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Acta Physica Sinica

Vortex pattern in spin-orbit coupled spin-1 Bose-Einstein condensate of 23Na

Chaofei Liu, Wan Wen-Juan, Zhang Gan-Yuan

Published Jan 1, 2013• 10 citations
Publisher

Abstract

摘要 利用阻尼映射Gross-Pitaevkii方程, 研究了二维体系中自旋轨道耦合的 23Na自旋-1 玻色-爱因斯坦凝聚体中的涡旋斑图, 探索自旋轨道耦合强度对涡旋斑图的影响. 研究发现, 较弱的自旋轨道耦合就可以完全破坏不考虑自旋轨道耦合情况下出现的周期性涡旋晶格; 在自旋轨道耦合较强的情况下, 各自旋态的涡旋易形成涡旋组, 它们绕凝聚体中心形成花瓣状涡旋斑图. 关键词: 玻色-爱因斯坦凝聚体 / 自旋 / 涡旋 Abstract Using the damped projecting Gross-Pitaevkii align, we study the vortex pattern in the two-dimensional spin-orbit coupled spin-1 Bose-Einstein condensate of 23Na. We concentrate on the influence of spin-orbit coupling on the vortex pattern and find that the periodic vortex lattice which would occur without any spin-orbit coupling, can be completely destroyed although the strength of spin-orbit coupling is not very strong. With a strong spin-orbit coupling, vortexes in the condensate of each spin state tend to form some vortex groups and then they create a flower-like lattice around the center. Keywords: Bose-Einstein condensate / spin / vortex 作者及机构信息 刘超飞1, 万文娟2, 张赣源2 1. 江西理工大学理学院, 赣州 341000; 2. 江西理工大学应用科学院, 赣州 341000 基金项目: 国家自然科学基金(批准号: 11247206, 11304130, 11365010)和江西省教育厅科学技术研究项目(批准号: GJJ13382, GJJ11467) 资助的课题. Authors and contacts Liu Chao-Fei1, Wan Wen-Juan2, Zhang Gan-Yuan2 1. School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China; 2. College of Applied Science, Jiangxi University of Science and Technology, Ganzhou 341000, China Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11247206, 11304130, 11365010) and the Science and Technology Project of Jiangxi Province, China (Grant Nos. GJJ13382, GJJ11467). 参考文献 [1] Bychkov Y A, Rashba E I 1984 J. Phys. C 17 6039 [2] Dresselhaus G 1955 Phys. Rev. 100 580 [3] Kato Y K, Myers R C, Gossard A C, Awschalom D D 2004 Science 306 1910 [4] König M, Wiedmann S, Brne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766 [5] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802 [6] Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757 [7] Hsieh D, Qian D, Wray L, Xia Y, Hor Y S, Cava R J, Hasan M Z 2008 Nature 452 970 [8] Sun K, Liu W V, Hemmerich A, Sarma S D 2012 Nature Phys. 8 67 [9] Lin Y J, Jiménez-García K, Spielman I B 2011 Nature 471 83 [10] Liao R, Yi-Xiang Y, Liu W M 2012 Phys. Rev. Lett. 108 080406 [11] Wang C, Gao C, Jian C M, Zhai H 2010 Phys. Rev. Lett. 105 160403 [12] Ho T L, Zhang S Z 2011 Phys. Rev. Lett. 107 150403 [13] Jian C M, Zhai H 2011 Phys. Rev. B 84 060508(R) [14] Sinha S, Nath R, Santos L 2011 Phys. Rev. Lett. 107 270401 [15] Hu H, Ramachandhran B, Pu H, Liu X J 2012 Phys. Rev. Lett. 108 010402 [16] Wu C, Mondragon-Shem I, Zhou X F 2011 Chin. Phys. Lett. 28 097102 [17] Liu C F, Fan H, Zhang Y C, Wang D S, Liu W M 2012 Phys. Rev. A 86 053616 [18] Xu X Q, Han J H 2011 Phys. Rev. Lett. 107 200401 [19] Zhou X F, Zhou J, Wu C 2011 Phys. Rev. A 84 063624 [20] Zhao L, Yang J, Xie Q Y, Tian M, Duan Y S 2012 Chin. Phys. B 21 057401 [21] Chen A X, Qiu W Y, Wang Z P 2008 Chin. Phys. B 17 4204 [22] Liu C F, Liu W M 2012 Phys. Rev. A 86 033602 [23] Bradley A S, Gardiner C W, Davis M J 2008 Phys. Rev. A 77 033616 [24] Rooney S J, Bradley A S, Blakie P B 2010 Phys. Rev. A 81 023630 [25] Liu C F, Yu Y M, Gou S C, Liu W M 2013 Phys. Rev. A 87 063630 [26] Su S W, Hsueh C H, Liu I K, Horng T L, Tsai Y C, Gou S C, Liu W M 2011 Phys. Rev. A 84 023601 施引文献

