Abstract

We derive the explicit analytical results of low-lying eigenenergies, eigenstates, momentum distributions, and all the two-order spatial correlation functions for a Bose–Hubbard model on a ring in the strong interaction limit by means of the first-order perturbation theory. We show explicitly that the ground and the low-lying excited states are all quantum entangled states in the incommensurate filling case and that certain correlation functions in some of these states, the ground state in particular, violate the Schwarz inequality, another indication of their nonclassicality.

© 2006 Optical Society of America

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  1. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, "Cold bosonic atoms in optical lattices," Phys. Rev. Lett. 81, 3108-3111 (1998).
    [CrossRef]
  2. M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, "Boson localization and the superfluid-insulator transition," Phys. Rev. B 40, 546-570 (1989).
    [CrossRef]
  3. 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 413, 39-44 (2002).
    [CrossRef]
  4. S. R. Clark and D. Jaksch, "Dynamics of the superfluid to Mott-insulator transition in one dimension," Phys. Rev. A 70, 043612/1-13 (2004).
    [CrossRef]
  5. D. van Oosten, P. van der Straten, and H. T. C. Stoof, "Quantum phases in an optical lattice," Phys. Rev. A 63, 053601/1-12 (2001).
    [CrossRef]
  6. D. B. M. Dickerscheid, D. van Oosten, P. J. H. Denteneer, and H. T. C. Stoof, "Ultracold atoms in optical lattices," Phys. Rev. A 68, 043623/1-13 (2003).
    [CrossRef]
  7. Y. Wu and X. Yang, "Analytical results for energy spectrum and eigenstates of Bose-Einstein condensate in Mott insulator state," Phys. Rev. A 68, 013608/1-7 (2003).
    [CrossRef]
  8. A. A. Svidzinsky and S. T. Chui, "Insulator-superfluid transition of spin-1 bosons in an optical lattice in magnetic field," Phys. Rev. A 68, 043612/1-8 (2003).
    [CrossRef]
  9. S. Tsuchiya, S. Kurihara, and T. Kimura, "Superfluid-Mott insulator transition of spin-1 bosons in an optical lattice," Phys. Rev. A 70, 043628/1-11 (2004).
    [CrossRef]
  10. S. Jin, J.-M. Hou, B.-H. Xie, L.-J. Tian, and M.-L. Ge, "Superfluid-Mott-insulator transition of spin-2 cold bosons in an optical lattice in a magnetic field," Phys. Rev. A 70, 023605/1-8 (2004).
    [CrossRef]
  11. K. V. Krutitsky and R. Graham, "Spin-1 bosons with coupled ground states in optical lattice," Phys. Rev. A 70, 063610/1-10 (2004).
    [CrossRef]
  12. K. V. Krutitsky, M. Timmer, and R. Graham, "First- and second-order superfluid-Mott-insulator phase transitions of spin-1 bosons with coupled ground states in optical lattices," Phys. Rev. A 71, 033623/1-4 (2005).
    [CrossRef]
  13. P. Jain and C. W. Gardiner, "A phase-space method for Bose-Hubbard model: application to mean-field models," J. Phys. B 37, 3649-3680 (2004).
    [CrossRef]
  14. W. Zwerger, "Mott-Hubbard transition of cold atoms in optical lattices," J. Opt. 5, S9-S16 (2003).
    [CrossRef]
  15. B. Damski, J. Zakrzewski, L. Santos, P. Zoller, and M. Lewenstein, "Atomic Bose and Anderson glasses in optical lattices," Phys. Rev. Lett. 91, 080403/1-4 (2003).
    [CrossRef]
  16. A. Polkovnikov and D. W. Wang, "Effect of quantum fluctuations on the dipolar motion of Bose-Einstein condensates in optical lattices," Phys. Rev. Lett. 93, 070401/1-4 (2004).
    [CrossRef]
  17. T. D. Kühner, S. R. White, and H. Monien, "One-dimensional Bose-Hubbard model with nearest-neighbor interaction," Phys. Rev. B 61, 12474-12489 (2000).
    [CrossRef]
  18. L. Amico and V. Penna, "Time-dependent mean-field theory of the superfluid-insulator phase transition," Phys. Rev. B 62, 1224-1237 (2000).
    [CrossRef]
  19. A. Buchleitner and A. Kolovsky, "Interaction-induced decoherence of atomic Bloch oscillations," Phys. Rev. Lett. 91, 253002/1-4 (2003).
    [CrossRef]
  20. M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective oscillations of strongly correlated one-dimensional bosons on a lattice," Phys. Rev. Lett. 95, 110402/1-4 (2005).
    [CrossRef]
  21. M. Rigol and A. Muramatsu, "Ground-state properties of hard-core bosons confined on one-dimensional optical lattices," Phys. Rev. A 72, 013604/1-13 (2005).
  22. J. Zakrzewski, "Mean-field dynamics of the superfluid-insulator phase transition in a gas of ultracold atoms," Phys. Rev. A 71, 043601/1-7 (2005).
    [CrossRef]
  23. C. Menotti, A. Smerzi, and A. Trombettoni, "Superfluid dynamics of a Bose-Einstein condensate in a periodic potential," New J. Phys. 5, 112/1-20 (2003).
    [CrossRef]
  24. D. C. Roberts and K. Burnett, "Probing states in the Mott insulator regime in the case of coherent bosons trapped in an optical lattice," Phys. Rev. Lett. 90, 150401/1-4 (2003).
    [CrossRef]
  25. V. A. Kashurnikov, N. V. Prokof'ev, and B. V. Svistunov, "Revealing the superfluid-Mott-insulator transition in an optical lattice," Phys. Rev. A 66, 031601(R)/l-4 (2002).
    [CrossRef]
  26. G. G. Batrouni, V. Rousseau, R. T. Scalettar, M. Rigol, A. Muramatsu, P. J. H. Denteneer, and M. Troyer, "Mott domains of bosons confined on optical lattices," Phys. Rev. Lett. 89, 117203/1-4 (2000).
  27. L. Amico and V. Penna, "Dynamical mean field theory of the Bose-Hubbard model," Phys. Rev. Lett. 80, 2189-2192 (1998).
    [CrossRef]
  28. L. Tonks, "The complete equation of state of one, two and three-dimensional gases of hard elastic spheres," Phys. Rev. 50, 955-963 (1936).
    [CrossRef]
  29. M. D. Girardeau, "Relationship between systems of impenetrable bosons and fermions in one dimension," J. Math. Phys. 1, 516-523 (1960).
    [CrossRef]
  30. E. H. Lieb and W. Liniger, "Exact analysis of an interacting Bose gas. I. The general solution and the ground state," Phys. Rev. 130, 1605-1616 (1963).
    [CrossRef]
  31. E. H. Lieb, "Exact analysis of an interacting Bose gas. II. The excitation spectrum," Phys. Rev. 130, 1616-1624 (1963).
    [CrossRef]
  32. M. D. Girardeau and E. M. Wright, "Breakdown of time-dependent mean field theory for a one-dimensional condensate of impenetrable bosons," Phys. Rev. Lett. 84, 5239-5243 (2000).
    [CrossRef] [PubMed]
  33. M. D. Girardeau, E. M. Wright, and J. M. Triscari, "Ground-state properties of a one-dimensional system of hard-core bosons in a harmonic trap," Phys. Rev. A 63, 033601/1-6 (2001).
    [CrossRef]
  34. R. Bhat, L. D. Carr, and M. J. Holland, "Bose-Einstein condensates in rotating lattices," Phys. Rev. Lett. 96, 060405/1-4 (2006).
    [CrossRef]

