Abstract

We investigate the energy spectrum of fermionized bosonic atoms, which behave very much like spinless noninteracting fermions, in optical lattices by means of the perturbation expansion and the retarded Green's function method. The results show that the energy spectrum splits into two energy bands with single-occupation; the fermionized bosonic atom occupies nonvanishing energy state and left hole has a vanishing energy at any given momentum, and the system is in Mott-insulating state with a energy gap. Using the characteristic of energy spectra we obtained a criterion with which one can judge whether the Tonks-Girardeau (TG) gas is achieved or not.

© 2005 Chinese Optics Letters

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2005 (3)

M. Yun and J. Yin, Chin. Opt. Lett. 3, 125 (2005).

J.-R. Han, J.-M. Liu, H. Jing, and Y.-Z. Wang, Commun. Theor. Phys. 43, 809 (2005).

J.-R. Han, Y.-Z. Wang, and W. M. Liu, J. Phys. B: At. Mol. Opt. Phys. 38, 1411 (2005).

2004 (6)

L. Pollet, S. M. A. Rombouts, and P. J. H. Denteneer, Phys. Rev. Lett. 93, 210401 (2004).

J.-R. Han, T. Zhang, Y.-Z. Wang, and W.-M. Liu, Phys. Lett. A 332, 131 (2004).

T. Stoferle, H. Moritz, C. Schori, M. Kohl, and T. Esslinger, Phys. Rev. Lett. 92, 130403 (2004).

B. Paredes, A. Widera, V. Murg, O. Mandel, S. Filling, I. Cirac, G. V. Shlyapnikov, T. W. Honsch, and I. Bloch, Nature (London) 429, 277 (2004).

T. Kinoshita, T. Wenger, and D. S. Weiss, Science 305, 1125 (2004).

L. Salasnich, A. Parola, and L. Reatto, Phys. Rev. A 70, 013606 (2004).

2003 (4)

P. Pedri and L. Santos, Phys. Rev. Lett. 91, 110401 (2003).

J.-J. Liang, J.-Q. Liang, and W.-M. Liu, Phys. Rev. A 68, 043605 (2003).

M. A. Cazalilla, Phys. Rev. A 67, 053606 (2003).

H. Moritz, T. Stoferle, M. Kohl, and T. Esslinger, Phys. Rev. Lett. 91, 250402 (2003).

2002 (2)

M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, Nature 415, 39 (2002).

P. Ohberg and L. Santos, Phys. Rev. Lett. 89, 240402 (2002).

2001 (9)

V. Dunjko, V. Lorent, and M. Olshanii, Phys. Rev. Lett. 86, 5413 (2001).

M. D. Girardeau, E. M. Wright, and J. M. Triscari, Phys. Rev. A 63, 033601 (2001).

W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, Nature 413, 498 (2001).

A. Gorlitz, J. M. Vogels, A. E. Leanhardt, C. Raman, T. L. Gustavson, J. R. Abo-Shaeer, A. P. Chikkatur, S. Gupta, S. Inouye, T. Rosenband, and W. Kefferle, Phys. Rev. Lett. 87, 130402 (2001).

F. Schreck, L. Khaykovich, K. L. Corwin, G. Ferrari, T. Bourdel, J. Cubizolles, and C. Salomon, Phys. Rev. Lett. 87, 080403 (2001).

O. Morsch, J. H. Muller, M. Cristiani, D. Ciampini, and E. Arimondo, Phys. Rev. Lett. 87, 140402 (2001).

W. K. Hensinger, H. Haffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. Mckenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Docnlop, and B. Upcroft, Nature (London) 412, 52 (2001).

F. S. Cataliotti, C. Fort, P. Maddaloni, F. Minardi, A. Trombeffoni, A. Smerzi, and H. Inguscio, Science 293, 843 (2001).

C. Orzel, A. K. Tuchman, M. L. Fenselan, M. Yasuda, and M. A. Kaserich, Science 291, 2386 (2001).

2000 (2)

S. L. Cornish, N. R. Claussen, J. L. Roberts, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 85, 1795 (2000).

E. B. Kolomeisky, T. J. Newman, J. P. Straley, and X. Y. Qi, Phys. Rev. Lett. 85, 1146 (2000).

1999 (1)

J. Stenger, S. Inouye, M. R. Andrews, H.-J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, Phys. Rev. Lett. 82, 2422 (1999).

1998 (2)

A. I. Safonov, S. A. Vasilyev, I. S. Yasnikov, I. I. Lukashevich, and S. Jaakkola, Phys. Rev. Lett. 81, 4545 (1998).

B. P. Anderson and M. A. Kasevich, Science 282, 1686 (1998).

1963 (2)

E. H. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963).

R. T. Whitlock and P. R. Zilsel, Phys. Rev. 131, 2409 (1963).

1960 (1)

M. Girardeau, J. Math. Phys. 1, 516 (1960).

Chin. Opt. Lett. (1)

Commun. Theor. Phys. (1)

J.-R. Han, J.-M. Liu, H. Jing, and Y.-Z. Wang, Commun. Theor. Phys. 43, 809 (2005).

