Abstract

We propose a new method of detecting quantum coherence of a Bose gas trapped in a one-dimensional optical lattice by measuring the light intensity from Raman scattering in cavity. After pump and displacement process, the intensity or amplitude of scattering light is different for different quantum states of a Bose gas, such as superfluid and Mott-Insulator states. This method can also be useful to detect quantum states of atoms with two components in an optical lattice.

© 2010 Optical Society of America

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  1. 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 atom,” Nature 415, 39–44 (2002).
    [CrossRef] [PubMed]
  2. I. Bloch, “Quantum coherence and entanglement with ultracold atoms in optical lattices,” Nature 453, 1016–1022 (2008).
    [CrossRef] [PubMed]
  3. E. W. Hagley, L. Deng, M. Kozuma, M. Trippenbach, Y. B. Band, M. Edwards, M. Doery, P. S. Julienne, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Measurement of the Coherence of a Bose-Einstein Condensate,” Phys. Rev. Lett. 83, 3112 (1999).
    [CrossRef]
  4. T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, “Transition from a Strongly Interacting 1D Superfluid to a Mott Insulator,” Phys. Rev. Lett. 92, 130403 (2004).
    [CrossRef] [PubMed]
  5. I. Bloch, T. W. Hänsch, and T. Esslinger, “Measurement of the spatial coherence of a trapped Bose gas at the phase transition,” Nature 403, 166–170 (2000).
    [CrossRef] [PubMed]
  6. E. Altman, E. Demler, and M. Lukin, “Probing many-body states of ultracold atoms via noise correlations,” Phys. Rev. A 70, 013603 (2004).
    [CrossRef]
  7. M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, A. Aspect, and C. I. Westbrook, “Hanbury Brown Twiss Effect for Ultracold Quantum Gases,” Science 310, 648–651 (2005).
    [CrossRef] [PubMed]
  8. S. Fölling, F. Gerbier, A. Widera, O. Mandel, T. Gericke, and I. Bloch, “Spatial quantum noise interferometry in expanding ultracold atom clouds,” Nature 434, 481–484 (2005).
    [CrossRef] [PubMed]
  9. T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
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    [CrossRef] [PubMed]
  12. F. Yang, X. Zhou, J. Li, Y. Chen, L. Xia, and X. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A 78, 043611 (2008).
    [CrossRef]
  13. Y. Wu, and X. Yang, “Fully quantized theory of four-wave mixing with bosonic matter waves,” Opt. Lett. 30, 311–313 (2005).
    [CrossRef] [PubMed]
  14. J. Cheng, and Y.-J. Yan, “Quantum dynamics of a molecular matter-wave amplifier,” Phys. Rev. A 75, 033614 (2007).
    [CrossRef]
  15. D. Cl’ement, N. Fabbri, L. Fallani, C. Fort, and M. Inguscio, “Exploring Correlated 1D Bose Gases from the Superfluid to the Mott-Insulator State by Inelastic Light Scattering,” Phys. Rev. Lett. 102, 155301 (2009).
    [CrossRef] [PubMed]
  16. X. Xu, X. J. Zhou, and X. Z. Chen, “Spectroscopy of superradiant scattering from an array of Bose-Einstein condensates,” Phys. Rev. A 79, 033605 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
  18. F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose-Einstein condensate,” Nature 450, 268–271 (2007).
    [CrossRef] [PubMed]
  19. Y. Wu, and X. Yang, “Algebraic method for solving a class of coupled-channel cavity QED models,” Phys. Rev. A 63, 043816 (2001).
    [CrossRef]
  20. I. B. Mekhov, C. Maschler, and H. Ritsch, “Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity quantum electrodynamics,” Nat. Phys. 3, 319–323 (2007).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  23. Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
    [CrossRef] [PubMed]
  24. R. B. Diener, Q. Zhou, H. Zhai, and T.-L. Ho, “Criterion for Bosonic Superfluidity in an Optical Lattice,” Phys. Rev. Lett. 98, 180404 (2007).
    [CrossRef] [PubMed]
  25. Y. Kato, Q. Zhou, N. Kawashima, and N. Trived, “Sharp peaks in the momentum distribution of bosons in optical lattices in the normal state,” Nat. Phys. 4, 617–621 (2008).
    [CrossRef]
  26. Y. Wu, X. Yang, and P. T. Leung, “Theory of microcavity-enhanced Raman gain,” Opt. Lett. 24, 345–347 (1999).
    [CrossRef]
  27. O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Coherent Transport of Neutral Atoms in Spin-Dependent Optical Lattice Potentials,” Phys. Rev. Lett. 91, 010407 (2003).
    [CrossRef] [PubMed]
  28. L.-M. Duan, E. Demler, and M. D. Lukin, “Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices,” Phys. Rev. Lett. 91, 090402 (2003).
    [CrossRef] [PubMed]
  29. G. H. Chen, and Y. S. Wu, “Quantum phase transition in a multicomponent Bose-Einstein condensate in optical lattices,” Phys. Rev. A 67, 013606 (2003).
    [CrossRef]

