An effective equation for quasi-one-dimensional funnel-shaped Bose–Einstein condensates with embedded vorticity

Santos, Mateus C. P. dos; Cardoso, Wesley B.; Malomed, Boris A.

doi:10.1140/epjs/s11734-021-00351-2

Cited by 6 publications

(4 citation statements)

References 73 publications

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“…In this paper we investigated the funnel-shaped BEC loaded into the symmetric double-well potential (axial direction). This system is well described by a NPSE [33,34], for which we obtain three types of groundstates: symmetric, asymmetric and collapsed states. Symmetric solutions present densities with even parity, i.e., the particle density is invariant by changing the sign of its spatial coordinate.…”

Section: Introductionmentioning

confidence: 94%

“…Several configurations have been investigated and recently in Refs. [33,34] the authors studied a BEC confined by a radial singular potential (∼ 1/r), demonstrating the effectiveness of NPSE in describing the longitudinal behavior of the ultracold gas even when confined by anharmonic potentials. This configuration, called the funnel shape, can be achieved using a vapor of magnetic atoms attracted by an axial electric current.…”

Section: Introductionmentioning

confidence: 96%

“…[25] the authors presented a dimensional reduction method via a variational approach in order to obtain an effective equation that correctly describes the longitudinal (transversal) profile of the BEC. This technique has been extensively tested for decades, showing great results [26][27][28][29][30][31][32][33][34]. In the case of BECs, starting from the Gross-Pitaevskii (GP) equation (a NLSE type), this approach allows us to derive a nonpolynomial Schr ödinger equation (NPSEs), which describes the reduced dynamics of the corresponding physical system.…”

Section: Introductionmentioning

confidence: 99%

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Symmetry Breaking in Bose-Einstein Condensates Confined by a Funnel Potential

Miranda,

Santos,

Cardoso

2022

Preprint

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In this work, we consider a Bose-Einstein condensate in the self-focusing regime, confined transversely by a funnel-like potential and axially by a double-well potential formed by the combination of two inverted P öschl-Teller potentials. The system is well described by a one-dimensional nonpolynomial Schr ödinger equation, for which we analyze the symmetry break of the wave function that describes the particle distribution of the condensate. The symmetry break was observed for several interaction strength values as a function of the minimum potential well. A quantum phase diagram was obtained, in which it is possible to recognize the three phases of the system, namely, symmetric phase (Josephson), asymmetric phase (spontaneous symmetry breaking -SSB), and collapsed states, i.e., those states for which the solution becomes singular, representing unstable solutions for the system. We analyzed our symmetric and asymmetric solutions using a real-time evolution method, in which it was possible to confirm the stability of the results. Finally, a comparison with the cubic nonlinear Schr ödinger equation and the full Gross-Pitaevskii equation were performed to check the accuracy of the effective equation used here.

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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Symmetry Breaking in Bose-Einstein Condensates Confined by a Funnel Potential

Miranda,

Santos,

Cardoso

2022

Preprint

Self Cite

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“…[34] presented a time-dependent nonpolynomial Schrödinger equation that accurately described an anisotropic BEC confined strongly in the transverse direction by a harmonic trap (cigar shaped), obtained through a variational approach. This technique has been widely used for several other models [39][40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Spontaneous symmetry breaking induced by interaction in linearly coupled binary Bose Einstein condensates

Santos¹,

Cardoso²

2022

Preprint

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We analyze the spontaneous symmetry breaking (SSB) induced by one specific component of a linearly coupled binary Bose-Einstein condensate (BEC). The model is based on linearly coupled Schrödinger equations with cubic nonlinearity and with a double-well (DW) potential acting on only one of the atomic components. By numerical simulations, symmetric and asymmetric ground-states were obtained, and an induced asymmetry in the partner field was observed. In this sense, we properly demonstrated that the linear coupling mixing the two-field component (Rabi coupling) promotes the (in)balance between atomic species, as well as the appearance of the Josephson and SSB phases.

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Spontaneous symmetry breaking induced by interaction in linearly coupled binary Bose–Einstein condensates

Santos

Cardoso²

2022

Nonlinear Dyn

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An effective equation for quasi-one-dimensional funnel-shaped Bose–Einstein condensates with embedded vorticity

Cited by 6 publications

References 73 publications

Symmetry Breaking in Bose-Einstein Condensates Confined by a Funnel Potential

Symmetry Breaking in Bose-Einstein Condensates Confined by a Funnel Potential

Spontaneous symmetry breaking induced by interaction in linearly coupled binary Bose Einstein condensates

Spontaneous symmetry breaking induced by interaction in linearly coupled binary Bose–Einstein condensates

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