2006

R. Bhat, L. D. Carr, and M. J. Holland, "Bose-Einstein condensates in rotating lattices," Phys. Rev. Lett. 96, 060405/1-4 (2006).
[CrossRef]

2005

M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective oscillations of strongly correlated one-dimensional bosons on a lattice," Phys. Rev. Lett. 95, 110402/1-4 (2005).
[CrossRef]

M. Rigol and A. Muramatsu, "Ground-state properties of hard-core bosons confined on one-dimensional optical lattices," Phys. Rev. A 72, 013604/1-13 (2005).

J. Zakrzewski, "Mean-field dynamics of the superfluid-insulator phase transition in a gas of ultracold atoms," Phys. Rev. A 71, 043601/1-7 (2005).
[CrossRef]

K. V. Krutitsky, M. Timmer, and R. Graham, "First- and second-order superfluid-Mott-insulator phase transitions of spin-1 bosons with coupled ground states in optical lattices," Phys. Rev. A 71, 033623/1-4 (2005).
[CrossRef]

2004

P. Jain and C. W. Gardiner, "A phase-space method for Bose-Hubbard model: application to mean-field models," J. Phys. B 37, 3649-3680 (2004).
[CrossRef]

A. Polkovnikov and D. W. Wang, "Effect of quantum fluctuations on the dipolar motion of Bose-Einstein condensates in optical lattices," Phys. Rev. Lett. 93, 070401/1-4 (2004).
[CrossRef]

S. R. Clark and D. Jaksch, "Dynamics of the superfluid to Mott-insulator transition in one dimension," Phys. Rev. A 70, 043612/1-13 (2004).
[CrossRef]

S. Tsuchiya, S. Kurihara, and T. Kimura, "Superfluid-Mott insulator transition of spin-1 bosons in an optical lattice," Phys. Rev. A 70, 043628/1-11 (2004).
[CrossRef]

S. Jin, J.-M. Hou, B.-H. Xie, L.-J. Tian, and M.-L. Ge, "Superfluid-Mott-insulator transition of spin-2 cold bosons in an optical lattice in a magnetic field," Phys. Rev. A 70, 023605/1-8 (2004).
[CrossRef]

K. V. Krutitsky and R. Graham, "Spin-1 bosons with coupled ground states in optical lattice," Phys. Rev. A 70, 063610/1-10 (2004).
[CrossRef]

2003

D. B. M. Dickerscheid, D. van Oosten, P. J. H. Denteneer, and H. T. C. Stoof, "Ultracold atoms in optical lattices," Phys. Rev. A 68, 043623/1-13 (2003).
[CrossRef]

Y. Wu and X. Yang, "Analytical results for energy spectrum and eigenstates of Bose-Einstein condensate in Mott insulator state," Phys. Rev. A 68, 013608/1-7 (2003).
[CrossRef]

A. A. Svidzinsky and S. T. Chui, "Insulator-superfluid transition of spin-1 bosons in an optical lattice in magnetic field," Phys. Rev. A 68, 043612/1-8 (2003).
[CrossRef]

A. Buchleitner and A. Kolovsky, "Interaction-induced decoherence of atomic Bloch oscillations," Phys. Rev. Lett. 91, 253002/1-4 (2003).
[CrossRef]

W. Zwerger, "Mott-Hubbard transition of cold atoms in optical lattices," J. Opt. 5, S9-S16 (2003).
[CrossRef]

B. Damski, J. Zakrzewski, L. Santos, P. Zoller, and M. Lewenstein, "Atomic Bose and Anderson glasses in optical lattices," Phys. Rev. Lett. 91, 080403/1-4 (2003).
[CrossRef]

C. Menotti, A. Smerzi, and A. Trombettoni, "Superfluid dynamics of a Bose-Einstein condensate in a periodic potential," New J. Phys. 5, 112/1-20 (2003).
[CrossRef]

D. C. Roberts and K. Burnett, "Probing states in the Mott insulator regime in the case of coherent bosons trapped in an optical lattice," Phys. Rev. Lett. 90, 150401/1-4 (2003).
[CrossRef]

