Effective equation for quasi-one dimensional tube-shaped Bose–Einstein condensates

Santos, Mateus C. P. dos; Cardoso, Wesley B.

doi:10.1016/j.physleta.2019.01.064

Cited by 12 publications

(4 citation statements)

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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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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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“…[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%

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

Miranda,

Santos,

Cardoso

2022

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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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“…In particular, studies of quasi-two-dimensional (quasi-2D) BEC with embedded 2D potentials have drawn much interest [35,55]. In this connection, approximations which make it possible to reduce the underlying 3D Gross-Pitaevskii equation (GPE) to effective 1D [56][57][58][59][60][61][62][63][64][65][66][67][68][69][70] and 2D [62,63,65,66,[71][72][73][74][75][76] equations have been elaborated. In particular, different effective low-dimensional equations were developed in Refs.…”

Section: Introductionmentioning

confidence: 99%

Double-layer Bose-Einstein condensates: A quantum phase transition in the transverse direction, and reduction to two dimensions

Santos,

Malomed,

Cardoso

2020

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We revisit the problem of the reduction of the three-dimensional (3D) dynamics of Bose-Einstein condensates, under the action of strong confinement in one direction (z), to a 2D mean-field equation. We address this problem for the confining potential with a singular term, viz., V z (z) = 2z 2 + ζ 2 /z 2 , with constant ζ. A quantum phase transition is induced by the latter term, between the ground state (GS) of the harmonic oscillator and the 3D condensate split in two parallel non-interacting layers, which is a manifestation of the "superselection" effect. A realization of the respective physical setting is proposed, making use of resonant coupling to an optical field, with the resonance detuning modulated along z. The reduction of the full 3D Gross-Pitaevskii equation (GPE) to the 2D nonpolynomial Schrödinger equation (NPSE) is based on the factorized ansatz, with the z-dependent multiplier represented by an exact GS solution of the Schrödinger equation with potential V(z). For both repulsive and attractive signs of the nonlinearity, the NPSE produces GS and vortex states, that are virtually indistinguishable from the respective numerical solutions provided by full 3D GPE. In the case of the self-attraction, the threshold for the onset of the collapse, predicted by the 2D NPSE, is also virtually identical to its counterpart obtained from the 3D equation. In the same case, stability and instability of vortices with topological charge S = 1, 2, and 3 are considered in detail. Thus, the procedure of the spatial-dimension reduction, 3D → 2D, produces very accurate results, and it may be used in other settings.

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Effective equation for quasi-one dimensional tube-shaped Bose–Einstein condensates

Cited by 12 publications

References 50 publications

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

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

Double-layer Bose-Einstein condensates: A quantum phase transition in the transverse direction, and reduction to two dimensions

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