2009 (3)

D. Cl’ement, N. Fabbri, L. Fallani, C. Fort, and M. Inguscio, “Exploring Correlated 1D Bose Gases from the Superfluid to the Mott-Insulator State by Inelastic Light Scattering,” Phys. Rev. Lett. 102, 155301 (2009).
[CrossRef] [PubMed]

X. Xu, X. J. Zhou, and X. Z. Chen, “Spectroscopy of superradiant scattering from an array of Bose-Einstein condensates,” Phys. Rev. A 79, 033605 (2009).
[CrossRef]

H. Zoubi, and H. Ritsch, “Quantum phases of bosonic atoms with two levels coupled by a cavity field in an optical lattice,” Phys. Rev. A 80, 053608 (2009).
[CrossRef]

2008 (3)

Y. Kato, Q. Zhou, N. Kawashima, and N. Trived, “Sharp peaks in the momentum distribution of bosons in optical lattices in the normal state,” Nat. Phys. 4, 617–621 (2008).
[CrossRef]

F. Yang, X. Zhou, J. Li, Y. Chen, L. Xia, and X. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A 78, 043611 (2008).
[CrossRef]

I. Bloch, “Quantum coherence and entanglement with ultracold atoms in optical lattices,” Nature 453, 1016–1022 (2008).
[CrossRef] [PubMed]

2007 (8)

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[CrossRef] [PubMed]

L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, “Coherence-Enhanced Imaging of a Degenerate Bose-Einstein Gas,” Phys. Rev. Lett. 98, 110401 (2007).
[CrossRef] [PubMed]

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose-Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

R. B. Diener, Q. Zhou, H. Zhai, and T.-L. Ho, “Criterion for Bosonic Superfluidity in an Optical Lattice,” Phys. Rev. Lett. 98, 180404 (2007).
[CrossRef] [PubMed]

I. B. Mekhov, C. Maschler, and H. Ritsch, “Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity quantum electrodynamics,” Nat. Phys. 3, 319–323 (2007).
[CrossRef]

I. B. Mekhov, C. Maschler, and H. Ritsch, “Cavity-Enhanced Light Scattering in Optical Lattices to Probe Atomic Quantum Statistics,” Phys. Rev. Lett. 98, 100402 (2007).
[CrossRef] [PubMed]

J. Cheng, and Y.-J. Yan, “Quantum dynamics of a molecular matter-wave amplifier,” Phys. Rev. A 75, 033614 (2007).
[CrossRef]

2005 (3)

Y. Wu, and X. Yang, “Fully quantized theory of four-wave mixing with bosonic matter waves,” Opt. Lett. 30, 311–313 (2005).
[CrossRef] [PubMed]

M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, A. Aspect, and C. I. Westbrook, “Hanbury Brown Twiss Effect for Ultracold Quantum Gases,” Science 310, 648–651 (2005).
[CrossRef] [PubMed]

S. Fölling, F. Gerbier, A. Widera, O. Mandel, T. Gericke, and I. Bloch, “Spatial quantum noise interferometry in expanding ultracold atom clouds,” Nature 434, 481–484 (2005).
[CrossRef] [PubMed]

2004 (2)

E. Altman, E. Demler, and M. Lukin, “Probing many-body states of ultracold atoms via noise correlations,” Phys. Rev. A 70, 013603 (2004).
[CrossRef]

T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, “Transition from a Strongly Interacting 1D Superfluid to a Mott Insulator,” Phys. Rev. Lett. 92, 130403 (2004).
[CrossRef] [PubMed]

2003 (3)

