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Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

Postal Subscription Code 80-965

2018 Impact Factor: 2.483

Front. Phys.    2018, Vol. 13 Issue (5) : 136402    https://doi.org/10.1007/s11467-018-0811-1
RESEARCH ARTICLE
Analytic calculation of high-order corrections to quantum phase transitions of ultracold Bose gases in bipartite superlattices
Zhi Lin1,2(), Wanli Liu1()
1. Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
2. Shenzhen Institute of Research and Innovation, The University of Hong Kong, Shenzhen 518063, China
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Abstract

We clarify some technical issues in the present generalized effective-potential Landau theory (GEPLT) to make the GEPLT more consistent and complete. Utilizing this clarified GEPLT, we analytically study the quantum phase transitions of ultracold Bose gases in bipartite superlattices at zero temperature. The corresponding quantum phase boundaries are analytically calculated up to the third-order hopping, which are in excellent agreement with the quantum Monte Carlo (QMC) simulations.

Keywords ultracold Bose gases      quantum phase transition      bipartite superlattice      generalized effective-potential Landau theory     
Corresponding Author(s): Zhi Lin,Wanli Liu   
Issue Date: 10 July 2018
 Cite this article:   
Zhi Lin,Wanli Liu. Analytic calculation of high-order corrections to quantum phase transitions of ultracold Bose gases in bipartite superlattices[J]. Front. Phys. , 2018, 13(5): 136402.
 URL:  
https://academic.hep.com.cn/fop/EN/10.1007/s11467-018-0811-1
https://academic.hep.com.cn/fop/EN/Y2018/V13/I5/136402
1 M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(De), and U. Sen, Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond, Adv. Phys. 56(2), 243 (2007)
https://doi.org/10.1080/00018730701223200
2 I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80(3), 885 (2008)
https://doi.org/10.1103/RevModPhys.80.885
3 J. Dalibard, F. Gerbier, G. Juzeliunas, and P. Öhberg, Artificial gauge potentials for neutral atoms, Rev. Mod. Phys. 83(4), 1523 (2011)
https://doi.org/10.1103/RevModPhys.83.1523
4 V. Galitski and I. B. Spielman, Spin–orbit coupling in quantum gases, Nature 494(7435), 49 (2013)
https://doi.org/10.1038/nature11841
5 N. Goldman, G. Juzeliunas, P. Öhberg, and I. B. Spielman, Light-induced gauge fields for ultracold atoms, Rep. Prog. Phys. 77(12), 126401 (2014)
https://doi.org/10.1088/0034-4885/77/12/126401
6 H. Zhai, Degenerate quantum gases with spin–orbit coupling: A review,Rep. Prog. Phys. 78(2), 026001 (2015)
https://doi.org/10.1088/0034-4885/78/2/026001
7 A. Eckardt, Atomic quantum gases in periodically driven optical lattices, Rev. Mod. Phys. 89(1), 011004 (2017)
https://doi.org/10.1103/RevModPhys.89.011004
8 I. Buluta and F. Nori, Quantum simulators, Science 326(5949), 108 (2009)
https://doi.org/10.1126/science.1177838
9 I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86(1), 153 (2014)
https://doi.org/10.1103/RevModPhys.86.153
10 C. Gross and I. Bloch, Microscopy of many-body states in optical lattices, Annu. Rev. Cold At. Mol. 3, 181 (2015)
https://doi.org/10.1142/9789814667746_0004
11 M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Boson localization and the superfluidinsulator transition, Phys. Rev. B 40(1), 546 (1989)
https://doi.org/10.1103/PhysRevB.40.546
12 D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Cold bosonic atoms in optical lattices, Phys. Rev. Lett. 81(15), 3108 (1998)
https://doi.org/10.1103/PhysRevLett.81.3108
13 M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature 415(6867), 39 (2002)
https://doi.org/10.1038/415039a
14 T. Lahaye, C. Menotti, L. Santos, M. Lewenstein, and T. Pfau, The physics of dipolar bosonic quantum gases, Rep. Prog. Phys. 72(12), 126401 (2009)
https://doi.org/10.1088/0034-4885/72/12/126401
15 C. Trefzger, C. Menotti, B. Capogrosso-Sansone, and M. Lewenstein, Ultracold dipolar gases in optical lattices, J. Phys. At. Mol. Opt. Phys. 44(19), 193001 (2011)
https://doi.org/10.1088/0953-4075/44/19/193001
16 A. Lauer, D. Muth, and M. Fleischhauer, Transportinduced melting of crystals of Rydberg dressed atoms in a one-dimensional lattice, New J. Phys. 14(9), 095009 (2012)