2002

V. A. Kashurnikov, N. V. Prokof'ev, and B. V. Svistunov, "Revealing the superfluid-Mott-insulator transition in an optical lattice," Phys. Rev. A 66, 031601(R)/l-4 (2002).
[CrossRef]

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 413, 39-44 (2002).
[CrossRef]

2001

D. van Oosten, P. van der Straten, and H. T. C. Stoof, "Quantum phases in an optical lattice," Phys. Rev. A 63, 053601/1-12 (2001).
[CrossRef]

M. D. Girardeau, E. M. Wright, and J. M. Triscari, "Ground-state properties of a one-dimensional system of hard-core bosons in a harmonic trap," Phys. Rev. A 63, 033601/1-6 (2001).
[CrossRef]

2000

M. D. Girardeau and E. M. Wright, "Breakdown of time-dependent mean field theory for a one-dimensional condensate of impenetrable bosons," Phys. Rev. Lett. 84, 5239-5243 (2000).
[CrossRef] [PubMed]

G. G. Batrouni, V. Rousseau, R. T. Scalettar, M. Rigol, A. Muramatsu, P. J. H. Denteneer, and M. Troyer, "Mott domains of bosons confined on optical lattices," Phys. Rev. Lett. 89, 117203/1-4 (2000).

T. D. Kühner, S. R. White, and H. Monien, "One-dimensional Bose-Hubbard model with nearest-neighbor interaction," Phys. Rev. B 61, 12474-12489 (2000).
[CrossRef]

L. Amico and V. Penna, "Time-dependent mean-field theory of the superfluid-insulator phase transition," Phys. Rev. B 62, 1224-1237 (2000).
[CrossRef]

1998

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, "Cold bosonic atoms in optical lattices," Phys. Rev. Lett. 81, 3108-3111 (1998).
[CrossRef]

L. Amico and V. Penna, "Dynamical mean field theory of the Bose-Hubbard model," Phys. Rev. Lett. 80, 2189-2192 (1998).
[CrossRef]

1989

M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, "Boson localization and the superfluid-insulator transition," Phys. Rev. B 40, 546-570 (1989).
[CrossRef]

1963

E. H. Lieb and W. Liniger, "Exact analysis of an interacting Bose gas. I. The general solution and the ground state," Phys. Rev. 130, 1605-1616 (1963).
[CrossRef]

E. H. Lieb, "Exact analysis of an interacting Bose gas. II. The excitation spectrum," Phys. Rev. 130, 1616-1624 (1963).
[CrossRef]

1960

M. D. Girardeau, "Relationship between systems of impenetrable bosons and fermions in one dimension," J. Math. Phys. 1, 516-523 (1960).
[CrossRef]

1936

L. Tonks, "The complete equation of state of one, two and three-dimensional gases of hard elastic spheres," Phys. Rev. 50, 955-963 (1936).
[CrossRef]

Amico, L.

L. Amico and V. Penna, "Time-dependent mean-field theory of the superfluid-insulator phase transition," Phys. Rev. B 62, 1224-1237 (2000).
[CrossRef]

L. Amico and V. Penna, "Dynamical mean field theory of the Bose-Hubbard model," Phys. Rev. Lett. 80, 2189-2192 (1998).
[CrossRef]

Batrouni, G. G.

G. G. Batrouni, V. Rousseau, R. T. Scalettar, M. Rigol, A. Muramatsu, P. J. H. Denteneer, and M. Troyer, "Mott domains of bosons confined on optical lattices," Phys. Rev. Lett. 89, 117203/1-4 (2000).

Bhat, R.

R. Bhat, L. D. Carr, and M. J. Holland, "Bose-Einstein condensates in rotating lattices," Phys. Rev. Lett. 96, 060405/1-4 (2006).
[CrossRef]

Bloch, I.

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 413, 39-44 (2002).
[CrossRef]

Bruder, C.

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, "Cold bosonic atoms in optical lattices," Phys. Rev. Lett. 81, 3108-3111 (1998).
[CrossRef]

Buchleitner, A.

A. Buchleitner and A. Kolovsky, "Interaction-induced decoherence of atomic Bloch oscillations," Phys. Rev. Lett. 91, 253002/1-4 (2003).
[CrossRef]

Burnett, K.

D. C. Roberts and K. Burnett, "Probing states in the Mott insulator regime in the case of coherent bosons trapped in an optical lattice," Phys. Rev. Lett. 90, 150401/1-4 (2003).
[CrossRef]

Carr, L. D.

R. Bhat, L. D. Carr, and M. J. Holland, "Bose-Einstein condensates in rotating lattices," Phys. Rev. Lett. 96, 060405/1-4 (2006).
[CrossRef]

Chui, S. T.

A. A. Svidzinsky and S. T. Chui, "Insulator-superfluid transition of spin-1 bosons in an optical lattice in magnetic field," Phys. Rev. A 68, 043612/1-8 (2003).
[CrossRef]

Cirac, J. I.

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, "Cold bosonic atoms in optical lattices," Phys. Rev. Lett. 81, 3108-3111 (1998).
[CrossRef]

Clark, S. R.

S. R. Clark and D. Jaksch, "Dynamics of the superfluid to Mott-insulator transition in one dimension," Phys. Rev. A 70, 043612/1-13 (2004).
[CrossRef]

Damski, B.

B. Damski, J. Zakrzewski, L. Santos, P. Zoller, and M. Lewenstein, "Atomic Bose and Anderson glasses in optical lattices," Phys. Rev. Lett. 91, 080403/1-4 (2003).
[CrossRef]

Denteneer, P. J. H.