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Coherent Transport of Neutral Atoms in Spin-Dependent Optical Lattice Potentials,” Phys. Rev. Lett. 91, 010407 (2003).
[CrossRef] [PubMed]

L.-M. Duan, E. Demler, and M. D. Lukin, “Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices,” Phys. Rev. Lett. 91, 090402 (2003).
[CrossRef] [PubMed]

G. H. Chen, and Y. S. Wu, “Quantum phase transition in a multicomponent Bose-Einstein condensate in optical lattices,” Phys. Rev. A 67, 013606 (2003).
[CrossRef]

2002 (1)

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 atom,” Nature 415, 39–44 (2002).
[CrossRef] [PubMed]

2001 (1)

Y. Wu, and X. Yang, “Algebraic method for solving a class of coupled-channel cavity QED models,” Phys. Rev. A 63, 043816 (2001).
[CrossRef]

2000 (1)

I. Bloch, T. W. Hänsch, and T. Esslinger, “Measurement of the spatial coherence of a trapped Bose gas at the phase transition,” Nature 403, 166–170 (2000).
[CrossRef] [PubMed]

1999 (3)

E. W. Hagley, L. Deng, M. Kozuma, M. Trippenbach, Y. B. Band, M. Edwards, M. Doery, P. S. Julienne, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Measurement of the Coherence of a Bose-Einstein Condensate,” Phys. Rev. Lett. 83, 3112 (1999).
[CrossRef]

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, “Superradiant Rayleigh Scattering from a Bose-Einstein Condensate,” Science 285, 571–574 (1999).
[CrossRef] [PubMed]

Y. Wu, X. Yang, and P. T. Leung, “Theory of microcavity-enhanced Raman gain,” Opt. Lett. 24, 345–347 (1999).
[CrossRef]

Altman, E.

E. Altman, E. Demler, and M. Lukin, “Probing many-body states of ultracold atoms via noise correlations,” Phys. Rev. A 70, 013603 (2004).
[CrossRef]

Aspect, A.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[CrossRef] [PubMed]

M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, A. Aspect, and C. I. Westbrook, “Hanbury Brown Twiss Effect for Ultracold Quantum Gases,” Science 310, 648–651 (2005).
[CrossRef] [PubMed]

Band, Y. B.

E. W. Hagley, L. Deng, M. Kozuma, M. Trippenbach, Y. B. Band, M. Edwards, M. Doery, P. S. Julienne, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Measurement of the Coherence of a Bose-Einstein Condensate,” Phys. Rev. Lett. 83, 3112 (1999).
[CrossRef]

Bloch, I.

I. Bloch, “Quantum coherence and entanglement with ultracold atoms in optical lattices,” Nature 453, 1016–1022 (2008).
[CrossRef] [PubMed]

S. Fölling, F. Gerbier, A. Widera, O. Mandel, T. Gericke, and I. Bloch, “Spatial quantum noise interferometry in expanding ultracold atom clouds,” Nature 434, 481–484 (2005).
[CrossRef] [PubMed]

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Coherent Transport of Neutral Atoms in Spin-Dependent Optical Lattice Potentials,” Phys. Rev. Lett. 91, 010407 (2003).
[CrossRef] [PubMed]

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 atom,” Nature 415, 39–44 (2002).
[CrossRef] [PubMed]

I. Bloch, T. W. Hänsch, and T. Esslinger, “Measurement of the spatial coherence of a trapped Bose gas at the phase transition,” Nature 403, 166–170 (2000).
[CrossRef] [PubMed]

Boiron, D.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[CrossRef] [PubMed]

M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, A. Aspect, and C. I. Westbrook, “Hanbury Brown Twiss Effect for Ultracold Quantum Gases,” Science 310, 648–651 (2005).
[CrossRef] [PubMed]

Bourdel, T.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose-Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

Brennecke, F.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose-Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

Chang, H.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[CrossRef] [PubMed]

Chen, G. H.

G. H. Chen, and Y. S. Wu, “Quantum phase transition in a multicomponent Bose-Einstein condensate in optical lattices,” Phys. Rev. A 67, 013606 (2003).
[CrossRef]

Chen, X.

F. Yang, X. Zhou, J. Li, Y. Chen, L. Xia, and X. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A 78, 043611 (2008).
[CrossRef]

Chen, X. Z.

X. Xu, X. J. Zhou, and X. Z. Chen, “Spectroscopy of superradiant scattering from an array of Bose-Einstein condensates,” Phys. Rev. A 79, 033605 (2009).
[CrossRef]

Chen, Y.

