环形运动势搅拌下偶极BEC中的非线性动力学

doi:10.19596/j.cnki.1001-246x.8527

摘要/Abstract

摘要：

数值研究谐振子势囚禁的偶极玻色-爱因斯坦凝聚体(BEC)在环形运动高斯势搅拌时的非线性动力学行为。随着高斯势运动速度以及尺寸的变化, BEC尾流中出现涡旋偶极子激发、涡团激发以及斜孤子激发三种激发模式。通过数值计算, 得到不同偶极相互作用下各种激发模式对应的参数区间, 分析偶极相互作用以及高斯势条件对激发模式的影响，并讨论不同激发的物理机制。

关键词: 偶极玻色-爱因斯坦凝聚体, 偶极子, 涡团, 斜孤子

Abstract:

Nonlinear dynamic behavior of a dipole Bose-Einstein condensate (BEC) trapped by harmonic potentials is numerically studied. We introduce a circular moving repulsive Gaussian potential to stir the condensate and study its emission phenomenon. The study is based on dimensionless two-dimensional GP equation. It reveals that there are three emission modes, namely vortex dipole emission, cluster emission and oblique soliton emission, in the wake. With a systematic numerical calculation, parameter regimes of dipole interactions corresponding to various excitation modes are obtained. Influences of dipole interactions and Gaussian potential conditions on excitation modes are analyzed, and physical mechanism of different emission modes is discussed.

Key words: dipolar Bose-Einstein condensate, vortex dipole, cluster, oblique soliton

席忠红, 赵永珍. 环形运动势搅拌下偶极BEC中的非线性动力学[J]. 计算物理, 2022, 39(6): 744-750.

Zhonghong XI, Yongzhen ZHAO. Nonlinear Dynamics in A Dipole Bose-Einstein Condensate Induced by A Circular Moving Potential[J]. Chinese Journal of Computational Physics, 2022, 39(6): 744-750.

图/表 5

图1 高斯势在偶极BEC中圆周运动时尾流密度分布(a)~(c)及相图(d)~(f)

Fig.1 Density (a)~(c) and phase (d)~(f) distributions of a dipolar BEC condensate circularly stirred by a Gaussian potential

图2 涡旋偶极子激发演化过程(a)~(d)与涡团激发演化过程(e)~(h)

Fig.2 Evolution of vortex dipole emission (a)~(d) and vortex cluster emission (e)~(h)

图3 斜孤子激发演化过程

Fig.3 Evolution of the oblique soliton emission

图4 斜孤子激发演化过程(图 3放大)高斯势周围密度分布(a)~(d)及相图(e)~(h)

Fig.4 Density distribution (a)~(d) and phase diagram (e)~(h) around a Gaussian potential (Amplification of the oblique soliton emission in Fig. 3)

图5 不同偶极相互作用下BEC各种激发模式的参数区间(a) g=100, add=0.2；(b) g=100, add=20；(c) g=100, add=40

Fig.5 Parameter regimes of vortex emission in dipole BEC under different dipole interactions (a) g=100, add=0.2; (b) g=100, add=20; (c) g=100, add=40