D. B. M. Dickerscheid, D. van Oosten, P. J. H. Denteneer, and H. T. C. Stoof, "Ultracold atoms in optical lattices," Phys. Rev. A 68, 043623/1-13 (2003).
[CrossRef]

G. G. Batrouni, V. Rousseau, R. T. Scalettar, M. Rigol, A. Muramatsu, P. J. H. Denteneer, and M. Troyer, "Mott domains of bosons confined on optical lattices," Phys. Rev. Lett. 89, 117203/1-4 (2000).

Dickerscheid, D. B. M.

D. B. M. Dickerscheid, D. van Oosten, P. J. H. Denteneer, and H. T. C. Stoof, "Ultracold atoms in optical lattices," Phys. Rev. A 68, 043623/1-13 (2003).
[CrossRef]

Esslinger, T.

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 413, 39-44 (2002).
[CrossRef]

Fisher, D. S.

M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, "Boson localization and the superfluid-insulator transition," Phys. Rev. B 40, 546-570 (1989).
[CrossRef]

Fisher, M. P. A.

M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, "Boson localization and the superfluid-insulator transition," Phys. Rev. B 40, 546-570 (1989).
[CrossRef]

Gardiner, C. W.

P. Jain and C. W. Gardiner, "A phase-space method for Bose-Hubbard model: application to mean-field models," J. Phys. B 37, 3649-3680 (2004).
[CrossRef]

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, "Cold bosonic atoms in optical lattices," Phys. Rev. Lett. 81, 3108-3111 (1998).
[CrossRef]

Ge, M.-L.

S. Jin, J.-M. Hou, B.-H. Xie, L.-J. Tian, and M.-L. Ge, "Superfluid-Mott-insulator transition of spin-2 cold bosons in an optical lattice in a magnetic field," Phys. Rev. A 70, 023605/1-8 (2004).
[CrossRef]

Girardeau, M. D.

M. D. Girardeau, E. M. Wright, and J. M. Triscari, "Ground-state properties of a one-dimensional system of hard-core bosons in a harmonic trap," Phys. Rev. A 63, 033601/1-6 (2001).
[CrossRef]

M. D. Girardeau and E. M. Wright, "Breakdown of time-dependent mean field theory for a one-dimensional condensate of impenetrable bosons," Phys. Rev. Lett. 84, 5239-5243 (2000).
[CrossRef] [PubMed]

M. D. Girardeau, "Relationship between systems of impenetrable bosons and fermions in one dimension," J. Math. Phys. 1, 516-523 (1960).
[CrossRef]

Graham, R.

K. V. Krutitsky, M. Timmer, and R. Graham, "First- and second-order superfluid-Mott-insulator phase transitions of spin-1 bosons with coupled ground states in optical lattices," Phys. Rev. A 71, 033623/1-4 (2005).
[CrossRef]

K. V. Krutitsky and R. Graham, "Spin-1 bosons with coupled ground states in optical lattice," Phys. Rev. A 70, 063610/1-10 (2004).
[CrossRef]

Greiner, M.

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 413, 39-44 (2002).
[CrossRef]

Grinstein, G.

M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, "Boson localization and the superfluid-insulator transition," Phys. Rev. B 40, 546-570 (1989).
[CrossRef]

Hänsch, T. W.

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 413, 39-44 (2002).
[CrossRef]

Holland, M. J.

R. Bhat, L. D. Carr, and M. J. Holland, "Bose-Einstein condensates in rotating lattices," Phys. Rev. Lett. 96, 060405/1-4 (2006).
[CrossRef]

Hou, J.-M.

S. Jin, J.-M. Hou, B.-H. Xie, L.-J. Tian, and M.-L. Ge, "Superfluid-Mott-insulator transition of spin-2 cold bosons in an optical lattice in a magnetic field," Phys. Rev. A 70, 023605/1-8 (2004).
[CrossRef]

Jain, P.

P. Jain and C. W. Gardiner, "A phase-space method for Bose-Hubbard model: application to mean-field models," J. Phys. B 37, 3649-3680 (2004).
[CrossRef]

Jaksch, D.

S. R. Clark and D. Jaksch, "Dynamics of the superfluid to Mott-insulator transition in one dimension," Phys. Rev. A 70, 043612/1-13 (2004).
[CrossRef]

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, "Cold bosonic atoms in optical lattices," Phys. Rev. Lett. 81, 3108-3111 (1998).
[CrossRef]

Jin, S.

S. Jin, J.-M. Hou, B.-H. Xie, L.-J. Tian, and M.-L. Ge, "Superfluid-Mott-insulator transition of spin-2 cold bosons in an optical lattice in a magnetic field," Phys. Rev. A 70, 023605/1-8 (2004).
[CrossRef]

Kashurnikov, V. A.

V. A. Kashurnikov, N. V. Prokof'ev, and B. V. Svistunov, "Revealing the superfluid-Mott-insulator transition in an optical lattice," Phys. Rev. A 66, 031601(R)/l-4 (2002).
[CrossRef]

Kimura, T.

S. Tsuchiya, S. Kurihara, and T. Kimura, "Superfluid-Mott insulator transition of spin-1 bosons in an optical lattice," Phys. Rev. A 70, 043628/1-11 (2004).
[CrossRef]

Kolovsky, A.

A. Buchleitner and A. Kolovsky, "Interaction-induced decoherence of atomic Bloch oscillations," Phys. Rev. Lett. 91, 253002/1-4 (2003).
[CrossRef]

Krutitsky, K. V.

K. V. Krutitsky, M. Timmer, and R. Graham, "First- and second-order superfluid-Mott-insulator phase transitions of spin-1 bosons with coupled ground states in optical lattices," Phys. Rev. A 71, 033623/1-4 (2005).
[CrossRef]

K. V. Krutitsky and R. Graham, "Spin-1 bosons with coupled ground states in optical lattice," Phys. Rev. A 70, 063610/1-10 (2004).
[CrossRef]

Kühner, T. D.

T. D. Kühner, S. R. White, and H. Monien, "One-dimensional Bose-Hubbard model with nearest-neighbor interaction," Phys. Rev. B 61, 12474-12489 (2000).
[CrossRef]

Kurihara, S.