F. Yang, X. Zhou, J. Li, Y. Chen, L. Xia, and X. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A 78, 043611 (2008).
[CrossRef]

Cheng, J.

J. Cheng, and Y.-J. Yan, “Quantum dynamics of a molecular matter-wave amplifier,” Phys. Rev. A 75, 033614 (2007).
[CrossRef]

Chikkatur, A. P.

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, “Superradiant Rayleigh Scattering from a Bose-Einstein Condensate,” Science 285, 571–574 (1999).
[CrossRef] [PubMed]

Cl’ement, D.

D. Cl’ement, N. Fabbri, L. Fallani, C. Fort, and M. Inguscio, “Exploring Correlated 1D Bose Gases from the Superfluid to the Mott-Insulator State by Inelastic Light Scattering,” Phys. Rev. Lett. 102, 155301 (2009).
[CrossRef] [PubMed]

Colombe, Y.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

Demler, E.

E. Altman, E. Demler, and M. Lukin, “Probing many-body states of ultracold atoms via noise correlations,” Phys. Rev. A 70, 013603 (2004).
[CrossRef]

L.-M. Duan, E. Demler, and M. D. Lukin, “Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices,” Phys. Rev. Lett. 91, 090402 (2003).
[CrossRef] [PubMed]

Deng, L.

E. W. Hagley, L. Deng, M. Kozuma, M. Trippenbach, Y. B. Band, M. Edwards, M. Doery, P. S. Julienne, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Measurement of the Coherence of a Bose-Einstein Condensate,” Phys. Rev. Lett. 83, 3112 (1999).
[CrossRef]

Diener, R. B.

R. B. Diener, Q. Zhou, H. Zhai, and T.-L. Ho, “Criterion for Bosonic Superfluidity in an Optical Lattice,” Phys. Rev. Lett. 98, 180404 (2007).
[CrossRef] [PubMed]

Doery, M.

E. W. Hagley, L. Deng, M. Kozuma, M. Trippenbach, Y. B. Band, M. Edwards, M. Doery, P. S. Julienne, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Measurement of the Coherence of a Bose-Einstein Condensate,” Phys. Rev. Lett. 83, 3112 (1999).
[CrossRef]

Donner, T.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose-Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

Duan, L.-M.

L.-M. Duan, E. Demler, and M. D. Lukin, “Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices,” Phys. Rev. Lett. 91, 090402 (2003).
[CrossRef] [PubMed]

Dubois, G.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

Edwards, M.

E. W. Hagley, L. Deng, M. Kozuma, M. Trippenbach, Y. B. Band, M. Edwards, M. Doery, P. S. Julienne, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Measurement of the Coherence of a Bose-Einstein Condensate,” Phys. Rev. Lett. 83, 3112 (1999).
[CrossRef]

Esslinger, T.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose-Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, “Transition from a Strongly Interacting 1D Superfluid to a Mott Insulator,” Phys. Rev. Lett. 92, 130403 (2004).
[CrossRef] [PubMed]

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 atom,” Nature 415, 39–44 (2002).
[CrossRef] [PubMed]

I. Bloch, T. W. Hänsch, and T. Esslinger, “Measurement of the spatial coherence of a trapped Bose gas at the phase transition,” Nature 403, 166–170 (2000).
[CrossRef] [PubMed]

Fabbri, N.

D. Cl’ement, N. Fabbri, L. Fallani, C. Fort, and M. Inguscio, “Exploring Correlated 1D Bose Gases from the Superfluid to the Mott-Insulator State by Inelastic Light Scattering,” Phys. Rev. Lett. 102, 155301 (2009).
[CrossRef] [PubMed]

Fallani, L.

D. Cl’ement, N. Fabbri, L. Fallani, C. Fort, and M. Inguscio, “Exploring Correlated 1D Bose Gases from the Superfluid to the Mott-Insulator State by Inelastic Light Scattering,” Phys. Rev. Lett. 102, 155301 (2009).
[CrossRef] [PubMed]

Fölling, S.

S. Fölling, F. Gerbier, A. Widera, O. Mandel, T. Gericke, and I. Bloch, “Spatial quantum noise interferometry in expanding ultracold atom clouds,” Nature 434, 481–484 (2005).
[CrossRef] [PubMed]

Fort, C.