DOI
10.7498/aps.62.200306

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摘要 利用阻尼映射Gross-Pitaevkii方程, 研究了二维体系中自旋轨道耦合的 23Na自旋-1 玻色-爱因斯坦凝聚体中的涡旋斑图, 探索自旋轨道耦合强度对涡旋斑图的影响. 研究发现, 较弱的自旋轨道耦合就可以完全破坏不考虑自旋轨道耦合情况下出现的周期性涡旋晶格; 在自旋轨道耦合较强的情况下, 各自旋态的涡旋易形成涡旋组, 它们绕凝聚体中心形成花瓣状涡旋斑图. 关键词: 玻色-爱因斯坦凝聚体 / 自旋 / 涡旋 Abstract Using the damped projecting Gross-Pitaevkii align, we study the vortex pattern in the two-dimensional spin-orbit coupled spin-1 Bose-Einstein condensate of 23Na. We concentrate on the influence of spin-orbit coupling on the vortex pattern and find that the periodic vortex lattice which would occur without any spin-orbit coupling, can be completely destroyed although the strength of spin-orbit coupling is not very strong. With a strong spin-orbit coupling, vortexes in the condensate of each spin state tend to form some vortex groups and then they create a flower-like lattice around the center. Keywords: Bose-Einstein condensate / spin / vortex 作者及机构信息 刘超飞1, 万文娟2, 张赣源2 1. 江西理工大学理学院, 赣州 341000; 2. 江西理工大学应用科学院, 赣州 341000 基金项目: 国家自然科学基金(批准号: 11247206, 11304130, 11365010)和江西省教育厅科学技术研究项目(批准号: GJJ13382, GJJ11467) 资助的课题. Authors and contacts Liu Chao-Fei1, Wan Wen-Juan2, Zhang Gan-Yuan2 1. School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China; 2. College of Applied Science, Jiangxi University of Science and Technology, Ganzhou 341000, China Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11247206, 11304130, 11365010) and the Science and Technology Project of Jiangxi Province, China (Grant Nos. GJJ13382, GJJ11467). 参考文献 [1] Bychkov Y A, Rashba E I 1984 J. Phys. C 17 6039 [2] Dresselhaus G 1955 Phys. Rev. 100 580 [3] Kato Y K, Myers R C, Gossard A C, Awschalom D D 2004 Science 306 1910 [4] König M, Wiedmann S, Brne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766 [5] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802 [6] Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757 [7] Hsieh D, Qian D, Wray L, Xia Y, Hor Y S, Cava R J, Hasan M Z 2008 Nature 452 970 [8] Sun K, Liu W V, Hemmerich A, Sarma S D 2012 Nature Phys. 8 67 [9] Lin Y J, Jiménez-García K, Spielman I B 2011 Nature 471 83 [10] Liao R, Yi-Xiang Y, Liu W M 2012 Phys. Rev. Lett. 108 080406 [11] Wang C, Gao C, Jian C M, Zhai H 2010 Phys. Rev. Lett. 105 160403 [12] Ho T L, Zhang S Z 2011 Phys. Rev. Lett. 107 150403 [13] Jian C M, Zhai H 2011 Phys. Rev. B 84 060508(R) [14] Sinha S, Nath R, Santos L 2011 Phys. Rev. Lett. 107 270401 [15] Hu H, Ramachandhran B, Pu H, Liu X J 2012 Phys. Rev. Lett. 108 010402 [16] Wu C, Mondragon-Shem I, Zhou X F 2011 Chin. Phys. Lett. 28 097102 [17] Liu C F, Fan H, Zhang Y C, Wang D S, Liu W M 2012 Phys. Rev. A 86 053616 [18] Xu X Q, Han J H 2011 Phys. Rev. Lett. 107 200401 [19] Zhou X F, Zhou J, Wu C 2011 Phys. Rev. A 84 063624 [20] Zhao L, Yang J, Xie Q Y, Tian M, Duan Y S 2012 Chin. Phys. B 21 057401 [21] Chen A X, Qiu W Y, Wang Z P 2008 Chin. Phys. B 17 4204 [22] Liu C F, Liu W M 2012 Phys. Rev. A 86 033602 [23] Bradley A S, Gardiner C W, Davis M J 2008 Phys. Rev. A 77 033616 [24] Rooney S J, Bradley A S, Blakie P B 2010 Phys. Rev. A 81 023630 [25] Liu C F, Yu Y M, Gou S C, Liu W M 2013 Phys. Rev. A 87 063630 [26] Su S W, Hsueh C H, Liu I K, Horng T L, Tsai Y C, Gou S C, Liu W M 2011 Phys. Rev. A 84 023601 施引文献