S. Tsuchiya, S. Kurihara, and T. Kimura, "Superfluid-Mott insulator transition of spin-1 bosons in an optical lattice," Phys. Rev. A 70, 043628/1-11 (2004).
[CrossRef]

Lewenstein, M.

B. Damski, J. Zakrzewski, L. Santos, P. Zoller, and M. Lewenstein, "Atomic Bose and Anderson glasses in optical lattices," Phys. Rev. Lett. 91, 080403/1-4 (2003).
[CrossRef]

Lieb, E. H.

E. H. Lieb and W. Liniger, "Exact analysis of an interacting Bose gas. I. The general solution and the ground state," Phys. Rev. 130, 1605-1616 (1963).
[CrossRef]

E. H. Lieb, "Exact analysis of an interacting Bose gas. II. The excitation spectrum," Phys. Rev. 130, 1616-1624 (1963).
[CrossRef]

Liniger, W.

E. H. Lieb and W. Liniger, "Exact analysis of an interacting Bose gas. I. The general solution and the ground state," Phys. Rev. 130, 1605-1616 (1963).
[CrossRef]

Mandel, O.

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 413, 39-44 (2002).
[CrossRef]

Menotti, C.

C. Menotti, A. Smerzi, and A. Trombettoni, "Superfluid dynamics of a Bose-Einstein condensate in a periodic potential," New J. Phys. 5, 112/1-20 (2003).
[CrossRef]

Monien, H.

T. D. Kühner, S. R. White, and H. Monien, "One-dimensional Bose-Hubbard model with nearest-neighbor interaction," Phys. Rev. B 61, 12474-12489 (2000).
[CrossRef]

Muramatsu, A.

M. Rigol and A. Muramatsu, "Ground-state properties of hard-core bosons confined on one-dimensional optical lattices," Phys. Rev. A 72, 013604/1-13 (2005).

G. G. Batrouni, V. Rousseau, R. T. Scalettar, M. Rigol, A. Muramatsu, P. J. H. Denteneer, and M. Troyer, "Mott domains of bosons confined on optical lattices," Phys. Rev. Lett. 89, 117203/1-4 (2000).

Penna, V.

L. Amico and V. Penna, "Time-dependent mean-field theory of the superfluid-insulator phase transition," Phys. Rev. B 62, 1224-1237 (2000).
[CrossRef]

L. Amico and V. Penna, "Dynamical mean field theory of the Bose-Hubbard model," Phys. Rev. Lett. 80, 2189-2192 (1998).
[CrossRef]

Polkovnikov, A.

A. Polkovnikov and D. W. Wang, "Effect of quantum fluctuations on the dipolar motion of Bose-Einstein condensates in optical lattices," Phys. Rev. Lett. 93, 070401/1-4 (2004).
[CrossRef]

Prokof'ev, N. V.

V. A. Kashurnikov, N. V. Prokof'ev, and B. V. Svistunov, "Revealing the superfluid-Mott-insulator transition in an optical lattice," Phys. Rev. A 66, 031601(R)/l-4 (2002).
[CrossRef]

Rigol, M.

M. Rigol and A. Muramatsu, "Ground-state properties of hard-core bosons confined on one-dimensional optical lattices," Phys. Rev. A 72, 013604/1-13 (2005).

M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective oscillations of strongly correlated one-dimensional bosons on a lattice," Phys. Rev. Lett. 95, 110402/1-4 (2005).
[CrossRef]

G. G. Batrouni, V. Rousseau, R. T. Scalettar, M. Rigol, A. Muramatsu, P. J. H. Denteneer, and M. Troyer, "Mott domains of bosons confined on optical lattices," Phys. Rev. Lett. 89, 117203/1-4 (2000).

Roberts, D. C.

D. C. Roberts and K. Burnett, "Probing states in the Mott insulator regime in the case of coherent bosons trapped in an optical lattice," Phys. Rev. Lett. 90, 150401/1-4 (2003).
[CrossRef]

Rousseau, V.

M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective oscillations of strongly correlated one-dimensional bosons on a lattice," Phys. Rev. Lett. 95, 110402/1-4 (2005).
[CrossRef]

G. G. Batrouni, V. Rousseau, R. T. Scalettar, M. Rigol, A. Muramatsu, P. J. H. Denteneer, and M. Troyer, "Mott domains of bosons confined on optical lattices," Phys. Rev. Lett. 89, 117203/1-4 (2000).

Santos, L.

B. Damski, J. Zakrzewski, L. Santos, P. Zoller, and M. Lewenstein, "Atomic Bose and Anderson glasses in optical lattices," Phys. Rev. Lett. 91, 080403/1-4 (2003).
[CrossRef]

Scalettar, R. T.

M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective oscillations of strongly correlated one-dimensional bosons on a lattice," Phys. Rev. Lett. 95, 110402/1-4 (2005).
[CrossRef]

G. G. Batrouni, V. Rousseau, R. T. Scalettar, M. Rigol, A. Muramatsu, P. J. H. Denteneer, and M. Troyer, "Mott domains of bosons confined on optical lattices," Phys. Rev. Lett. 89, 117203/1-4 (2000).

Singh, R. R. P.

M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective oscillations of strongly correlated one-dimensional bosons on a lattice," Phys. Rev. Lett. 95, 110402/1-4 (2005).
[CrossRef]

Smerzi, A.

C. Menotti, A. Smerzi, and A. Trombettoni, "Superfluid dynamics of a Bose-Einstein condensate in a periodic potential," New J. Phys. 5, 112/1-20 (2003).
[CrossRef]

Stoof, H. T. C.