D. Cl’ement, N. Fabbri, L. Fallani, C. Fort, and M. Inguscio, “Exploring Correlated 1D Bose Gases from the Superfluid to the Mott-Insulator State by Inelastic Light Scattering,” Phys. Rev. Lett. 102, 155301 (2009).
[CrossRef] [PubMed]

Gerbier, F.

S. Fölling, F. Gerbier, A. Widera, O. Mandel, T. Gericke, and I. Bloch, “Spatial quantum noise interferometry in expanding ultracold atom clouds,” Nature 434, 481–484 (2005).
[CrossRef] [PubMed]

Gericke, T.

S. Fölling, F. Gerbier, A. Widera, O. Mandel, T. Gericke, and I. Bloch, “Spatial quantum noise interferometry in expanding ultracold atom clouds,” Nature 434, 481–484 (2005).
[CrossRef] [PubMed]

Greiner, M.

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Coherent Transport of Neutral Atoms in Spin-Dependent Optical Lattice Potentials,” Phys. Rev. Lett. 91, 010407 (2003).
[CrossRef] [PubMed]

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 atom,” Nature 415, 39–44 (2002).
[CrossRef] [PubMed]

Hagley, E. W.

E. W. Hagley, L. Deng, M. Kozuma, M. Trippenbach, Y. B. Band, M. Edwards, M. Doery, P. S. Julienne, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Measurement of the Coherence of a Bose-Einstein Condensate,” Phys. Rev. Lett. 83, 3112 (1999).
[CrossRef]

Hänsch, T. W.

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Coherent Transport of Neutral Atoms in Spin-Dependent Optical Lattice Potentials,” Phys. Rev. Lett. 91, 010407 (2003).
[CrossRef] [PubMed]

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 atom,” Nature 415, 39–44 (2002).
[CrossRef] [PubMed]

I. Bloch, T. W. Hänsch, and T. Esslinger, “Measurement of the spatial coherence of a trapped Bose gas at the phase transition,” Nature 403, 166–170 (2000).
[CrossRef] [PubMed]

Helmerson, K.

E. W. Hagley, L. Deng, M. Kozuma, M. Trippenbach, Y. B. Band, M. Edwards, M. Doery, P. S. Julienne, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Measurement of the Coherence of a Bose-Einstein Condensate,” Phys. Rev. Lett. 83, 3112 (1999).
[CrossRef]

Higbie, J. M.

L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, “Coherence-Enhanced Imaging of a Degenerate Bose-Einstein Gas,” Phys. Rev. Lett. 98, 110401 (2007).
[CrossRef] [PubMed]

Ho, T.-L.

R. B. Diener, Q. Zhou, H. Zhai, and T.-L. Ho, “Criterion for Bosonic Superfluidity in an Optical Lattice,” Phys. Rev. Lett. 98, 180404 (2007).
[CrossRef] [PubMed]

Hogervorst, W.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[CrossRef] [PubMed]

Hoppeler, R.

M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, A. Aspect, and C. I. Westbrook, “Hanbury Brown Twiss Effect for Ultracold Quantum Gases,” Science 310, 648–651 (2005).
[CrossRef] [PubMed]

Hunger, D.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

Inguscio, M.

D. Cl’ement, N. Fabbri, L. Fallani, C. Fort, and M. Inguscio, “Exploring Correlated 1D Bose Gases from the Superfluid to the Mott-Insulator State by Inelastic Light Scattering,” Phys. Rev. Lett. 102, 155301 (2009).
[CrossRef] [PubMed]

Inouye, S.

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, “Superradiant Rayleigh Scattering from a Bose-Einstein Condensate,” Science 285, 571–574 (1999).
[CrossRef] [PubMed]

Jeltes, T.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[CrossRef] [PubMed]

Julienne, P. S.

E. W. Hagley, L. Deng, M. Kozuma, M. Trippenbach, Y. B. Band, M. Edwards, M. Doery, P. S. Julienne, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Measurement of the Coherence of a Bose-Einstein Condensate,” Phys. Rev. Lett. 83, 3112 (1999).
[CrossRef]

Kato, Y.

Y. Kato, Q. Zhou, N. Kawashima, and N. Trived, “Sharp peaks in the momentum distribution of bosons in optical lattices in the normal state,” Nat. Phys. 4, 617–621 (2008).
[CrossRef]

Kawashima, N.