The dissertation explores the effects of synthetic spin-orbit coupling on the behaviour of quantum gases in several different contexts. We first study realistic methods to create vortices in spin-orbit-coupled (SOC) Bose-Einstein condensates (BEC). We propose two different methods to induce thermodynamically stable static vortex configurations: (1) to rotate both the Raman lasers and the anisotropic trap; and (2) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. We solve the Gross-Pitaevskii equation for several experimentally relevant regimes and find new interesting effects such as spatial separation of left- and right-moving spin-orbit-coupled condensates, and the appearance of unusual vortex arrangements. Next we consider cold atoms in an optical lattice with synthetic SOC in the Mott-insulator regime. We calculate the parameters of the corresponding tight-binding model and derive the low-energy spin Hamiltonian which is a combination of Heisenberg model, quantum compass model and Dzyaloshinskii-Moriya interaction. We find that the Hamiltonian supports a rich classical phase diagram with collinear, spiral and vortex phases. Next we study the time evolution of the magnetization in a Rashba spin-orbit-coupled Fermi gas, starting from a fully-polarized initial state. We model the dynamics using a Boltzmann equation, which we solve in the Hartree-Fock approximation. The resulting non-linear system of equations gives rise to three distinct dynamical regimes controlled by the ratio of interaction and spin-orbit-coupling strength λ: for small λ, the magnetization decays to zero. For intermediate λ, it displays undamped oscillations about zero and for large λ, a partially magnetized state is dynamically stabilized. Motivated by an interesting stripe phase which appears in BEC with SOC [Li et al., Phys. Rev. Lett. 108, 225301 (2011)], we study the finite-temperature phase diagram of a pseudospin-1/2 Bose gas with contact interactions. We show that strong inter-spin interactions can lead to the appearance of magnetically ordered phases at temperatures above the superfluid transition. For the case of inter-spin attraction, we also discuss the possibility of a bosonic analogue of the Cooper-paired phase, however this state is not energetically favourable. We extend our calculations to a spin-orbit-coupled Bose gas to investigate the possibility of stripe ordering in the normal phase. However, within our approximations, we do not find an instability towards stripe formation. Finally, we consider a two-dimensional Bose gas at zero temperature with an underlying quartic single-particle dispersion in one spatial direction. This Hamiltonian can be realized using the NIST scheme of spin-orbit coupling [Y.-J. Lin, K. Jimenez-Garcia, and I. B. Spielman, Nature 471, 83 (2011)], or using the shaken lattice scheme of Parker et al. [C. V. Parker, L.-C. Ha and C. Chin, Nature Physics 9, 769 (2013)]. By numerically comparing energies of various trial wave-functions, we show that, at low densities, the ground state is strongly correlated, in contrast to a typical mean-field BEC. The trial wave-function with the lowest energy is of Jastrow-type and it describes a state with finite, but strongly reduced, condensate fraction.