D. B. M. Dickerscheid, D. van Oosten, P. J. H. Denteneer, and H. T. C. Stoof, "Ultracold atoms in optical lattices," Phys. Rev. A 68, 043623/1-13 (2003).
[CrossRef]

D. van Oosten, P. van der Straten, and H. T. C. Stoof, "Quantum phases in an optical lattice," Phys. Rev. A 63, 053601/1-12 (2001).
[CrossRef]

Svidzinsky, A. A.

A. A. Svidzinsky and S. T. Chui, "Insulator-superfluid transition of spin-1 bosons in an optical lattice in magnetic field," Phys. Rev. A 68, 043612/1-8 (2003).
[CrossRef]

Svistunov, B. V.

V. A. Kashurnikov, N. V. Prokof'ev, and B. V. Svistunov, "Revealing the superfluid-Mott-insulator transition in an optical lattice," Phys. Rev. A 66, 031601(R)/l-4 (2002).
[CrossRef]

Tian, L.-J.

S. Jin, J.-M. Hou, B.-H. Xie, L.-J. Tian, and M.-L. Ge, "Superfluid-Mott-insulator transition of spin-2 cold bosons in an optical lattice in a magnetic field," Phys. Rev. A 70, 023605/1-8 (2004).
[CrossRef]

Timmer, M.

K. V. Krutitsky, M. Timmer, and R. Graham, "First- and second-order superfluid-Mott-insulator phase transitions of spin-1 bosons with coupled ground states in optical lattices," Phys. Rev. A 71, 033623/1-4 (2005).
[CrossRef]

Tonks, L.

L. Tonks, "The complete equation of state of one, two and three-dimensional gases of hard elastic spheres," Phys. Rev. 50, 955-963 (1936).
[CrossRef]

Triscari, J. M.

M. D. Girardeau, E. M. Wright, and J. M. Triscari, "Ground-state properties of a one-dimensional system of hard-core bosons in a harmonic trap," Phys. Rev. A 63, 033601/1-6 (2001).
[CrossRef]

Trombettoni, A.

C. Menotti, A. Smerzi, and A. Trombettoni, "Superfluid dynamics of a Bose-Einstein condensate in a periodic potential," New J. Phys. 5, 112/1-20 (2003).
[CrossRef]

Troyer, M.

G. G. Batrouni, V. Rousseau, R. T. Scalettar, M. Rigol, A. Muramatsu, P. J. H. Denteneer, and M. Troyer, "Mott domains of bosons confined on optical lattices," Phys. Rev. Lett. 89, 117203/1-4 (2000).

Tsuchiya, S.

S. Tsuchiya, S. Kurihara, and T. Kimura, "Superfluid-Mott insulator transition of spin-1 bosons in an optical lattice," Phys. Rev. A 70, 043628/1-11 (2004).
[CrossRef]

van der Straten, P.

D. van Oosten, P. van der Straten, and H. T. C. Stoof, "Quantum phases in an optical lattice," Phys. Rev. A 63, 053601/1-12 (2001).
[CrossRef]

van Oosten, D.

D. B. M. Dickerscheid, D. van Oosten, P. J. H. Denteneer, and H. T. C. Stoof, "Ultracold atoms in optical lattices," Phys. Rev. A 68, 043623/1-13 (2003).
[CrossRef]

D. van Oosten, P. van der Straten, and H. T. C. Stoof, "Quantum phases in an optical lattice," Phys. Rev. A 63, 053601/1-12 (2001).
[CrossRef]

Wang, D. W.

A. Polkovnikov and D. W. Wang, "Effect of quantum fluctuations on the dipolar motion of Bose-Einstein condensates in optical lattices," Phys. Rev. Lett. 93, 070401/1-4 (2004).
[CrossRef]

Weichman, P. B.

M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, "Boson localization and the superfluid-insulator transition," Phys. Rev. B 40, 546-570 (1989).
[CrossRef]

White, S. R.

T. D. Kühner, S. R. White, and H. Monien, "One-dimensional Bose-Hubbard model with nearest-neighbor interaction," Phys. Rev. B 61, 12474-12489 (2000).
[CrossRef]

Wright, E. M.

M. D. Girardeau, E. M. Wright, and J. M. Triscari, "Ground-state properties of a one-dimensional system of hard-core bosons in a harmonic trap," Phys. Rev. A 63, 033601/1-6 (2001).
[CrossRef]

M. D. Girardeau and E. M. Wright, "Breakdown of time-dependent mean field theory for a one-dimensional condensate of impenetrable bosons," Phys. Rev. Lett. 84, 5239-5243 (2000).
[CrossRef] [PubMed]

Wu, Y.

Y. Wu and X. Yang, "Analytical results for energy spectrum and eigenstates of Bose-Einstein condensate in Mott insulator state," Phys. Rev. A 68, 013608/1-7 (2003).
[CrossRef]

Xie, B.-H.

S. Jin, J.-M. Hou, B.-H. Xie, L.-J. Tian, and M.-L. Ge, "Superfluid-Mott-insulator transition of spin-2 cold bosons in an optical lattice in a magnetic field," Phys. Rev. A 70, 023605/1-8 (2004).
[CrossRef]

Yang, X.

Y. Wu and X. Yang, "Analytical results for energy spectrum and eigenstates of Bose-Einstein condensate in Mott insulator state," Phys. Rev. A 68, 013608/1-7 (2003).
[CrossRef]

Zakrzewski, J.

J. Zakrzewski, "Mean-field dynamics of the superfluid-insulator phase transition in a gas of ultracold atoms," Phys. Rev. A 71, 043601/1-7 (2005).
[CrossRef]

B. Damski, J. Zakrzewski, L. Santos, P. Zoller, and M. Lewenstein, "Atomic Bose and Anderson glasses in optical lattices," Phys. Rev. Lett. 91, 080403/1-4 (2003).
[CrossRef]

Zoller, P.

