深圳大学学报理工版

利用密度矩阵重整化群(density-matrix-renormalization-group,DMRG)方法,研究自旋轨道耦合和Zeeman场作用下处于一维光学晶格中的排斥费米气体的量子相变.研究表明,当自旋轨道耦合与Zeeman场共同作用于系统时,自旋轨道耦合效应将增强系统的金属性,同时削弱Zeeman场对系统的极化作用.当自旋轨道耦合作用较弱使系统保持为Mott绝缘态时,随自旋轨道耦合强度的变化,Zeeman场的极化效应使系统呈现不同的量子态.

By using the density-matrix-renormalization-group(DMRG)method, the phase transition of ultra-cold repulsive Fermi gases loaded on one-dimensional optical lattices is investigated when spin-orbit coupling(SOC)and Zeeman field are involved. It is found that the SOC effects enhance the metal phase and reduce the polarization of the system in the presence of both the SOC and a large Zeeman field. Furthermore, when the system keeps a Mott insulation state under the weak spin orbit coupling, it is shown at different SOC strengths, the system appears as different quantum states due to the polarization effect of Zeeman field.

引言
1 理论模型
2 模拟结果及分析
3 结语

图1 自旋轨道耦合与Zeeman场作用在金属态上ni、n↑、n↓、n↑-n↓及Δi的变化 <br/>Fig.1 The distribution of particle density and variance of the local density with SOC and Zeeman field on the metallic phase

图1 自旋轨道耦合与Zeeman场作用在金属态上ni、n↑、n↓、n↑-n↓及Δi的变化
Fig.1 The distribution of particle density and variance of the local density with SOC and Zeeman field on the metallic phase

图2 自旋轨道耦合与Zeeman场作用在Mott绝缘态上ni、n↑、n↓、n↑-n↓以及Δi的变化<br/>Fig.2 The distribution of particle density and variance of the local density with SOC and Zeeman field on the Mott insulator phase

图2 自旋轨道耦合与Zeeman场作用在Mott绝缘态上ni、n↑、n↓、n↑-n↓以及Δi的变化
Fig.2 The distribution of particle density and variance of the local density with SOC and Zeeman field on the Mott insulator phase

图3 自旋轨道耦合与Zeeman场作用在金属—绝缘态上ni、n↑、n↓、n↑-n↓以及Δi的变化<br/>Fig.3 The distribution of particle density and varianceof the local density with SOC and Zeeman field on the metallic and insulator phase

图3 自旋轨道耦合与Zeeman场作用在金属—绝缘态上ni、n↑、n↓、n↑-n↓以及Δi的变化
Fig.3 The distribution of particle density and varianceof the local density with SOC and Zeeman field on the metallic and insulator phase

图4 自旋轨道耦合对相变临界值Uc的影响<br/>Fig.4 The influence of spin-orbit interaction on the critical value Uc of phase transition

图4 自旋轨道耦合对相变临界值Uc的影响
Fig.4 The influence of spin-orbit interaction on the critical value Uc of phase transition

图5 极化率P和熵S随λ的变化 <br/>Fig.5 Variance of the P and S with λ(L = 30, N = 20,U = 8, V = 15)

图5 极化率P和熵S随λ的变化
Fig.5 Variance of the P and S with λ(L = 30, N = 20,U = 8, V = 15)

