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

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

doi:10.1103/physreve.102.042209

Cited by 14 publications

(7 citation statements)

References 108 publications

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“…( 10) and (12), as the HO trapping potential does not play a significant role for the singular states. On the other hand, the HO potential produces an essential effect if applied to the flat-vortex mode (16), since it distorts the flat profile, as shown in Fig. 4.…”

Section: A Singular and Intermediate Statesmentioning

confidence: 99%

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Singular and regular vortices on top of a background pulled to the center

Chen,

Malomed

2021

Preprint

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A recent analysis has revealed singular but physically relevant localized 2D vortex states with density ∼ r −4/3 at r → 0 and a convergent total norm, which are maintained by the interplay of the potential of the attraction to the center, ∼ −r −2 , and a self-repulsive quartic nonlinearity, produced by the Lee-Huang-Yang correction to the mean-field dynamics of Bose-Einstein condensates. In optics, a similar setting, with the density singularity ∼ r −1 , is realized with the help of quintic selfdefocusing. Here we present physically relevant antidark singular-vortex states in these systems, existing on top of a flat background. Numerical solutions for them are very accurately approximated by the Thomas-Fermi wave function. Their stability exactly obeys an analytical criterion derived from analysis of small perturbations. The singular-vortex states exist as well in the case when the effective potential is weakly repulsive. It is demonstrated that the singular vortices can be excited by the input in the form of the ordinary nonsingular vortices, hence the singular modes can be created in the experiment. We also consider regular (dark) vortices maintained by the flat background, under the action of the repulsive central potential ∼ +r −2 . The dark modes with vorticities l = 0 and 1 are completely stable. In the case when the central potential is attractive, but the effective one, which includes the centrifugal term, is repulsive, and, in addition, a weak trapping potential ∼ r 2 is applied, dark vortices with l = 1 feature an intricate pattern of alternating stability and instability regions. Under the action of the instability, states with l = 1 travel along tangled trajectories, which stay in a finite area defined by the trap. The analysis is also reported for dark vortices with l = 2, which feature a complex structure of alternating intervals of stability and instability against splitting. Lastly, simple but novel flat vortices are found at the border between the anidark and dark ones.

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Section: A Singular and Intermediate Statesmentioning

confidence: 99%

“…FIG.4:The numerically found profile of the intermediate vortex model with U l = 0 (the one which has the flat profile(16) in the absence of the HO potential), for µ = 4, k = 0.2, and α = 3.…”

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confidence: 99%

Singular and regular vortices on top of a background pulled to the center

Chen,

Malomed

2021

Preprint

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“…While the realization of this model in optics in not straightforward, it may be implemented for matter waves in a dual-core "pancake-shaped" holder of BEC [18,71]. In polar coordinates (r, θ), particular exact solutions of linear equations (34), with all integer values of the vorticity, S = 0, 1, 2, ..., are found as…”

Section: Exact Solutions For One-and Two-dimensional Bound States In ...mentioning

confidence: 99%

Nonlinear dynamics of wave packets in tunnel-coupled harmonic-oscillator traps

Hacker¹,

Malomed²

2021

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We consider a two-component linearly-coupled system with the intrinsic cubic nonlinearity and the harmonic-oscillator (HO) confining potential. The system models binary settings in BEC and optics. In the symmetric system, with the HO trap acting in both components, we consider Josephson oscillations (JO) initiated by an input in the form of the HO's ground state (GS) or dipole mode (DM), placed in one component. With the increase of the strength of the self-focusing nonlinearity, spontaneous symmetry breaking (SSB) between the components takes place in the dynamical JO state. Under still stronger nonlinearity, the regular JO initiated by the GS input carry over into a chaotic dynamical state. For the DM input, the chaotization happens at smaller powers than for the GS, which is followed by SSB at a slightly stronger nonlinearity. In the system with the defocusing nonlinearity, SSB does not take place, and dynamical chaos occurs in a small area of the parameter space. In the asymmetric half-trapped system, with the HO potential applied to a single component, we first focus on the spectrum of confined binary modes in the linearized system. The spectrum is found analytically in the limits of weak and strong inter-component coupling, and numerically in the general case. Under the action of the coupling, the existence region of the confined modes shrinks for GSs and expands for DMs. In the full nonlinear system, the existence region for confined modes is identified in the numerical form. They are constructed too by means of the Thomas-Fermi approximation, in the case of the defocusing nonlinearity. Lastly, particular (non-generic) exact analytical solutions for confined modes, including vortices, in one-and two-dimensional asymmetric linearized systems are found. They represent bound states in the continuum.

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

Cited by 14 publications

References 108 publications

Singular and regular vortices on top of a background pulled to the center

Singular and regular vortices on top of a background pulled to the center

Nonlinear dynamics of wave packets in tunnel-coupled harmonic-oscillator traps

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

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