B. Damski, J. Zakrzewski, L. Santos, P. Zoller, and M. Lewenstein, "Atomic Bose and Anderson glasses in optical lattices," Phys. Rev. Lett. 91, 080403/1-4 (2003).
[CrossRef]

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, "Cold bosonic atoms in optical lattices," Phys. Rev. Lett. 81, 3108-3111 (1998).
[CrossRef]

Zwerger, W.

W. Zwerger, "Mott-Hubbard transition of cold atoms in optical lattices," J. Opt. 5, S9-S16 (2003).
[CrossRef]

J. Math. Phys.

M. D. Girardeau, "Relationship between systems of impenetrable bosons and fermions in one dimension," J. Math. Phys. 1, 516-523 (1960).
[CrossRef]

J. Opt.

W. Zwerger, "Mott-Hubbard transition of cold atoms in optical lattices," J. Opt. 5, S9-S16 (2003).
[CrossRef]

J. Phys. B

P. Jain and C. W. Gardiner, "A phase-space method for Bose-Hubbard model: application to mean-field models," J. Phys. B 37, 3649-3680 (2004).
[CrossRef]

Nature

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 413, 39-44 (2002).
[CrossRef]

New J. Phys.

C. Menotti, A. Smerzi, and A. Trombettoni, "Superfluid dynamics of a Bose-Einstein condensate in a periodic potential," New J. Phys. 5, 112/1-20 (2003).
[CrossRef]

Phys. Rev.

L. Tonks, "The complete equation of state of one, two and three-dimensional gases of hard elastic spheres," Phys. Rev. 50, 955-963 (1936).
[CrossRef]

E. H. Lieb and W. Liniger, "Exact analysis of an interacting Bose gas. I. The general solution and the ground state," Phys. Rev. 130, 1605-1616 (1963).
[CrossRef]

E. H. Lieb, "Exact analysis of an interacting Bose gas. II. The excitation spectrum," Phys. Rev. 130, 1616-1624 (1963).
[CrossRef]

Phys. Rev. A

M. D. Girardeau, E. M. Wright, and J. M. Triscari, "Ground-state properties of a one-dimensional system of hard-core bosons in a harmonic trap," Phys. Rev. A 63, 033601/1-6 (2001).
[CrossRef]

V. A. Kashurnikov, N. V. Prokof'ev, and B. V. Svistunov, "Revealing the superfluid-Mott-insulator transition in an optical lattice," Phys. Rev. A 66, 031601(R)/l-4 (2002).
[CrossRef]

M. Rigol and A. Muramatsu, "Ground-state properties of hard-core bosons confined on one-dimensional optical lattices," Phys. Rev. A 72, 013604/1-13 (2005).

J. Zakrzewski, "Mean-field dynamics of the superfluid-insulator phase transition in a gas of ultracold atoms," Phys. Rev. A 71, 043601/1-7 (2005).
[CrossRef]

S. R. Clark and D. Jaksch, "Dynamics of the superfluid to Mott-insulator transition in one dimension," Phys. Rev. A 70, 043612/1-13 (2004).
[CrossRef]

D. van Oosten, P. van der Straten, and H. T. C. Stoof, "Quantum phases in an optical lattice," Phys. Rev. A 63, 053601/1-12 (2001).
[CrossRef]

D. B. M. Dickerscheid, D. van Oosten, P. J. H. Denteneer, and H. T. C. Stoof, "Ultracold atoms in optical lattices," Phys. Rev. A 68, 043623/1-13 (2003).
[CrossRef]

Y. Wu and X. Yang, "Analytical results for energy spectrum and eigenstates of Bose-Einstein condensate in Mott insulator state," Phys. Rev. A 68, 013608/1-7 (2003).
[CrossRef]

A. A. Svidzinsky and S. T. Chui, "Insulator-superfluid transition of spin-1 bosons in an optical lattice in magnetic field," Phys. Rev. A 68, 043612/1-8 (2003).
[CrossRef]

S. Tsuchiya, S. Kurihara, and T. Kimura, "Superfluid-Mott insulator transition of spin-1 bosons in an optical lattice," Phys. Rev. A 70, 043628/1-11 (2004).
[CrossRef]

S. Jin, J.-M. Hou, B.-H. Xie, L.-J. Tian, and M.-L. Ge, "Superfluid-Mott-insulator transition of spin-2 cold bosons in an optical lattice in a magnetic field," Phys. Rev. A 70, 023605/1-8 (2004).
[CrossRef]

K. V. Krutitsky and R. Graham, "Spin-1 bosons with coupled ground states in optical lattice," Phys. Rev. A 70, 063610/1-10 (2004).
[CrossRef]

K. V. Krutitsky, M. Timmer, and R. Graham, "First- and second-order superfluid-Mott-insulator phase transitions of spin-1 bosons with coupled ground states in optical lattices," Phys. Rev. A 71, 033623/1-4 (2005).
[CrossRef]

Phys. Rev. B

M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, "Boson localization and the superfluid-insulator transition," Phys. Rev. B 40, 546-570 (1989).
[CrossRef]

T. D. Kühner, S. R. White, and H. Monien, "One-dimensional Bose-Hubbard model with nearest-neighbor interaction," Phys. Rev. B 61, 12474-12489 (2000).
[CrossRef]

L. Amico and V. Penna, "Time-dependent mean-field theory of the superfluid-insulator phase transition," Phys. Rev. B 62, 1224-1237 (2000).
[CrossRef]

Phys. Rev. Lett.

