正方光学超晶格中超冷玻色子系统的量子相变
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摘要
文章利用推广的有效势方法,在金兹堡朗道场论的框架下给出了正方光学超晶格中超冷玻色子系统莫特绝缘态/密度波态到超流态的量子相变的相界方程,并利用瑞利-薛定谔微扰理论的加藤表示,结合过程链算法对该相界方程进行了定量求解,给出了最高为6-阶微扰下的全域相图。对这些通过微扰计算得到的数据进行分析,借助于线性拟合外推技术,进一步将相图计算结果推广到无穷阶微扰的情形,得到了更加精确的相图。这一理论计算结果可以用来为相关实验及数值计算提供相应的理论参考。
The quantum phase transition of ultracold Bose gases in an optical superlattice is investigated within the framework of the Ginzburg-Landau field theory.By combining Kato representation of RayleighSchr9 dinger perturbation theory and process chain algorithm,the phase boundary between superfluid state and Mott-insulating/density-wave state is determined in the whole parameter space with high accuracy.Based on the approximations up to 6th order,an infinite order perturbation data is obtained using linear fit extrapolation technique.This global phase diagram with different filling factors can be a useful reference object for both experimental and theoretical studies in the future.
The quantum phase transition of ultracold Bose gases in an optical superlattice is investigated within the framework of the Ginzburg-Landau field theory.By combining Kato representation of RayleighSchr9 dinger perturbation theory and process chain algorithm,the phase boundary between superfluid state and Mott-insulating/density-wave state is determined in the whole parameter space with high accuracy.Based on the approximations up to 6th order,an infinite order perturbation data is obtained using linear fit extrapolation technique.This global phase diagram with different filling factors can be a useful reference object for both experimental and theoretical studies in the future.
引文
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[2] Bloch I,Dalibard J,Zwerger W.Many-body Physics with Ultracold Gases[J].Reviews of Modern Physics,2008,80:885-964.DOI:10.1103/RevModPhys.80.885.
[3] Lewenstein M,Sanpera A,Ahufinger V,et al.Ultracold Atomic Gases in Optical Lattices:mimicking Condensed Matter Physics and Beyond[J].Advances in Physics,2007,56:243-379.DOI:10.1080/00018730701223200.
[4] Lewenstein M,Sanpera A,Ahufinger V.Ultracold Atoms in Optical Lattices:Simulating Quantum Many Body Systems[M].Oxford:Oxford University Press,2012.
[5] Jaksch D,Bruder C,Cirac J I,et al.Cold Bosonic Atoms in Optical Lattices[J].Physical Review Letters,1998,81:3108-3111.DOI:10.1103/PhysRevLett.81.3108.
[6] Jaksch D,Zoller P.The Cold Atom Hubbard Toolbox[J].Annals of Physics,2005,315:52-79.DOI:10.1016/j.aop.2004.09.010.
[7] Fisher M P A,Weichman P B,Grinstein G,et al.Boson Localization and the Superfluid-insulator Transition[J].Physical Review B,1989,40:546-570.DOI:10.1103/PhysRevB.40.546.
[8] Amico L,Penna V.Dynamical Mean Field Theory of the Bose-Hubbard Model[J].Physical Review Letters,1998,80:2189-2192.DOI:10.1103/PhysRevLett.80.2189.
[9] Freericks J K,Monien H.Strong-coupling Expansions for the Pure and Disordered Bose-Hubbard Model[J].Physical Review B,1996,53:2691-2700.DOI:10.1103/PhysRevB.53.2691.
[10] Capogrosso-Sansone B,Prokof′ev N V,Svistunov B V.Phase Diagram and Thermodynamics of the Three-dimensional Bose-Hubbard Model[J].Physical Review B,2007,75:134302.DOI:10.1103/PhysRevB.75.134302.
[11] dos Santos F E A,Pelster A.Quantum Phase Diagram of Bosons in Optical Lattices[J].Physical Review A,2009,79:013614.DOI:10.1103/PhysRevA.79.013614.
