A G-FDTD scheme for solving multi-dimensional open dissipative Gross–Pitaevskii equations

Moxley, Frederick Ira; Byrnes, Tim; Ma, Bao‐Qing; Yan, Yun; Dai, Weizhong

doi:10.1016/j.jcp.2014.11.021

Cited by 15 publications

(6 citation statements)

References 33 publications

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“…Finite-difference methods have become popular for solving the time-dependent GPE because of their simplicity [39][40][41]. Alternative spectral methods [42][43][44][45] are also widely used.…”

Section: Time Integrationmentioning

confidence: 99%

Three-dimensional splitting dynamics of giant vortices in Bose-Einstein condensates

et al. 2018

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We study the splitting dynamics of giant vortices in dilute Bose-Einstein condensates by numerically integrating the three-dimensional Gross-Pitaevskii equation in time. By taking advantage of tetrahedral tiling in the spatial discretization, we decrease the error and increase the reliability of the numerical method. An extensive survey of vortex splitting symmetries is presented for different aspect ratios of the harmonic trapping potential. The symmetries of the splitting patterns observed in the simulated dynamics are found to be in good agreement with predictions obtained by solving the dominant dynamical instabilities from the corresponding Bogoliubov equations. Furthermore, we observe intertwining of the split vortices in prolate condensates and a split-and-revival phenomenon in a spherical condensate.

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Section: Time Integrationmentioning

confidence: 99%

Three-dimensional splitting dynamics of giant vortices in Bose-Einstein condensates

et al. 2018

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“…Finally, the derivatives in space are approximated using higher-order finite difference methods. The G-FDTD has been successfully applied for solving both linear and nonlinear Schrödinger equations [51,52].…”

Section: B Exciton-polariton Bec Dynamicsmentioning

confidence: 99%

Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates

et al. 2016

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We investigate prospects of using counter-rotating vortex superposition states in non-equilibrium exciton-polariton Bose-Einstein condensates for the purposes of Sagnac interferometry. We first investigate the stability of vortex-antivortex superposition states, and show that they survive at steady-state in a variety of configurations. Counter-rotating vortex superpositions are of potential interest to gyroscope and seismometer applications for detecting rotations. Methods of improving the sensitivity are investigated by targeting high momentum states via metastable condensation, and the application of periodic lattices. The sensitivity of the polariton gyroscope is compared to its optical and atomic counterparts. Due to the large interferometer areas in optical systems and small de Broglie wavelengths for atomic BECs, the sensitivity per detected photon is found to be considerably less for the polariton gyroscope than with competing methods. However, polariton gyroscopes have an advantage over atomic BECs in a high signal-to-noise ratio, and have other practical advantages such as room-temperature operation and robust design. We estimate that the final sensitivities including signal-to-noise aspects are competitive with existing methods.

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“…It is clear that all matrices indicated with a tilde are real and symmetric. Proving the stability of ( 5) is equivalent to proving the stability of (27).…”

Section: G =mentioning

confidence: 99%

“…A multitude of different implementations exist, depending on the spatial discretization and the time propagation, each having their strengths and weaknesses. Moreover, the FDTD method has also been applied to various related equations such as the non-linear Schrödinger equation [20][21][22][23][24][25][26], the Gross-Pitaevskii equations [27], and the stationary Schrödinger equation by performing a Wick rotation [28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

An alternating-direction hybrid implicit-explicit finite-difference time-domain method for the Schrödinger equation

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Londersele

Rogier

et al. 2022

Journal of Computational and Applied Mathematics

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A G-FDTD scheme for solving multi-dimensional open dissipative Gross–Pitaevskii equations

Cited by 15 publications

References 33 publications

Three-dimensional splitting dynamics of giant vortices in Bose-Einstein condensates

Three-dimensional splitting dynamics of giant vortices in Bose-Einstein condensates

Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates

An alternating-direction hybrid implicit-explicit finite-difference time-domain method for the Schrödinger equation

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