves (or by other names, acoustic waves, phonons, or Bogoliubov excitations) and also MI (where sound waves have complex-valued frequencies) may be represented by small perturbations to a cw solution [17,33,35,36,[45][46][47][48][70][71][72][73],…”

Section: B Sound Waves and Modulational Instabilitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…First and foremost, there is magnetism. More complicated phenomena in spinor BECs that do not occur in a scalar BEC are some forms of MI [17,[33][34][35][36], oscillatory coherent spin mixing [37-39], formation of spin textures, i.e., patterns of spatial variation of the magnetization [18], and certain forms of vortices with magnetization [11][12][13]18], including fractional vortices and non-Abelian vortices [14].Here we examine sound waves (phonons, acoustic waves, Bogoliubov excitations) that propagate on top of continuous wave (cw) solutions of F = 1 spinor BECs [40][41][42][43][44][45]. When the frequencies of the sound waves have (do not have) imaginary parts, they grow exponentially (do not grow), which implies that the background is unstable (stable).…”

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confidence: 99%

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Sound waves and modulational instabilities on continuous-wave solutions in spinor Bose-Einstein condensates

Tasgal

Band

2015

Phys. Rev. A

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We analyze sound waves (phonons, Bogoliubov excitations) propagating on continuous wave (cw) solutions of repulsive F = 1 spinor Bose-Einstein condensates (BECs), such as 23 Na (which is antiferromagnetic or polar) and 87 Rb (which is ferromagnetic). Zeeman splitting by a uniform magnetic field is included. All cw solutions to ferromagnetic BECs with vanishing MF = 0 particle density and non-zero components in both MF = ±1 fields are subject to modulational instability (MI). Modulational instability increases with increasing particle density. Modulational instability also increases with differences in the components' wave numbers; this effect is larger at lower densities but becomes insignificant at higher particle densities. Continuous wave solutions to anti-ferromagnetic (polar) BECs with vanishing MF = 0 particle density and non-zero components in both MF = ±1 fields do not suffer MI if the wave numbers of the components are the same. If there is a wave number difference, MI initially increases with increasing particle density, then peaks before dropping to zero beyond a given particle density. The cw solutions with particles in both MF = ±1 components and non-vanishing MF = 0 components do not have MI if the wave numbers of the components are the same, but do exhibit MI when the wave numbers are different. Direct numerical simulations of a cw with weak white noise confirm that weak noise grows fastest at wave numbers with the largest MI, and show some of the results beyond small amplitude perturbations. Phonon dispersion curves are computed numerically; we find analytic solutions for the phonon dispersion in a variety of limiting cases. PACS numbers: 03.75.Mn, 03.75.Kk, 42.65.Sf, 67.85.Fg I. INTRODUCTIONBose-Einstein condensates (BECs) [1][2][3][4][5] hold the promise of opening many new vistas in physics, e.g., macroscopic systems that exhibit quantum effects, higher resolution measurements of time, inertia, and other quantities, and a medium with which to carry out quantum computing and to simulate quantum systems [6][7][8][9][10]. Many interesting phenomena in BECs either occur against simpler backgrounds or are prepared from initially simpler states, which are often plane waves or approximations thereof. For example, vortices [11][12][13][14] and dark solitons [15][16][17] are typically imbedded on plane waves, and a spin texture [18] may be composed of, in part, many regions that are approximately plane waves. When the dynamics of plane waves are understood better, the structures that sit on them may be understood better. It is useful to know-especially if those simpler states are not quite as simple as had been thought-when they can and cannot exhibit more complex dynamics, and what those dynamics are.Bose-Einstein condensates can be composed of particles with non-zero total angular momentum (F > 0). For example, there is H [19], 7 Li [20], 23 Na [5, 21], 41 K [22], 52 Cr [23], 84 Sr [24], 85 Rb [25], 87 Rb [4], 133 Cs [26], 164 Dy [27], and 170 Yb [28]. An optical (as opposed to magnetic) trap can hold...

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“…Modulation instability of spinor BECs in a ring geometry has been studied theoretically in Ref. [36]. Let us substitute the cw trial function (7) into the dynamical equations (2).…”

Section: A Continuous Wave Solutionsmentioning

confidence: 99%

Section: B Sound Waves and Modulational Instabilitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Sound waves and modulational instabilities on continuous-wave solutions in spinor Bose-Einstein condensates

Tasgal

Band

2015

Phys. Rev. A

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“…The population imbalance and fixed phase relation between multiple components bring persistent flows novel stability features [18][19][20][21][22]. It has been found that rich phase diagram and interesting collective excitations can exist in interacting two-component [23][24][25][26] and three-component [27][28][29] toroidal BECs.…”

Section: Introductionmentioning

confidence: 99%

Spin-orbit-coupled spin-1 Bose-Einstein condensates in a toroidal trap: even-petal-number necklacelike state and persistent flow

Liu,

He,

Wang

et al. 2021

Preprint

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Spin-orbit coupling has novel spin-flip symmetries, a spin-1 spinor Bose-Einstein condensate owns meaningful interactions, and a toroidal trap is topologically nontrivial. We incorporate the three together and study the ground-state phase diagram in a Rashba spin-orbit-coupled spin-1 Bose-Einstein condensate with a toroidal trap. The spin-flip symmetries give rise to two different interesting phases: persistent flows with a unit phase winding difference between three components, and necklace states with even petal-number. The existing parameter regimes and properties of these phases are characterized by two-dimension numerical calculations and an azimuthal analytical one-dimension model.

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Counting rule of Nambu–Goldstone modes for internal and spacetime symmetries: Bogoliubov theory approach

2015

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When continuous symmetry is spontaneously broken, there appear Nambu-Goldstone modes (NGMs) with linear or quadratic dispersion relation, which is called type-I or type-II, respectively. We propose a framework to count these modes including the coefficients of the dispersion relations by applying the standard Gross-Pitaevskii-Bogoliubov theory. Our method is mainly based on (i) zero-mode solutions of the Bogoliubov equation originated from spontaneous symmetry breaking and (ii) their generalized orthogonal relations, which naturally arise from well-known Bogoliubov transformations and are referred to as "σ-orthogonality" in this paper. Unlike previous works, our framework is applicable without any modification to the cases where there are additional zero modes, which do not have a symmetry origin, such as quasi-NGMs, and/or where spacetime symmetry is spontaneously broken in the presence of a topological soliton or a vortex. As a by-product of the formulation, we also give a compact summary for mathematics of bosonic Bogoliubov equations and Bogoliubov transformations, which becomes a foundation for any problem of Bogoliubov quasiparticles. The general results are illustrated by various examples in spinor Bose-Einstein condensates (BECs). In particular, the result on the spin-3 BECs includes new findings such as a type-I-type-II transition and an increase of the type-II dispersion coefficient caused by the presence of a linearly-independent pair of zero modes.

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Metastable spin textures and Nambu-Goldstone modes of a ferromagnetic spin-1 Bose-Einstein condensate confined in a ring trap

Cited by 5 publications

References 67 publications

Sound waves and modulational instabilities on continuous-wave solutions in spinor Bose-Einstein condensates

Sound waves and modulational instabilities on continuous-wave solutions in spinor Bose-Einstein condensates

Spin-orbit-coupled spin-1 Bose-Einstein condensates in a toroidal trap: even-petal-number necklacelike state and persistent flow

Counting rule of Nambu–Goldstone modes for internal and spacetime symmetries: Bogoliubov theory approach

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