Ground State of Bose-Einstein Condensates in a Spin-dependent Optical Lattice

doi:10.19596/j.cnki.1001-246x.8478

Abstract

Abstract:

Based on Gross-Pitaevskii equation, we studied numerically ground-state density distribution of Bose-Einstein condensates trapped in a combined potential of a spin-dependent optical lattice potential and an infinite deep potential. We discuss specifically the influence of propagation directions and the ratio of wave numbers (l) of the two lasers, which produce the spin-dependent optical lattice on the ground-state of the Bose-Einstein condensate. As the wave number is small, two beams of light spread forward to each other. The two components exhibit continuous stripes with l < 2. And with l≥2 both components show discontinuous stripes. As the two beams of light propagate vertically, with the increase of l, component 1 changes gradually from continuous to discontinuous stripes, and component 2 behaves oppositely. The number of ground state density fringes increases with the increase of wave number, while the number of vortices remains unchanged.

Key words: spin-dependent optical lattice potential, numerical simulation, density of ground state

Liyuan WU, Suying ZHANG. Ground State of Bose-Einstein Condensates in a Spin-dependent Optical Lattice[J]. Chinese Journal of Computational Physics, 2022, 39(5): 617-623.

Figures/Tables 4

Fig.1 (a) Schematic of spin-dependent optical lattice; (b) Joint potential and its cross section at x = 0

Fig.2 Ground state density profiles and phases for two counterpropagating laser beams (The first row is ground state density profiles. The second row is corresponding phase plots.) and corresponding optical lattice potential

Fig.3 Schematic of velocity components of the condensates along y direction as k1=1, k2=2

Fig.4 (a) Schematic of optical lattice potential; (b), (c), (d) Ground state density profiles and phases for two vertical propagating laser beams (The first row is ground state density profiles. The second row is corresponding phase plots.)

References 25

1	WEN Y C , ZHANG P M , YANG S J . A rotating Bose-Einstein condensation in a toroidal trap[J]. Commun Theor Phys, 2011, 56 (6): 1031- 1034. DOI
2	MASON P . Ground states of two-component condensates in a harmonic plus Gaussian trap[J]. Eur Phys J B, 2013, 86 (11): 1- 14.
3	WANG S S , ZHANG S Y . Giant vortex states of Bose-Einstein condensate in a harmonic plus Gaussian trap[J]. Chinese Journal of Computational Physics, 2021, 38 (1): 113- 119.
4	JOSE M B . Comment on "Bose-Einstein condensation with a finite number of particles in a power-law trap"[J]. Phys Rev A, 2015, 92 (1): 017601. DOI
5	JAOUADI A , TELMINI M , CHARRON E . Reply to "Comment on 'Bose-Einstein condensation with a finite number of particles in a power-law trap'"[J]. Phys Rev A, 2015, 92 (1): 017602. DOI
6	ABHINAV P , SERGEJ M , VICTOR G , et al. Multiply quantized vortices in fermionic superfluids: Angular momentum, unpaired fermions, and spectral asymmetry[J]. Phys Rev Lett, 2017, 119 (6): 067003. DOI
7	ANDREW J , TAPIO P , DAVID M , et al. Onsager vortex formation in Bose-Einstein condensates in two-dimensional power-law traps[J]. Phys Rev A, 2016, 93 (4): 043614. DOI
8	MASON P , AFTALION A . Classification of the ground states and topological defects in a rotating two-component Bose-Einstein condensate[J]. Phys Rev A, 2011, 84 (3): 033611. DOI
9	JIN J J , ZHANG S Y , HAN W , et al. The ground states and spin textures of rotating two-component Bose-Einstein condensates in an annular trap[J]. J Phys B: At Mol Opt Phys, 2013, 46 (7): 075302. DOI
10	XU Z F , KAWAGUCHI Y , YOU L , et al. Symmetry classification of spin-orbit coupled spinor Bose-Einstein condensates[J]. Phys Rev A, 2012, 86 (3): 033628. DOI
11	HUA W , LV Y , LIU S X , et al. Dynamic study of cubic-quantic nonlinear Schrödinger equation and pattern drifting[J]. Chinese Journal of Computational Physics, 2017, 34 (4): 495- 504. DOI
12	FU F F , KONG L H , WANG L , et al. High order compact splitting multisymplectic schemes for 1D Gross-Pitaevskii equation[J]. Chinese Journal of Computational Physics, 2018, 35 (6): 657- 667.
13	WANG L X , DONG B , CHEN G P , et al. Vortices of a rotating two-component dipolar Bose-Einstein condensate in an optical lattice[J]. Phys Lett A, 2016, 380 (3): 435- 438. DOI
14	GALLI D E , REATTO L , ROSSI M . Quantum Monte Carlo study of a vortex in superfluid ⁴He and search for a vortex state in the solid[J]. Phys Rev B, 2014, 89 (22): 817- 824.
15	MITHUN T , PORSEZIAN K , DEY B . Pinning of hidden vortices in Bose-Einstein condensate[J]. Phys Rev A, 2014, 89 (5): 168- 169.
16	HASSAN A S , ABDEL-GANY H A , ELLITHI A Y , et al. Thermodynamic properties of a rotating Bose-Einstein condensation in a deep optical lattice[J]. Turkish Journal of Physics, 2014, 447 (7): 54- 57.
17	ANTOINE X , DUBOSCQ R . GPELab, a matlab toolbox to solve Gross-Pitaevskii equations I: Computation of stationary solutions[J]. Computer Physics Communications, 2014, 185 (11): 2969- 2991. DOI
18	WANG D S , SONG S W , XIONG B . Quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction[J]. Phys Rev A, 2011, 84 (5): 053607. DOI
19	JI A C , LIU W M , SONG J L , et al. Dynamical creation of fractionalized vortices and vortex lattices[J]. Phys Rev Lett, 2008, 101 (1): 010402. DOI
20	ETO M , KASAMATSU K , NITTA M , et al. Interaction of half-quantized vortices in two-component Bose-Einstein condensates[J]. Phys Rev A, 2011, 83 (6): 063603. DOI
21	JIN J J , ZHANG S Y , HAN W . Spin domain wall in rotating two-component Bose-Einstein condensates[J]. J Phys B, 2011, 44 (16): 165302. DOI
22	KASAMATSU K , TSUBOTA M . Vortex sheet in rotating two-component Bose-Einstein condensates[J]. Phys Rev A, 2009, 79 (2): 023606. DOI
23	HAN W , ZHANG S Y , JIN J J , et al. Half-vortex sheets and domain-wall trains of rotating two-component Bose-Einstein condensates in spin-dependent optical lattices[J]. Phys Rev A, 2012, 85 (4): 043626. DOI
24	CHIOFALO M L , SUCCI S , TOSI M P . Gound state of trapped interacting Bose-Einstein condensates by an explicit imaginary－time algorithm[J]. Physical Review E, 2000, 62 (5): 7438- 7444. DOI
25	BAO W Z , CHERN I L , LIM F Y . Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose－Einstein condensates[J]. Journal of Computational Physics, 2006, (219): 836- 854.

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