图6 系统粒子数密度分布随λ的变化<br/>Fig.6 Variance of the with λ

图6 系统粒子数密度分布随λ的变化
Fig.6 Variance of the with λ

[1] Anderson M H, Ensher J R, Matthews M R. Observation of Bose-Einstein condensation in a dilute stomic vapor[J]. Science, 1995, 269(5221): 198-201.
[2] Davis K B, Mewes M O, Andrews M R, et al. Bose-Einstein condensation in a gas of sodium atoms[J]. Physical Review Letters, 1995, 75(22):3969-3973.
[3] Bradley C C, Sackett C A, Tollett J J, et al. Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions[J]. Physical Review Letters, 1995, 75: 1687-1690.
[4] O'Hara K M, Hemmer S L, Gehm M E, et al. Observation of a strongly interacting degenerate Fermi gas of atoms[J]. Science, 2002, 298(5061): 2179-2182.
[5] Zwierlein M W, Stan C A, Schunck C H, et al. Observation of Bose-Einstein condensation of molecules[J]. Physical Review Letters, 2003, 91(25): 250401-1-250401-5.
[6] Gong Ming, Chen Gang, Jia Suotang, et al. Searching for majorana fermions in 2D spin-orbit coupled Fermi superfluids at finite temperature[J]. Physical Review Letters, 2012,109(10): 105302-1-105302- 6.
[7] Iskin M, Subasi A L. Topological superfluid phases of an atomic Fermi gas with in- and out-of-plane Zeeman fields and equal Rashba-Dresselhaus spin-orbit coupling[J]. Physical Review A, 2013, 87(06): 063627-1- 063627-5.
[8] Seo K, Han L. Emergence of majorana and Dirac particles in ultracold fermions via tunable interactions, spin-orbit effects, and Zeeman fields[J]. Physical Review Letters, 2012, 109(10): 105303-1-105303-5.
[9] Hu Hui, Jiang Lei, Han Pu, et al. Universal impurity-induced bound state in topological superfluids[J]. Physical Review Letters, 2013, 110(2): 020401-1- 020401-5.
[10] Xiong Hongwei, Lu Baolong, Liu Shujuan, et al. New advances in ultracold Fermi gases[J]. Progress in Physics, 2005, 25(3): 296-316.(in Chinese)
[11] Wan Langhui,Wang Bin,Wei Yadong.Nonlinear thermoelectric transport of carbon nanotube[J]. Journal of Shenzhen University Science and Engineering, 2009, 26(4):356-359.(in Chinese)
[12] Liang Junjun,Zhou Xiaofan,Chui Pak Hong,et al.Spin-orbit coupling induced unconventional pairings in a one-dimensional lattice [J]. Theoretical Model, 2013, 1404.3009v1.
[13] Li Xiaolei, Liang Junjun. Suoerfluidity in a trappped gas of repulsive Fermi gases loaded on an optical lattice[J]. Journal of Shanxi University Natural Science Edition, 2013, 36(2): 204-207.(in Chinese)
[14] Chen Ahai, Gao Xianlong. Pure Fulde-Ferrell-Larkin ovchinnikov state in optical lattices[J]. Physical Review B, 2012, 85(13):134203-1-134203-5.
[15] Chen Ahai, Gao Xianlong. Phase separation in optical lattices in a spin-dependent external potential[J]. Physical Review A, 2010, 81(1): 013628-1- 013628- 6.
[16] Chen Gang, Gong Ming, Zhang Chuanwei. BCS-BEC crossover in spin-orbit-coupled two-dimensional Fermi gases[J]. Physical Review A, 2012, 85(1): 013601-1- 013601- 6.
[17] Rigol M, Muramatsu A, Batrouni G G, et al. Local quantum criticality in confined fermions on optical lattices[J]. Physical Review Letters, 2003, 91(13): 130403-1-130403-4.
[18] Machida M, Okumura M, Yamada S, et al. Mott phase in polarized two-component atomic Fermi lattice gas[J]. Physical Review B, 2008, 78(23): 235117-1-235117-5.
[19] Zhang Jinyi, Ji Sicong, Chen Zhu, et al. Collective dipole oscillations of a spin-orbit coupled bose-einstein conden[J]. Physical Review Letters, 2012, 109(11): 115301-1-115301-5.
[20] Qu Chunlei, Hamner C, Gong Ming, et al. Observation of Zitterbewegung in a spin-orbit-coupled Bose-Einstein condensate[J]. Physical Review A, 2013, 88(2): 021604-1- 021604-5.
[21] Wang Pengjun, Yu Zengqiang, Fu Zhengkun, et al. Spin-orbit coupled degenerate Fermi gases[J]. Physical Review Letters, 2012, 109(9): 095301-1- 095301-5.
[22] Williams R A, Beeler M C, LeBlanc L J, et al. Raman-induced interactions in a single-component Fermi gas near an s-wave feshbach resonance[J]. Physical Review Letters, 2013,111(9): 095301-1- 095301-5.
[23] Cheuk L W, Sommer A T, Hadzibabic Z, et al. Spin-injection spectroscopy of a spin-orbit coupled Fermi gas[J]. Physical Review Letters, 2012, 109(9): 095302-1- 095302-5.
[24] Zhang Chuanwei, Sumanta Tewari, Roman M, et al. px+ipy superfluid from s-wave interactions of fermionic cold atoms[J]. Physical Review Letters, 2008, 101(16): 160401-1-160401-4.
[25] Liu Xiaji, Hu Hui. Topological Fulde-Ferrell superfluid in spin-orbit-coupled atomic Fermi gases[J]. Physical Review A, 2013, 88(2): 023622-1- 023622-5.
[26] Fulde P, Ferrell R A. Superconductivity in a strong spin-exchange field[J]. Physical Review, 1964, 135(3A): A550-A562.

备注

引言

1 理论模型

2 模拟结果及分析

3 结语

期刊信息

备注

引言

1 理论模型

2 模拟结果及分析

3 结 语

期刊信息

3 结语