[12] Lin Z,Zhang J,Jiang Y.Quantum Phase Transitions of Ultracold Bose Systems in Nonrectangular Optical Lattices[J].Physical Review A,2012,85:023619.DOI:10.1103/PhysRevA.85.023619.
[13] Kato T.On the Convergence of the Perturbation Method[J].Progress of Theoretical Physics,1949,5:95-101.DOI:10.1143/ptp/5.1.95.
[14] Eckardt A.Process Chain Approach to High-order Perturbation Calculus for Quantum Lattice Models[J].Physical Review B,2009,79:195131.DOI:10.1103/PhysRevB.79.195131.
[15] Teichmann N,Hinrichs D,Holthaus M,et al.Process-chain Approach to the Bose-Hubbard Model:Ground-state Properties and Phase Diagram[J].Physical Review B,2009,79:224515.DOI:10.1103/PhysRevB.79.224515.
[16] Becker C,Soltanpanahi P,et al.Ultracold Quantum Gases in Triangular Optical Lattices[J].New Journal of Physics,2010,12:065025.DOI:10.1088/1367-2630/12/6/065025.
[17] Soltanpanahi P,Struck J,Hauke P,et al.Multi-component Quantum Gases in Spin-dependent Hexagonal Lattices[J].Nature Physics,2011,7:434-440.DOI:10.1038/nphys1916.
[18] Jo G B,Guzman J,Thomas C K,et al.Ultracold Atoms in a Tunable Optical Kagome Lattice[J].Physical Review Letters,2012,108:045305.DOI:10.1103/PhysRevLett.108.045305.
[19] Lahaye T,Menotti C,Santos L,et al.The Physics of Dipolar Bosonic Quantum Gases[J].Reports on Progress in Physics,2009,72:126401.DOI:10.1088/0034-4885/72/12/126401.
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[24] Chen B L,Kou S P,Zhang Y,et al.Quantum Phases of the Bose-Hubbard Model in Optical Superlattices[J].Physical Review A,2010,81:053608.DOI:10.1103/PhysRevA.81.053608.
[25] Thomas C K,Barter T H,Leung T H,et al.Mean-Field Scaling of the Superfluid to Mott Insulator Transition in a 2D Optical Superlattice[J].Physical Review Letters,2017,119:100402.DOI:10.11-3/PhysRevLett.119.100402.
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[27] Zhang W,Sun H,Xu P,et al.Efficient Generation of Many-body Singlet States of Spin-1Bosons[J].Physical Review A,2017,95:063624.DOI:10.1103/PhysRevA.95.063624.
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[31] Buonsante P,Vezzani A.Phase Diagram for Ultracold Bosons in Optical Lattices and Superlattices[J].Physical Review A,2004,70:033608.DOI:10.1103/PhysRevA.70.033608.
[32] Wei F,Zhang J,Jiang Y.Quantum Phase Diagram and Time-of-flight Absorption Pictures of Ultracold Bose System in a Square Optical Superlattice[J].EPL,2016,113:16004.DOI:10.1209/0295-5075/113/16004.
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[34] Lin Z,Liu W.Analytic Calculations of High-order Corrections to Quantum Phase Transition of Ultracold Bose Gases in Bipartite Superlattices[J].Front Phys,2018,13:136402.DOI:10.1007/s11467-018-0811-1.
[35] Oosten D V,Straten P V D,Stoof H T C.Quantum Phases in an Optical Lattice[J].Physical Review A,2001,63:053601.DOI:10.1103/PhysRevA.63.053601.
[36] Kleinert H,Schulte-Frohlinde V.Critical Properties of4-Theories[M].Singapore:World Scientific,2001.
[37] Justin J Z.Quantum Field Theory and Critical Phenomena[M].New York:Oxford University Press,2002.DOI:10.1093/acprof:oso/9780198509233.001.0001.