Mean-field regime and Thomas–Fermi approximations of trapped Bose–Einstein condensates with higher-order interactions in one and two dimensions

Ruan, Xinran; Cai, Yongyong; Bao, Weizhu

doi:10.1088/0953-4075/49/12/125304

Cited by 10 publications

(22 citation statements)

References 32 publications

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“…By contrast, singlemode condensates are well confined, and display spatially smooth density profiles with minimal shot-to-shot fluctuations. Figure 3 shows the transition from a multi-mode con- This single-mode condensate has all the signatures of a spatial Thomas-Fermi distribution typical of an interacting Bose-Einstein condensate in a finite, two-dimensional circular box potential 35,48,49 , namely a well-defined energy (chemical potential) and a 'top-hat' density distribution [ Fig. 3(d,e)].…”

Section: Condensation In the Thomas-fermi Regimementioning

confidence: 99%

Direct measurement of polariton-polariton interaction strength in the Thomas-Fermi regime of exciton-polariton condensation

et al. 2019

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Bosonic condensates of exciton polaritons (light-matter quasiparticles in a semiconductor) provide a solid-state platform for studies of non-equilibrium quantum systems with a spontaneous macroscopic coherence. These driven, dissipative condensates typically coexist and interact with an incoherent reservoir, which undermines measurements of key parameters of the condensate. Here, we overcome this limitation by creating a high-density exciton-polariton condensate in an opticallyinduced box trap. In this so-called Thomas-Fermi regime, the condensate is fully separated from the reservoir and its behaviour is dominated by interparticle interactions. We use this regime to directly measure the polariton-polariton interaction strength, and reduce the existing uncertainty in its value from four orders of magnitude to within three times the theoretical prediction. The Thomas-Fermi regime has previously been demonstrated only in ultracold atomic gases in thermal equilibrium. In a non-equilibrium exciton-polariton system, this regime offers a novel opportunity to study interaction-driven effects unmasked by an incoherent reservoir.

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Section: Condensation In the Thomas-fermi Regimementioning

confidence: 99%

Direct measurement of polariton-polariton interaction strength in the Thomas-Fermi regime of exciton-polariton condensation

et al. 2019

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“…In experiments, the confinement induced by the external potential might be strong in one or two directions. As a result, the BEC in 3D could be well described by the MGPE in 2D or 1D, respectively, by performing a proper dimension reduction [34,13,35]. Finally, we get the dimensionless modified GPE (MGPE) in d-dimensions (d = 1, 2, 3) as 4) with mass N (t) := R d |ψ(x, t)| 2 dx and energy E(ψ(·, t)) :=…”

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confidence: 99%

A normalized gradient flow method with attractive–repulsive splitting for computing ground states of Bose–Einstein condensates with higher-order interaction

Ruan

2018

Journal of Computational Physics

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In this paper, we generalize the normalized gradient flow method to compute the ground states of Bose-Einstein condensates (BEC) with higher order interactions (HOI), which is modelled via the modified Gross-Pitaevskii equation (MGPE). Schemes constructed in naive ways suffer from severe stability problems due to the high restrictions on time steps. To build an efficient and stable scheme, we split the HOI term into two parts with each part treated separately. The part corresponding to a repulsive/positive energy is treated semi-implicitly while the one corresponding to an attractive/negative energy is treated fully explicitly. Based on the splitting, we construct the BEFD-splitting and BESP-splitting schemes. A variety of numerical experiments shows that the splitting will improve the stability of the schemes significantly. Besides, we will show that the methods can be applied to multidimensional problems and to the computation of the first excited state as well.

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“…As shown in the figure, both the strong contact interaction and the strong HOI effect will spread the ground state, but in different ways. The detailed limiting Thomas-Fermi approximations of the ground states could be referred to [7,42]. The subfigures (c) and (d) in Figure 5.2 show explicitly how the value of β and δ is related to the difference ρ ε g − ρ g .…”

Section: Effect Of Interaction Strengthmentioning

confidence: 99%

“…where z = x 1 − x 2 ∈ R 3 , δ(·) and g 0 are defined as before, and g 1 , the strength of the HOI, is defined as g 1 = a 2 s 3 − asre 2 with r e being the effective range of the two-body interaction. With the new binary interaction (1.2), the dimensionless modified Gross-Pitaveskii equation (MGPE) in d-dimensions (d=1,2,3) can be derived as [23,29,30,41,42,43]…”

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Computing Ground States of Bose--Einstein Condensates with Higher Order Interaction via a Regularized Density Function Formulation

Bao¹,

Ruan²

2019

SIAM J. Sci. Comput.

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We propose and analyze a new numerical method for computing the ground state of the modified Gross-Pitaevskii equation for modeling the Bose-Einstein condensate with a higher order interaction by adapting the density function formulation and the accelerated projected gradient method. By reformulating the energy functional E(φ) with φ, the wave function, in terms of the density ρ = |φ| 2 , the original non-convex minimization problem for defining the ground state is then reformulated to a convex minimization problem. In order to overcome the semi-smoothness of the function √ ρ in the kinetic energy part, a regularization is introduced with a small parameter 0 < ε 1. Convergence of the regularization is established when ε → 0. The regularized convex optimization problem is discretized by the second order finite difference method. The convergence rates in terms of the density and energy of the discretization are established. The accelerated projected gradient method is adapted for solving the discretized optimization problem. Numerical results are reported to demonstrate the efficiency and accuracy of the proposed numerical method. Our results show that the proposed method is much more efficient than the existing methods in the literature, especially in the strong interaction regime.

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Mean-field regime and Thomas–Fermi approximations of trapped Bose–Einstein condensates with higher-order interactions in one and two dimensions

Cited by 10 publications

References 32 publications

Direct measurement of polariton-polariton interaction strength in the Thomas-Fermi regime of exciton-polariton condensation

Direct measurement of polariton-polariton interaction strength in the Thomas-Fermi regime of exciton-polariton condensation

A normalized gradient flow method with attractive–repulsive splitting for computing ground states of Bose–Einstein condensates with higher-order interaction

Computing Ground States of Bose--Einstein Condensates with Higher Order Interaction via a Regularized Density Function Formulation

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