Mott-Hubbard transition of cold atoms in optical lattices

We discuss the superfluid (SF) to Mott-insulator transition of cold atoms in optical lattices recently observed by Greiner et al (2002 Nature 415 39). The fundamental properties of both phases and their experimental signatures ar ed iscussed carefully, including the limitations of the standard Gutzwiller approximation. It is shown that in a one-dimensional dilute Bose-gas with a strong transverse confinement (Tonks-gas), even an arbitrary weak optical lattice is able to induce a Mott-like state with crystalline order, provided the dimensionless interactio np arameter is larger than a critical value of order one. The SF–insulator transition of the Bose–Hubbard model in this case continuously evolves into a transition of the commensurate–incommensurate type with decreasing strength of the external optical lattice.

[1]  Immanuel Bloch,et al.  Collapse and revival of the matter wave field of a Bose–Einstein condensate , 2002, Nature.

[2]  A. Arnold,et al.  Adaptive inelastic magnetic mirror for Bose-Einstein condensates , 2001, cond-mat/0103586.

[3]  Bradley,et al.  Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions. , 1995, Physical review letters.

[4]  J. Cirac,et al.  High-temperature superfluidity of fermionic atoms in optical lattices. , 2002, Physical review letters.

[5]  Robin Kaiser,et al.  Coherent atomic matter waves , 2001 .

[6]  T. Hänsch,et al.  Measurement of the spatial coherence of a trapped Bose gas at the phase transition , 2000, Nature.

[7]  W. Ketterle,et al.  Observation of Interference Between Two Bose Condensates , 1997, Science.

[8]  D. Rokhsar,et al.  Gutzwiller projection for bosons. , 1991, Physical review. B, Condensed matter.

[9]  F. Dalfovo,et al.  Theory of Bose-Einstein condensation in trapped gases , 1998, cond-mat/9806038.

[10]  Carl E. Wieman,et al.  Atom–molecule coherence in a Bose–Einstein condensate , 2002, Nature.

[11]  C. Gardiner,et al.  Cold Bosonic Atoms in Optical Lattices , 1998, cond-mat/9805329.

[12]  E. Lieb.  Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum , 1963 .

[13]  Density matrix renormalization group for disordered bosons in one dimension , 1999, cond-mat/9901080.

[14]  M. Girardeau.  Comment on “Particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas” , 1998 .

[15]  A. Leggett,et al.  Bose-Einstein condensation in the alkali gases: Some fundamental concepts , 2001 .

[16]  Walter Kohn,et al.  Analytic Properties of Bloch Waves and Wannier Functions , 1959 .

[17]  P. Zoller,et al.  Entanglement of Atoms via Cold Controlled Collisions , 1998, quant-ph/9810087.

[18]  J. Cirac,et al.  Creation of a molecular condensate by dynamically melting a Mott insulator. , 2002, Physical review letters.

[19]  R Raussendorf,et al.  A one-way quantum computer. , 2001, Physical review letters.

[20]  H. R. Krishnamurthy,et al.  Superfluid and insulating phases in an interacting-boson model: mean-field theory and the RPA , 1993 .

[21]  T. D. Kuehner,et al.  Phases of the one-dimensional Bose-Hubbard model , 1997, cond-mat/9712307.

[22]  F. Haldane,et al.  Effective Harmonic-Fluid Approach to Low-Energy Properties of One-Dimensional Quantum Fluids , 1981 .

[23]  Reynolds,et al.  Three-Body Recombination of Ultracold Atoms to a Weakly Bound s Level. , 1996, Physical review letters.

[24]  M. Girardeau,et al.  Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension , 1960 .

[25]  Oscillating superfluidity of bosons in optical lattices. , 2002, Physical review letters.

[26]  H. Briegel,et al.  Persistent entanglement in arrays of interacting particles. , 2000, Physical review letters.

[27]  V Dunjko,et al.  Bosons in cigar-shaped traps: Thomas-Fermi regime, Tonks-Girardeau regime, and in between. , 2001, Physical review letters.

[28]  Cornish,et al.  Stable 85Rb bose-einstein condensates with widely tunable interactions , 2000, Physical review letters.

[29]  Fisher,et al.  Boson localization and the superfluid-insulator transition. , 1989, Physical review. B, Condensed matter.

[30]  A. Tsvelik,et al.  Bosonization and Strongly Correlated Systems , 1999 .

[31]  Dalibard,et al.  Vortex formation in a stirred bose-einstein condensate , 1999, Physical review letters.

[32]  E. Lieb,et al.  EXACT ANALYSIS OF AN INTERACTING BOSE GAS. I. THE GENERAL SOLUTION AND THE GROUND STATE , 1963 .

[33]  K. B. Davis,et al.  Bose-Einstein Condensation in a Gas of Sodium Atoms , 1995, EQEC'96. 1996 European Quantum Electronic Conference.

[34]  Petrov,et al.  Regimes of quantum degeneracy in trapped 1D gases , 2000, Physical review letters.

[35]  T. Hänsch,et al.  Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms , 2002, Nature.

[36]  H P Büchler,et al.  Commensurate-incommensurate transition of cold atoms in an optical lattice. , 2003, Physical review letters.

[37]  C. Wieman,et al.  Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor , 1995, Science.

[38]  I Bloch,et al.  Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. , 2001, Physical review letters.

[39]  D. Jin,et al.  Onset of fermi degeneracy in a trapped atomic Gas , 1999, Science.

[40]  Y. Castin,et al.  Low-temperature Bose-Einstein condensates in time-dependent traps: Beyond the U(1) symmetry-breaking approach , 1998 .