J. Math. Phys. (1)

M. Girardeau, J. Math. Phys. 1, 516 (1960).

J. Phys. B: At. Mol. Opt. Phys. (1)

J.-R. Han, Y.-Z. Wang, and W. M. Liu, J. Phys. B: At. Mol. Opt. Phys. 38, 1411 (2005).

Nature (2)

M. Greiner, O. Mandel, T. Esslinger, T. W. Hansch, and I. Bloch, Nature 415, 39 (2002).

W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, Nature 413, 498 (2001).

Nature (London) (2)

W. K. Hensinger, H. Haffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. Mckenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Docnlop, and B. Upcroft, Nature (London) 412, 52 (2001).

B. Paredes, A. Widera, V. Murg, O. Mandel, S. Filling, I. Cirac, G. V. Shlyapnikov, T. W. Honsch, and I. Bloch, Nature (London) 429, 277 (2004).

Phys. Lett. A (1)

J.-R. Han, T. Zhang, Y.-Z. Wang, and W.-M. Liu, Phys. Lett. A 332, 131 (2004).

Phys. Rev. (2)

R. T. Whitlock and P. R. Zilsel, Phys. Rev. 131, 2409 (1963).

E. H. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963).

Phys. Rev. A (4)

L. Salasnich, A. Parola, and L. Reatto, Phys. Rev. A 70, 013606 (2004).

J.-J. Liang, J.-Q. Liang, and W.-M. Liu, Phys. Rev. A 68, 043605 (2003).

M. A. Cazalilla, Phys. Rev. A 67, 053606 (2003).

M. D. Girardeau, E. M. Wright, and J. M. Triscari, Phys. Rev. A 63, 033601 (2001).

Phys. Rev. Lett. (13)

H. Moritz, T. Stoferle, M. Kohl, and T. Esslinger, Phys. Rev. Lett. 91, 250402 (2003).

T. Stoferle, H. Moritz, C. Schori, M. Kohl, and T. Esslinger, Phys. Rev. Lett. 92, 130403 (2004).

J. Stenger, S. Inouye, M. R. Andrews, H.-J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, Phys. Rev. Lett. 82, 2422 (1999).

S. L. Cornish, N. R. Claussen, J. L. Roberts, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 85, 1795 (2000).

A. I. Safonov, S. A. Vasilyev, I. S. Yasnikov, I. I. Lukashevich, and S. Jaakkola, Phys. Rev. Lett. 81, 4545 (1998).

O. Morsch, J. H. Muller, M. Cristiani, D. Ciampini, and E. Arimondo, Phys. Rev. Lett. 87, 140402 (2001).

A. Gorlitz, J. M. Vogels, A. E. Leanhardt, C. Raman, T. L. Gustavson, J. R. Abo-Shaeer, A. P. Chikkatur, S. Gupta, S. Inouye, T. Rosenband, and W. Kefferle, Phys. Rev. Lett. 87, 130402 (2001).

F. Schreck, L. Khaykovich, K. L. Corwin, G. Ferrari, T. Bourdel, J. Cubizolles, and C. Salomon, Phys. Rev. Lett. 87, 080403 (2001).

P. Ohberg and L. Santos, Phys. Rev. Lett. 89, 240402 (2002).

L. Pollet, S. M. A. Rombouts, and P. J. H. Denteneer, Phys. Rev. Lett. 93, 210401 (2004).

V. Dunjko, V. Lorent, and M. Olshanii, Phys. Rev. Lett. 86, 5413 (2001).

P. Pedri and L. Santos, Phys. Rev. Lett. 91, 110401 (2003).

E. B. Kolomeisky, T. J. Newman, J. P. Straley, and X. Y. Qi, Phys. Rev. Lett. 85, 1146 (2000).

Science (4)

B. P. Anderson and M. A. Kasevich, Science 282, 1686 (1998).

F. S. Cataliotti, C. Fort, P. Maddaloni, F. Minardi, A. Trombeffoni, A. Smerzi, and H. Inguscio, Science 293, 843 (2001).

C. Orzel, A. K. Tuchman, M. L. Fenselan, M. Yasuda, and M. A. Kaserich, Science 291, 2386 (2001).

T. Kinoshita, T. Wenger, and D. S. Weiss, Science 305, 1125 (2004).

Other (3)

M. A. Cazalilla, Phys. Rev. A 70, 041604(R) (2004).

C. Cohen-Tannoudji, J. Dupont-Roc, and C. Grynberg, Atom-Photon Interactions (Wiley Inter-Science, New York, 1992).

S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 2000).

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