Analytic calculation of high-order corrections to quantum phase transitions of ultracold Bose gases in bipartite superlattices

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

References

[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)

[2] I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80(3), 885 (2008)

[3] J. Dalibard, F. Gerbier, G. Juzeliunas, and P. Öhberg, Artificial gauge potentials for neutral atoms, Rev. Mod. Phys. 83(4), 1523 (2011)

[4] V. Galitski and I. B. Spielman, Spin–orbit coupling in quantum gases, Nature 494(7435), 49 (2013)

[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)

[6] H. Zhai, Degenerate quantum gases with spin–orbit coupling: A review,Rep. Prog. Phys. 78(2), 026001 (2015)

[7] A. Eckardt, Atomic quantum gases in periodically driven optical lattices, Rev. Mod. Phys. 89(1), 011004 (2017)

[8] I. Buluta and F. Nori, Quantum simulators, Science 326(5949), 108 (2009)

[9] I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86(1), 153 (2014)

[10] C. Gross and I. Bloch, Microscopy of many-body states in optical lattices, Annu. Rev. Cold At. Mol. 3, 181 (2015)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[30] M. Boninsegni and N. V. Prokof’ev, Supersolids: What and where are they? Rev. Mod. Phys. 84(2), 759 (2012)

[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)

[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)

[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)

[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)

[35] P. Buonsante and A. Vezzani, Phase diagram for ultracold bosons in optical lattices and superlattices, Phys. Rev. A 70(3), 033608 (2004)

[36] J. M. Hou, Quantum phases of ultracold bosonic atoms in a two-dimensional optical superlattice, Mod. Phys. Lett. B 23(01), 25 (2009)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[51] F. E. A. dos Santos and A. Pelster, Quantum phase diagram of bosons in optical lattices, Phys. Rev. A 79(1), 013614 (2009)

[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)

[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)

[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)

RIGHTS & PERMISSIONS

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature