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

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dc.creatorSantos, Mateus Calixto Pereira dos
dc.creatorMalomed, Boris A.
dc.creatorCardoso, Wesley Bueno
dc.date.accessioned2024-07-15T12:16:43Z
dc.date.available2024-07-15T12:16:43Z
dc.date.issued2020
dc.description.abstractWe 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., 𝑉𝑧⁡(𝑧)=2⁢𝑧2+𝜁2/𝑧2, 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 noninteracting 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 1D Schrödinger equation with potential 𝑉𝑧⁡(𝑧). For both repulsive and attractive signs of the nonlinearity, the 2D 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.
dc.identifier.citationSANTOS, Mateus C. P. dos; MALOMED, Boris A. ; CARDOSO, Wesley B. Double-layer Bose-Einstein condensates: a quantum phase transition in the transverse direction, and reduction to two dimensions. Physical Review E, New York, v. 102, e042209, 2020. DOI: 10.1103/PhysRevE.102.042209. Disponível em: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.102.042209. Acesso em: 1 jun.2023.
dc.identifier.doi10.1103/PhysRevE.102.042209
dc.identifier.issn2470-0045
dc.identifier.issne- 2470-0053
dc.identifier.urihttps://journals.aps.org/pre/abstract/10.1103/PhysRevE.102.042209
dc.language.isoeng
dc.publisher.countryEstados unidos
dc.publisher.departmentInstituto de Física - IF (RMG)
dc.rightsAcesso Restrito
dc.titleDouble-layer Bose-Einstein condensates: a quantum phase transition in the transverse direction, and reduction to two dimensions
dc.typeArtigo

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