We consider the quasi-two-dimensional two-component Bose-Einstein condensates with Rashba spin-orbit (SO) coupling in a rotating trap. The rotation angular velocity couples to the mechanical angular momentum, which contains a noncanonical part arising from SO coupling. The effects of an external Zeeman term favoring spin polarization along the radial direction is also considered, which has the same form as the noncanonical part of the mechanical angular momentum. The rotating condensate exhibits a variety of rich structures by varying the strengths of the trapping potential and interaction. With a strong trapping potential, the condensate exhibits a half-quantum vortex-lattice configuration. Such a configuration is driven to the normal one by introducing the external radial Zeeman field. In the case of a weak trap potential, the condensate exhibits a multidomain pattern of plane-wave states under the external radial Zeeman field.
We present an analysis of two-dimensional (2D) matter-wave solitons, governed by the pseudospinor system of Gross-Pitaevskii equations with self- and cross attraction, which includes the spin-orbit coupling (SOC) in the general Rashba-Dresselhaus form, and, separately, the Rashba coupling and the Zeeman splitting. Families of semivortex (SV) and mixed-mode (MM) solitons are constructed, which exist and are stable in free space, as the SOC terms prevent the onset of the critical collapse and create the otherwise missing ground states in the form of the solitons. The Dresselhaus SOC produces a destructive effect on the vortex solitons, while the Zeeman term tends to convert the MM states into the SV ones, which eventually suffer delocalization. Existence domains and stability boundaries are identified for the soliton families. For physically relevant parameters of the SOC system, the number of atoms in the 2D solitons is limited by ∼1.5×10^{4}. The results are obtained by means of combined analytical and numerical methods.
A finite-size quasi-two-dimensional Bose-Einstein condensate collapses if the attraction between atoms is sufficiently strong. Here we present a theory of collapse for condensates with the interatomic attraction and spin-orbit coupling. We consider two realizations of spin-orbit coupling: the axial Rashba coupling and the balanced, effectively one-dimensional Rashba-Dresselhaus one. In both cases spin-dependent ``anomalous'' velocity, proportional to the spin-orbit-coupling strength, plays a crucial role. For the Rashba coupling, this velocity forms a centrifugal component in the density flux opposite to that arising due to the attraction between particles and prevents the collapse at a sufficiently strong coupling. For the balanced Rashba-Dresselhaus coupling, the spin-dependent velocity can spatially split the initial state in one dimension and form spin-projected wave packets, reducing the total condensate density. Depending on the spin-orbit-coupling strength, interatomic attraction, and initial state, this splitting either prevents the collapse or modifies the collapse process. These results show that the collapse can be controlled by a spin-orbit coupling, thus extending the domain of existence of condensates of attracting atoms.
The Gross–Pitaevskii equation for two-component rotating Bose–Einstein condensates with the Rashba-type spin–orbit (SO) coupling is studied with numerical simulations and variational analyses. A multiquantum vortex state becomes a ground state in a harmonic potential when mutual interaction is absent. When the attractive interaction is strong, the multiquantum vortex state exhibits modulational instability in the azimuthal direction, and a soliton-like state appears. When the repulsive interaction is strong, a vortex lattice state with a multiquantum vortex at the center is created. We find that the vortex lattice state is approximated at a linear combination of multiquantum vortex states.