自旋相关光晶格中玻色-爱因斯坦凝聚体的基态

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

摘要/Abstract

摘要：

基于Gross-Pitaevskii方程数值研究自旋相关光晶格势和无限深势阱的联合势阱中玻色-爱因斯坦凝聚体的基态密度分布。重点讨论产生自旋相关光晶格势的两束激光传播方向和波数之比(l)对基态密度分布的影响。在两束激光的波数较小, 两束光相向传播, 且l < 2时, 两分量的基态密度条纹都是连续的, l≥2时, 两分量的基态密度均出现不连续条纹。两束光垂直传播时, 随着l的增大, 组分1的基态密度从连续条纹逐渐转变为不连续条纹, 组分2则正好相反。基态密度条纹数随着波数的增加而增多, 但涡旋个数保持不变。

关键词: 自旋相关光晶格势, 数值模拟, 基态密度

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

吴丽媛, 张素英. 自旋相关光晶格中玻色-爱因斯坦凝聚体的基态[J]. 计算物理, 2022, 39(5): 617-623.

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.

图/表 4

图1 (a) 自旋相关光晶格的示意图[23]；(b) 联合势的示意图及其沿x轴的横切面

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

图2 两束激光相向传播时，不同波数对应凝聚体的基态密度分布和相位分布(第一行为密度，第二行为相位。)以及相应的光晶格势

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

图3 k1=1, k2=2时, 凝聚体沿y方向的速度分量示意图

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

图4 (a) 光晶格势示意图；(b), (c), (d)为两束激光垂直传播时不同波数对应的凝聚体基态密度分布和相位分布 (第一行为密度，第二行为相位。)

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.)

参考文献 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.

[1]	刘利, 牛胜利, 朱金辉, 左应红, 谢红刚, 商鹏. 临近空间核爆炸碎片云运动的数值模拟[J]. 计算物理, 2022, 39(5): 521-528.
[2]	杜旭林, 程林松, 牛烺昱, 陈玉明, 曹仁义, 谢永红. 考虑水力压裂缝和天然裂缝动态闭合的三维离散缝网数值模拟[J]. 计算物理, 2022, 39(4): 453-464.
[3]	孙梦营, 马明, 过海龙, 姚孟君, 徐猛, 张莹. 零重力点热源马兰戈尼FTM数值模拟[J]. 计算物理, 2022, 39(2): 191-200.
[4]	赵腾飞, 张华. 气泡碰撞过程中形变及破碎现象分析[J]. 计算物理, 2022, 39(1): 41-52.
[5]	关富荣, 李成乾, 邓敏艺. 激发介质相对不应态对螺旋波动力学行为的影响[J]. 计算物理, 2021, 38(6): 749-756.
[6]	王俊捷, 寇继生, 蔡建超, 潘益鑫, 钟振. 基于Tolman长度的Lucas-Washburn渗吸模型改进及数值模拟[J]. 计算物理, 2021, 38(5): 521-533.
[7]	杨展康, 牛奕. 温度及围护通风对独头巷道氡浓度分布的影响[J]. 计算物理, 2021, 38(4): 456-464.
[8]	胡少亮, 徐小文, 郑宇腾, 赵振国, 王卫杰, 徐然, 安恒斌, 莫则尧. 系统级封装应用中时谐Maxwell方程大规模计算的求解算法:现状与挑战[J]. 计算物理, 2021, 38(2): 131-145.
[9]	陈皓, 蔡汝铭. 平流层飞艇气动外形优化设计:螺旋桨的影响[J]. 计算物理, 2020, 37(5): 562-570.
[10]	王子墨, 李凌. 超短激光打孔中快速相变的格子玻尔兹曼模拟[J]. 计算物理, 2020, 37(3): 299-306.
[11]	王智, 邹高域, 宫敬, 白剑锋, 翟博文. 一维双流体模型的压力修正算法[J]. 计算物理, 2019, 36(4): 413-420.
[12]	张珑慧, 由长福. 基于有限体积虚拟区域方法的两相流动直接模拟[J]. 计算物理, 2019, 36(3): 291-297.
[13]	徐丞君, 徐胜利. SPH二阶粒子近似光滑函数的充分条件及数值验证[J]. 计算物理, 2019, 36(1): 25-38.
[14]	王烨, 王艺, 胡文婷, 王良璧. POD方法在扁管管翅式换热器研究中的应用[J]. 计算物理, 2018, 35(5): 587-596.
[15]	孙婷婷, 韩赛赛, 许明田. 求解对流-扩散-反应问题的改进有限积分法[J]. 计算物理, 2018, 35(3): 269-274.