FORTRESS: FORTRAN programs for solving coupled Gross–Pitaevskii equations for spin–orbit coupled spin-1 Bose–Einstein condensate

Kaur, Pardeep; Roy, Arko; Gautam, Sandeep

doi:10.1016/j.cpc.2020.107671

Cited by 26 publications

(16 citation statements)

References 91 publications

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“…We have chosen the value of dissipation parameter γ = 0.03 [45] in the present work. We solve CGPEs (1a)-(1b) on a two-dimensional 512×512 spatial grid with a space-step ∆x = ∆y = 0.1 and a time step ∆t = 0.005 using timesplitting Fourier spectral method [40]. We start with an initial guess solution corresponding to the ground state solution for an SO-coupled spin-1 BEC without rotation, and then CGPEs (1a)-(1b) are solved in real time till the equilibrium solution is achieved.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In Eq. ( 4), H d consists of trapping potential and diagonal interaction terms, H nd consists of coherent coupling and off-diagonal interaction terms, and H SOC consists of SO-coupling terms of the Hamiltonian [40,42]. We use time-splitting Fourier spectral method to solve Eq.…”

Section: Gross-pitaevskii Equations For a Rotating So-coupled Spin-1 Becmentioning

confidence: 99%

“…The procedure to solve the split equations corresponding to H d , H nd , and H SOC is same as discussed in Refs. [40][41][42].…”

Section: Gross-pitaevskii Equations For a Rotating So-coupled Spin-1 Becmentioning

confidence: 99%

See 2 more Smart Citations

Effective potentials in a rotating spin-orbit-coupled spin-1 spinor condensate

Banger¹,

Kumar²,

Bradley³

et al. 2021

Preprint

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The spin-orbit and coherent couplings along with rotation can combine together to result in scalar potentials which can modify the trapping potential to yield a variety of effective potentials experienced by a particle. The bosons in these rotating SO-and coherently-coupled Bose-Einstein condensates (BECs) can thus be subjected to rotating effective potentials equivalent to a toroidal, a symmetric double-well, an asymmetric double-well potentials, etc. With the increase in rotation frequency, the magnitude of spin-expectation per particle for even an antiferromagnetic SO-coupled BEC tends to unity, which is consistent with our analysis of the eigenfunctions and eigenenergies of the non-interacting Hamiltonian. The breakdown in the degeneracy of the minimum energy eigenfunctions of the non-interacting Hamiltonian results in the similar behavior of ferromagnetic and antiferromagnetic SO-coupled BECs. This is illustrated by the similar static vortex-lattice patterns, associated spin-textures, and mass-currents for the two systems at fast rotations.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Gross-pitaevskii Equations For a Rotating So-coupled Spin-1 Becmentioning

confidence: 99%

See 1 more Smart Citation

Effective potentials in a rotating spin-orbit-coupled spin-1 spinor condensate

Banger¹,

Kumar²,

Bradley³

et al. 2021

Preprint

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“…The results obtained with these finite difference schemes are compared with results from Fourier spectral method. The latter method has been used by us to solve CGPEs for SO-coupled spin-1 [27] and spin-2 condensates [28].…”

Section: Time-splitting Finite Difference Methodsmentioning

confidence: 99%

“…A wide range of numerical techniques have been employed in literature to study the scalar BEC [19,20,21,22] and spinor BECs [23,24,25,26]. In our earlier works, we also provided sets of Fortran 90/95 codes to solve the mean-field model of SO coupled f = 1 [27] and f = 2 [28] spinor BECs with Rashba SO-coupling using time-splitting Fourier spectral (TSFS) method. In the present work, we describe time-splitting finite-difference methods to solve the 2f + 1 CGPEs of spin-f (f = 1/2, 1, 2) spinor BECs in quasi-one-dimensional (q1D), quasi-twodimensional (q2D) traps with SO and coherent couplings.…”

Section: Introductionmentioning

confidence: 99%

Semi-Implicit finite-difference methods to study the spin-orbit and coherently coupled spinor Bose-Einstein condensates

Banger,

Kaur,

Gautam

2021

Preprint

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We develop time-splitting finite difference methods, using implicit Backward-Euler and semi-implicit Crank-Nicolson discretization schemes, to study the spin-orbit coupled spinor Bose Einstein condensates with coherent coupling in quasi-one and quasi-two-dimensional traps. The split equations involving kinetic energy and spin-orbit coupling operators are solved using either time implicit Backward-Euler or semi-implicit Crank-Nicolson methods. We explicitly develop the method for pseudospin-1/2, spin-1 and spin-2 condensates. The results for ground states obtained with time-splitting Backward-Euler and Crank-Nicolson methods are in excellent agreement with time-splitting Fourier spectral method which is one of the popular methods to solve the mean-field models for spin-orbit coupled spinor condensates. We confirm the emergence of different phases in spin-orbit coupled pseudospin-1/2, spin-1 and spin-2 condensates with coherent coupling.

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Vortex Lattice Formation in Spin–Orbit-Coupled Spin-2 Bose–Einstein Condensate Under Rotation

Banger

2023

J Low Temp Phys

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FORTRESS: FORTRAN programs for solving coupled Gross–Pitaevskii equations for spin–orbit coupled spin-1 Bose–Einstein condensate

Cited by 26 publications

References 91 publications

Effective potentials in a rotating spin-orbit-coupled spin-1 spinor condensate

Effective potentials in a rotating spin-orbit-coupled spin-1 spinor condensate

Semi-Implicit finite-difference methods to study the spin-orbit and coherently coupled spinor Bose-Einstein condensates

Vortex Lattice Formation in Spin–Orbit-Coupled Spin-2 Bose–Einstein Condensate Under Rotation

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