A. Buchleitner and A. Kolovsky, "Interaction-induced decoherence of atomic Bloch oscillations," Phys. Rev. Lett. 91, 253002/1-4 (2003).
[CrossRef]

M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective oscillations of strongly correlated one-dimensional bosons on a lattice," Phys. Rev. Lett. 95, 110402/1-4 (2005).
[CrossRef]

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, "Cold bosonic atoms in optical lattices," Phys. Rev. Lett. 81, 3108-3111 (1998).
[CrossRef]

B. Damski, J. Zakrzewski, L. Santos, P. Zoller, and M. Lewenstein, "Atomic Bose and Anderson glasses in optical lattices," Phys. Rev. Lett. 91, 080403/1-4 (2003).
[CrossRef]

A. Polkovnikov and D. W. Wang, "Effect of quantum fluctuations on the dipolar motion of Bose-Einstein condensates in optical lattices," Phys. Rev. Lett. 93, 070401/1-4 (2004).
[CrossRef]

D. C. Roberts and K. Burnett, "Probing states in the Mott insulator regime in the case of coherent bosons trapped in an optical lattice," Phys. Rev. Lett. 90, 150401/1-4 (2003).
[CrossRef]

G. G. Batrouni, V. Rousseau, R. T. Scalettar, M. Rigol, A. Muramatsu, P. J. H. Denteneer, and M. Troyer, "Mott domains of bosons confined on optical lattices," Phys. Rev. Lett. 89, 117203/1-4 (2000).

L. Amico and V. Penna, "Dynamical mean field theory of the Bose-Hubbard model," Phys. Rev. Lett. 80, 2189-2192 (1998).
[CrossRef]

R. Bhat, L. D. Carr, and M. J. Holland, "Bose-Einstein condensates in rotating lattices," Phys. Rev. Lett. 96, 060405/1-4 (2006).
[CrossRef]

M. D. Girardeau and E. M. Wright, "Breakdown of time-dependent mean field theory for a one-dimensional condensate of impenetrable bosons," Phys. Rev. Lett. 84, 5239-5243 (2000).
[CrossRef] [PubMed]

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Equations (24)

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H ̂ = U 2 j = 0 M 1 n ̂ j 2 J j = 0 M 1 ( c ̂ j c ̂ j + 1 + c ̂ j + 1 c ̂ j ) ,
k = 1 q ( α j k + α j k + ) = λ α j , jj k ± C M ,
Ψ n = j C M det m , k = 1 q [ 1 M exp ( 2 π i n m j k M ) ] ψ j ( 0 ) ,
E n = [ N 2 + q ( M q ) ] U 2 M 2 J ( N b + 1 ) s = 1 q cos ( 2 π n s M ) ,
c j + m c j n = c ̂ j c ̂ j + m n * = 2 ( N b + 1 ) M s = i q e i 2 π m n s M ,
c j + m c j gr = 2 ( N b + 1 ) M [ 1 + e i y π m q M + 2 ( 1 δ q , 2 ) k = 1 q 2 2 cos ( 2 π m k M ) ] , even q with n g y , y = ± ,
= 2 ( N b + 1 ) M [ 1 + 2 k = 1 q 1 2 cos ( 2 π m k M ) ] , odd q .
s = 1 q e i 2 π m n s M M N b + q 2 ( N b + 1 ) ,
sin ( q m π M ) q m π M ζ 2 η , ζ = M sin ( m π M ) m π ,
P n ( κ ) = ϖ ( κ ) 2 M m = 0 M 1 c m c 0 n e i κ x m ,
P n ( κ k ) ϖ ( κ k ) 2 = M s = 1 q ( δ κ , n s + δ κ , M n s ) .
P ground ( κ k ) M ϖ ( κ k ) 2 = δ k , 0 + ( 1 δ q , 2 ) s = 1 q 2 2 δ k , s + δ k , y q 2 , even q with n g y , y = ± ,
= δ k , 0 + s = 1 q 1 2 δ k , s , odd q .
c ̂ j c ̂ j + m n + c ̂ j + m c ̂ j n = 2 N b + 1 M s = 1 q cos ( 2 π m n s M ) .
U 1 c ̂ j U = c ̂ j e i j θ U 1 H ̂ ( m ) U n = J j 0 M 1 ( c ̂ j c ̂ j + m e i m θ + c ̂ j + m c ̂ j e i m θ ) n = J M ( c ̂ j c ̂ j + m e i m θ + c ̂ j + m c ̂ j e i m θ ) n .
U Ψ n = e i ϕ det m , k = 1 q { 1 M exp [ i ( 2 π n m M + θ ) j k ] } ψ j ( 0 ) = e i ϕ Ψ n n s n s + M θ 2 π .
U 1 H ̂ ( m ) U n = ( U Ψ n ) H ̂ ( m ) ( U Ψ n ) = [ E n ( 1 ) ( m ) ] n s n s + M θ 2 π = 2 J ( N b + 1 ) s = 1 M 1 cos ( 2 π m n s M + m θ ) .
Ψ n = ( N b + 1 ) q 2 Q ̂ N b , N b , , N b ,
Q ̂ = j C M det m , k = 1 q [ 1 M exp ( 2 π i n m j k M ) ] c ̂ j 1 c ̂ j 2 c ̂ j q .
a ̂ k = 1 M j = 0 M 1 e i 2 π j k M c ̂ j c ̂ j = 1 M j = 0 M 1 e i 2 π j k M a ̂ k ,
a ̂ k = 1 M j = 0 M 1 e i 2 π j k M c ̂ j c ̂ j = 1 M j = 0 M 1 e i 2 π j k M a ̂ k .
Ψ n = ( N b + 1 ) q 2 a ̂ n 1 a ̂ n 2 a ̂ n q N b , N b , , N b .
H ̂ = H ̂ 0 + H ̂ , H ̂ 0 = U 2 j = 0 M 1 n ̂ j 2 ,
H ̂ = j = 0 M 1 [ J ( c ̂ j c ̂ j + 1 + c ̂ j + 1 c ̂ j ) + i Ω ( c ̂ j c ̂ j + 1 c ̂ j + 1 c ̂ j ) ] = j = 0 M 1 [ ( J + i Ω ) c ̂ j c ̂ j + 1 + ( J i Ω ) c ̂ j + 1 c ̂ j ] .

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