https://doi.org/10.1088/1367-2630/14/9/095009
17 P. Schauß, M. Cheneau, M. Endres, T. Fukuhara, S. Hild, A. Omran, T. Pohl, C. Gross, S. Kuhr, and I. Bloch, Observation of spatially ordered structures in a two-dimensional Rydberg gas, Nature 491(7422), 87 (2012)
https://doi.org/10.1038/nature11596
18 A. Safavi-Naini, S. G. Soyler, G. Pupillo, H. R. Sadeghpour, and B. Capogrosso-Sansone, Quantum phases of dipolar bosons in bilayer geometry, New J. Phys. 15(1), 013036 (2013)
https://doi.org/10.1088/1367-2630/15/1/013036
19 E. Altman, W. Hofstetter, E. Demler, and M. D. Lukin, Phase diagram of two-component bosons on an optical lattice, New J. Phys. 5, 113 (2003)
https://doi.org/10.1088/1367-2630/5/1/113
20 P. Soltan-Panahi, D. Lühmann, J. Struck, P. Windpassinger, and K. Sengstock, Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices, Nat. Phys. 8(1), 71 (2012)
21 A. Eckardt, P. Hauke, P. Soltan-Panahi, C. Becker, K. Sengstock, and M. Lewenstein, Frustrated quantum antiferromagnetism with ultracold bosons in a triangular lattice, Europhys. Lett. 89(1), 10010 (2010)
https://doi.org/10.1209/0295-5075/89/10010
22 S. Pielawa, E. Berg, and S. Sachdev, Frustrated quantum Ising spins simulated by spinless bosons in a tilted lattice: From a quantum liquid to antiferromagnetic order, Phys. Rev. B 86(18), 184435 (2012)
https://doi.org/10.1103/PhysRevB.86.184435
23 J. Ye, K. Zhang, Y. Li, Y. Chen, and W. Zhang, Optical Bragg, atomic Bragg and cavity QED detections of quantum phases and excitation spectra of ultracold atoms in bipartite and frustrated optical lattices,Ann. Phys. 328, 103 (2013)
https://doi.org/10.1016/j.aop.2012.09.006
24 S. Peil, J. V. Porto, B. Laburthe Tolra, J. M. Obrecht, B. E. King, M. Subbotin, S. L. Rolston, and W. D. Phillips, Patterned loading of a Bose–Einstein condensate into an optical lattice, Phys. Rev. A 67, 051603(R) (2003)
25 J. Sebby-Strabley, M. Anderlini, P. S. Jessen, and J. V. Porto, Lattice of double wells for manipulating pairs of cold atoms, Phys. Rev. A 73(3), 033605 (2006)
https://doi.org/10.1103/PhysRevA.73.033605
26 S. Fölling, S. Trotzky, P. Cheinet, M. Feld, R. Saers, A. Widera, T. Müller, and I. Bloch, Direct observation of second-order atom tunnelling, Nature 448(7157), 1029 (2007)
https://doi.org/10.1038/nature06112
27 P. Cheinet, S. Trotzky, M. Feld, U. Schnorrberger, M. Moreno-Cardoner, S. Fölling, and I. Bloch, Counting atoms using interaction blockade in an optical superlattice, Phys. Rev. Lett. 101(9), 090404 (2008)
https://doi.org/10.1103/PhysRevLett.101.090404
28 G. B. Jo, J. Guzman, C. K. Thomas, P. Hosur, A. Vishwanath, and D. M. Stamper-Kurn, Ultracold atoms in a tunable optical Kagome lattice, Phys. Rev. Lett. 108(4), 045305 (2012)
https://doi.org/10.1103/PhysRevLett.108.045305
29 O. Dutta, M. Gajda, P. Hauke, M. Lewenstein, D. S. Lühmann, B. A. Malomed, T. Sowinski, and J. Zakrzewski, Non-standard Hubbard models in optical lattices: A review, Rep. Rrog. Phys. 78(6), 066001 (2015)
https://doi.org/10.1088/0034-4885/78/6/066001
30 M. Boninsegni and N. V. Prokof’ev, Supersolids: What and where are they? Rev. Mod. Phys. 84(2), 759 (2012)
https://doi.org/10.1103/RevModPhys.84.759
31 A. B. Kuklov and B. V. Svistunov, Counterflow superfluidity of two-species ultracold atoms in a commensurate optical lattice, Phys. Rev. Lett. 90(10), 100401 (2003)
https://doi.org/10.1103/PhysRevLett.90.100401
32 V. G. Rousseau, D. P. Arovas, M. Rigol, F. Hebert, G. G. Batrouni, and R. T. Scalettar, Exact study of the one-dimensional boson Hubbard model with a superlattice potential, Phys. Rev. B 73(17), 174516 (2006)
https://doi.org/10.1103/PhysRevB.73.174516
33 G. Roux, T. Barthel, I. P. McCulloch, C. Kollath, U. Schollwöck, and T. Giamarchi, Quasiperiodic Bose–Hubbard model and localization in one-dimensional cold atomic gases, Phys. Rev. A 78(2), 023628 (2008)
https://doi.org/10.1103/PhysRevA.78.023628
34 A. Dhar, T. Mishra, R. V. Pai, and B. P. Das, Quantum phases of ultracold bosonic atoms in a one-dimensional optical superlattice, Phys. Rev. A 83(5), 053621 (2011)
https://doi.org/10.1103/PhysRevA.83.053621