参考文献 31

1	FUJIMOTO K , TSUBOTA M . Synergy dynamics of vortices and solitons in an atomic Bose-Einstein condensate excited by an oscillating potential[J]. Phys Rev A, 2010, 82 (4): 043611. DOI
2	FUJIMOTO K , TSUBOTA M . Nonlinear dynamics in a trapped atomic Bose-Einstein condensate induced by an oscillating Gaussian potential[J]. Phys Rev A, 2011, 83 (5): 053609. DOI
3	FETTER A L . Rotating trapped Bose-Einstein condensates[J]. Rev Mod Phys, 2009, 81 (2): 647- 691. DOI
4	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.
5	HENN E A L , SEMAN J A , ROATI G , et al. Emergence of turbulence in an oscillating Bose-Einstein condensate[J]. Phys Rev Lett, 2009, 103 (4): 045301. DOI
6	TSUBOTA M , KASAMATSU K , UEDA M . Vortex lattice formation in a rotating Bose-Einstein condensate[J]. Phys Rev A, 2002, 65 (2): 023603. DOI
7	KASAMATSU K , TSUBOTA M , UEDA M . Nonlinear dynamics of vortex lattice formation in a rotating Bose-Einstein condensate[J]. Phys Rev A, 2003, 67 (3): 033610. DOI
8	FRISCH T , POMEAU Y , RICA S . Transition to dissipation in a model of superflow[J]. Phys Rev Lett, 1992, 69 (11): 1644- 1647. DOI
9	JACKSON B , MCCANN J F , ADAMS C S . Vortex formation in dilute inhomogeneous Bose-Einstein condensates[J]. Phys Rev Lett, 1998, 80 (18): 3903- 3096. DOI
10	JACKSON B , MCCANN J F , ADAMS C S . Dissipation and vortex creation in Bose-Einstein condensed gases[J]. Phys Rev A, 2000, 61 (5): 051603. DOI
11	RAMAN C , KOHL M , ONOFRIO R , et al. Evidence for a critical velocity in a Bose-Einstein condensed gas[J]. Phys Rev Lett, 1999, 83 (5): 2502- 2505.
12	NEELY T W , SAMSON E C , BRADLEY A S , et al. Observation of vortex dipoles in an oblate Bose-Einstein condensate[J]. Phys Rev Lett, 2010, 104 (16): 160401. DOI
13	SASAKI K , SUZUKI N , SAITO H . Bénard-von Kármán vortex street in a Bose-Einstein condensate[J]. Phys Rev Lett, 2010, 104 (15): 150404. DOI
14	KWON W J , MOON G , CHOI J , et al. Relaxation of superfluid turbulence in highly oblate Bose-Einstein condensates[J]. Phys Rev A, 2014, 90 (6): 063627. DOI
15	KWON W J , SEO S W , SHIN Y . Periodic shedding of vortex dipoles from a moving penetrable obstacle in a Bose-Einstein condensate[J]. Phys Rev A, 2015, 92 (3): 033613. DOI
16	KWON W J , MOON G , CHOI J , et al. Observation of von Kármán vortex street in an atomic superfluid gas[J]. Phys Rev Lett, 2016, 117 (24): 245301. DOI
17	REEVES M T , ANDERSON B P , BRADLEY A S . Classical and quantum regimes of two-dimensional turbulence in trapped Bose-Einstein condensates[J]. Phys Rev A, 2012, 86 (5): 053621. DOI
18	WANG D S , SONG S W , XIONG B , et al. Quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction[J]. Phys Rev A, 2011, 84 (5): 053607. DOI
19	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
20	LI Y S . Influence of dipolar interaction on domain distribution in a spin-orbit coupled f =1 spinor condensate[J]. Chinese Journal of Computational Physics, 2021, 38 (1): 120- 126.
21	CAI Y Y , MATTHIAS R , LEI Z , et al. Mean-field regime of trapped dipolar Bose-Einstein condensates in one and two dimensions[J]. Phys Rev A, 2010, 82 (4): 043623. DOI
22	LIANG Z X , ZHANG Z D , LIU W M . Dynamics of a bright soliton in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential[J]. Phys Rev Lett, 2005, 94 (5): 050402. DOI
23	JI A C , SUN Q , XIE X C , et al. Josephson effect for photons in two weakly linked microcavities[J]. Phys Rev Lett, 2009, 102 (2): 023602. DOI
24	GIOVANAZZI S , GORLITZ A , PFAU T . Tuning the dipolar interaction in quantum gases[J]. Phys Rev Lett, 2002, 89 (13): 130401. DOI
25	NATH R , PEDRI P , SANTOS L . Phonon instability with respect to soliton formation in two-dimensional dipolar Bose-Einstein condensates[J]. Phys Rev Lett, 2009, 102 (5): 050401. DOI
26	PEDRI P , SANTOS L . Two-dimensional bright solitons in dipolar Bose-Einstein condensates[J]. Phys Rev Lett, 2005, 95 (20): 200404. DOI
27	LI J , LIU B . Quantum analysis of BCS-BEC crossover in Feshbach resonances[J]. Chinese Journal of Computational Physics, 2012, 29 (3): 466- 474. DOI
28	BAO W , WANG H . An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose-Einstein condensates[J]. J Comput Phys, 2006, 217 (2): 612- 626. DOI
29	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.
30	XI Z H , ZHAO Y Z , SHI Y R . Bénard-von Kármán vortex street in a dipolar Bose-Einstein condensate[J]. Phys A, 2021, 572 (1): 125866.
31	SADLER L E , HIGBIE J M , LESLIE S R , et al. Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose-Einstein condensate[J]. Nature, 2006, 443 (7109): 312- 315. DOI

[1]	杨帅帅, 孙玉发. 应用AWE技术和等效偶极子法快速计算目标宽带RCS[J]. 计算物理, 2012, 29(3): 406-410.
[2]	类成新, 吴振森. 随机取向烟幕凝聚粒子的消光特性[J]. 计算物理, 2010, 27(4): 593-597.
[3]	毕增军, 盛松林, 范丽思, 刘尚合. 静电放电火花产生的电磁场特征分析[J]. 计算物理, 2004, 21(1): 86-90.
[4]	沈金松. 用边有限元方法计算磁偶极子的三维电磁响应[J]. 计算物理, 2002, 19(6): 537-543.
[5]	朱景辉. 有限平板绕流的数值模拟[J]. 计算物理, 1990, 7(3): 363-370.