Abstract
The Hubbard model was originally developed to describe electrons in narrow conduction bands [17]. Its bosonic version, the Bose-Hubbard model [8], yields a very good description of ultracold bosonic atoms trapped in deep optical lattices, as first noted in Ref. [19]. The model shows a phase transition at zero temperature from a superfluid to a Mott-insulating phase, which forms one of the paradigm examples of a quantum phase transition [27].
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Altland A, Simons B (2006) Condensed matter field theory. Cambridge University Press, Cambridge. ISBN 0521845084
Ashcroft NW, Mermin ND (1976) Solid state physics. Saunders, Philadelphia. ISBN 0030839939
Bakr WS, Peng A, Tai ME, Ma R, Simon J, Gillen JI, Fölling S, Pollet L, Greiner M (2010) Probing the superfluid-to-Mott insulator transition at the single-atom level. Science 329:547–550
Bloch I, Dalibard J, Zwerger W (2008) Many-body physics with ultracold gases. Rev Mod Phys 80:885–964
Capogrosso-Sansone B, Prokof’ev N, Svistunov B (2007) Phase diagram and thermodynamics of the three-dimensional Bose-Hubbard model. Phys Rev B 75:134302
Capogrosso-Sansone B, Söyler S, Prokof’ev N, Svistunov B (2008) Monte Carlo study of the two-dimensional Bose-Hubbard model. Phys Rev A 77:015602
Dalibard J (1999) Collisional dynamics of ultra-cold atomic gases. In: Proceedings of the International School of Physics-Enrico Fermi, vol 321
Fisher MPA, Weichman PB, Grinstein G, Fisher DS (1989) Boson localization and the superfluid-insulator transition. Phys Rev B 40:546–570
Fölling S (2008) Probing strongly correlated states of ultracold atoms in optical lattices. PhD thesis, Johannes-Gutenberg-Universität Mainz, Mainz
Gerbier F (2007) Boson Mott insulators at finite temperatures. Phys Rev Lett 99:120405
Gerry C, Knight P (2004) Introductory quantum optics. Cambridge University Press, Cambridge. ISBN 052152735X
Glauber R (1963) Coherent and incoherent states of the radiation field. Phys Rev 131:2766–2788
Greiner M (2003) Ultracold quantum gases in three-dimensional optical lattice potentials. PhD thesis, Ludwig-Maximilians-Universität München, München
Greiner M, Mandel O, Esslinger T, Hänsch TW, Bloch I (2002) Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415:39–44
Grimm R, Weidemüller M, Ovchinnikov YB (2000) Optical dipole traps for neutral atoms. Adv Atom Mol Opt Phys 42:95–170
Haas M, Jentschura UD, Keitel CH (2006) Comparison of classical and second quantized description of the dynamic stark shift. Am J Phys 74:77
Hubbard J (1963) Electron correlations in narrow energy bands. Proc R Soc A 276:238–257
Huber SD, Altman E, Buchler HP, Blatter G (2007) Dynamical properties of ultracold bosons in an optical lattice. Phys Rev B 75:85106
Jaksch D, Bruder C, Cirac JI, Gardiner C, Zoller P (1998) Cold bosonic atoms in optical lattices. Phys Rev Lett 81:3108–3111
Kashurnikov V, Svistunov B (1996) Exact diagonalization plus renormalization-group theory: accurate method for a one-dimensional superfluid-insulator-transition study. Phys Rev B 53:11776–11778
Kohn W (1959) Analytic properties of bloch waves and wannier functions. Phys Rev 115:809–821
Kühner TD, White SR, Monien H (2000) One-dimensional Bose-Hubbard model with nearest-neighbor interaction. Phys Rev B 61:12474–12489
Leggett A (2006) Quantum liquids: Bose condensation and cooper pairing in condensed-matter systems. Oxford University Press, USA
Menotti C, Trivedi N (2008) Spectral weight redistribution in strongly correlated bosons in optical lattices. Phys Rev B 77:235120
I. A. S. Milton Abramowitz (1972) Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover Publications, New York. ISBN 0486612724
Pethick CJ, Smith H (2001) Bose-Einstein condensation in dilute gases. Cambridge University Press, Cambridge
Sachdev S (2011) Quantum phase transitions. Cambridge University Press, Cambridge, 2nd edn. ISBN 0521514681
Sherson JF, Weitenberg C, Endres M, Cheneau M, Bloch I, Kuhr S (2010) Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467:68–72
Trotzky S, Pollet L, Gerbier F, Schnorrberger U, Bloch I, Prokofev NV, Svistunov B, Troyer M (2010) Suppression of the critical temperature for superfluidity near the Mott transition. Nat Phys 6:998–1004
Van Kempen EGM, Kokkelmans SJJMF, Heinzen DJ, Verhaar BJ (2002) Interisotope determination of ultracold rubidium interactions from three high-precision experiments. Phys Rev Lett 88:093201
van Oosten D (2004) Quantum gases in optical lattices: the atomic Mott insulator. PhD thesis, Universiteit Utrecht, Utrecht
Wannier G (1937) The structure of electronic excitation levels in insulating crystals. Phys Rev 52:191–197
Wessel S, Alet F, Troyer M, Batrouni G (2004) Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices. Phys Rev A 70:053615
Will S (2011) Interacting bosons and fermions in three-dimensional optical lattice potentials. PhD thesis, Johannes Gutenberg-Universität Mainz, Mainz
Zwerger W (2003) Mott-Hubbard transition of cold atoms in optical lattices. J Opt B Quantum Semiclass 5:9–16
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Endres, M. (2014). Superfluid-Mott-Insulator Transition. In: Probing Correlated Quantum Many-Body Systems at the Single-Particle Level. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-05753-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-05753-8_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05752-1
Online ISBN: 978-3-319-05753-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)