35 P. Buonsante and A. Vezzani, Phase diagram for ultracold bosons in optical lattices and superlattices, Phys. Rev. A 70(3), 033608 (2004)
https://doi.org/10.1103/PhysRevA.70.033608
36 J. M. Hou, Quantum phases of ultracold bosonic atoms in a two-dimensional optical superlattice, Mod. Phys. Lett. B 23(01), 25 (2009)
https://doi.org/10.1142/S0217984909017820
37 B. L. Chen, S. P. Kou, Y. Zhang, and S. Chen, Quantum phases of the Bose–Hubbard model in optical superlattices, Phys. Rev. A 81(5), 053608 (2010)
https://doi.org/10.1103/PhysRevA.81.053608
38 A. Dhar, M. Singh, R. V. Pai, and B. P. Das, Meanfield analysis of quantum phase transitions in a periodic optical superlattice, Phys. Rev. A 84(3), 033631 (2011)
https://doi.org/10.1103/PhysRevA.84.033631
39 P. Buonsante, V. Penna, and A. Vezzani, Analytical mean-field approach to the phase-diagram of ultracold bosons in optical superlattices, Laser Phys. 15(2), 361 (2005)
40 D. Muth, A. Mering, and M. Fleischhauer, Ultracold bosons in disordered superlattices: Mott insulators induced by tunneling, Phys. Rev. A 77(4), 043618 (2008)
https://doi.org/10.1103/PhysRevA.77.043618
41 P. Pisarski, R. M. Jones, and R. J. Gooding, Application of a multisite mean-field theory to the disordered Bose–Hubbard model, Phys. Rev. A 83(5), 053608 (2011)
https://doi.org/10.1103/PhysRevA.83.053608
42 T. McIntosh, P. Pisarski, R. J. Gooding, and E. Zaremba, Multisite mean-field theory for cold bosonic atoms in optical lattices, Phys. Rev. A 86(1), 013623 (2012)
https://doi.org/10.1103/PhysRevA.86.013623
43 P. Buonsante and A. Vezzani, Cell strong-coupling perturbative approach to the phase diagram of ultracold bosons in optical superlattices, Phys. Rev. A 72(1), 013614 (2005)
https://doi.org/10.1103/PhysRevA.72.013614
44 P. Buonsante, V. Penna, and A. Vezzani, Phase coherence, visibility, and the superfluid–Mott-insulator transition on one-dimensional optical lattices, Phys. Rev. A 72, 031602(R) (2005)
45 Z. Lin, J. Zhang, and Y. Jiang, Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green’s function method, Front. Phys. 13(4), 136401 (2018)
https://doi.org/10.1007/s11467-018-0751-9
46 J. Zhang and Y. Jiang, Quantum phase diagrams and time-of-flight pictures of spin-1 Bose systems in honeycomb optical lattices, Laser Phys. 26(9), 095501 (2016)
https://doi.org/10.1088/1054-660X/26/9/095501
47 F. Wei, J. Zhang, and Y. Jiang, Quantum phase diagram and time-of-flight absorption pictures of an ultracold Bose system in a square optical superlattice, Europhys. Lett. 113, 16004 (2016)
https://doi.org/10.1209/0295-5075/113/16004
48 T. Wang, X. F. Zhang, S. Eggert, and A. Pelster, Generalized effective-potential Landau theory for bosonic quadratic superlattices, Phys. Rev. A 87(6), 063615 (2013)
https://doi.org/10.1103/PhysRevA.87.063615
49 Z. Lin, J. Zhang, and Y. Jiang, Quantum phase transitions of ultracold Bose systems in nonrectangular optical lattices, Phys. Rev. A 85(2), 023619 (2012)
https://doi.org/10.1103/PhysRevA.85.023619
50 S. Paul and E. Tiesinga, Formation and decay of Bose–Einstein condensates in an excited band of a double-well optical lattice, Phys. Rev. A 88(3), 033615 (2013)
https://doi.org/10.1103/PhysRevA.88.033615
51 F. E. A. dos Santos and A. Pelster, Quantum phase diagram of bosons in optical lattices, Phys. Rev. A 79(1), 013614 (2009)
https://doi.org/10.1103/PhysRevA.79.013614
52 N. Teichmann, D. Hinrichs, M. Holthaus, and A. Eckardt, Process-chain approach to the Bose–Hubbard model: Ground-state properties and phase diagram, Phys. Rev. B 79(22), 224515 (2009)
https://doi.org/10.1103/PhysRevB.79.224515
53 N. Teichmann, D. Hinrichs, and M. Holthaus, Reference data for phase diagrams of triangular and hexagonal bosonic lattices, Europhys. Lett. 91(1), 10004 (2010)
https://doi.org/10.1209/0295-5075/91/10004
54 M. Iskin, Route to supersolidity for the extended Bose–Hubbard model, Phys. Rev. A 83, 051606(R) (2011)
55 M. Di Liberto, T. Comparin, T. Kock, M. Ölschläger, A. Hemmerich, and C. M. Smith, Controlling coherence via tuning of the population imbalance in a bipartite optical lattice, Nat. Commun. 5(1), 5735 (2014)
https://doi.org/10.1038/ncomms6735
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