Y. Kato, Q. Zhou, N. Kawashima, and N. Trived, “Sharp peaks in the momentum distribution of bosons in optical lattices in the normal state,” Nat. Phys. 4, 617–621 (2008).
[CrossRef]

Ketterle, W.

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, “Superradiant Rayleigh Scattering from a Bose-Einstein Condensate,” Science 285, 571–574 (1999).
[CrossRef] [PubMed]

Köhl, M.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose-Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, “Transition from a Strongly Interacting 1D Superfluid to a Mott Insulator,” Phys. Rev. Lett. 92, 130403 (2004).
[CrossRef] [PubMed]

Kozuma, M.

E. W. Hagley, L. Deng, M. Kozuma, M. Trippenbach, Y. B. Band, M. Edwards, M. Doery, P. S. Julienne, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Measurement of the Coherence of a Bose-Einstein Condensate,” Phys. Rev. Lett. 83, 3112 (1999).
[CrossRef]

Krachmalnicoff, V.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[CrossRef] [PubMed]

Leslie, S. R.

L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, “Coherence-Enhanced Imaging of a Degenerate Bose-Einstein Gas,” Phys. Rev. Lett. 98, 110401 (2007).
[CrossRef] [PubMed]

Leung, P. T.

Li, J.

F. Yang, X. Zhou, J. Li, Y. Chen, L. Xia, and X. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A 78, 043611 (2008).
[CrossRef]

Linke, F.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

Lukin, M.

E. Altman, E. Demler, and M. Lukin, “Probing many-body states of ultracold atoms via noise correlations,” Phys. Rev. A 70, 013603 (2004).
[CrossRef]

Lukin, M. D.

L.-M. Duan, E. Demler, and M. D. Lukin, “Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices,” Phys. Rev. Lett. 91, 090402 (2003).
[CrossRef] [PubMed]

Mandel, O.

S. Fölling, F. Gerbier, A. Widera, O. Mandel, T. Gericke, and I. Bloch, “Spatial quantum noise interferometry in expanding ultracold atom clouds,” Nature 434, 481–484 (2005).
[CrossRef] [PubMed]

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Coherent Transport of Neutral Atoms in Spin-Dependent Optical Lattice Potentials,” Phys. Rev. Lett. 91, 010407 (2003).
[CrossRef] [PubMed]

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 atom,” Nature 415, 39–44 (2002).
[CrossRef] [PubMed]

Maschler, C.

I. B. Mekhov, C. Maschler, and H. Ritsch, “Cavity-Enhanced Light Scattering in Optical Lattices to Probe Atomic Quantum Statistics,” Phys. Rev. Lett. 98, 100402 (2007).
[CrossRef] [PubMed]

I. B. Mekhov, C. Maschler, and H. Ritsch, “Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity quantum electrodynamics,” Nat. Phys. 3, 319–323 (2007).
[CrossRef]

McNamara, J. M.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[CrossRef] [PubMed]

Mekhov, I. B.

I. B. Mekhov, C. Maschler, and H. Ritsch, “Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity quantum electrodynamics,” Nat. Phys. 3, 319–323 (2007).
[CrossRef]

I. B. Mekhov, C. Maschler, and H. Ritsch, “Cavity-Enhanced Light Scattering in Optical Lattices to Probe Atomic Quantum Statistics,” Phys. Rev. Lett. 98, 100402 (2007).
[CrossRef] [PubMed]

Moritz, H.

T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, “Transition from a Strongly Interacting 1D Superfluid to a Mott Insulator,” Phys. Rev. Lett. 92, 130403 (2004).
[CrossRef] [PubMed]

Perrin, A.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[CrossRef] [PubMed]

M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, A. Aspect, and C. I. Westbrook, “Hanbury Brown Twiss Effect for Ultracold Quantum Gases,” Science 310, 648–651 (2005).
[CrossRef] [PubMed]

Phillips, W. D.

E. W. Hagley, L. Deng, M. Kozuma, M. Trippenbach, Y. B. Band, M. Edwards, M. Doery, P. S. Julienne, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Measurement of the Coherence of a Bose-Einstein Condensate,” Phys. Rev. Lett. 83, 3112 (1999).
[CrossRef]

Pritchard, D. E.

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, “Superradiant Rayleigh Scattering from a Bose-Einstein Condensate,” Science 285, 571–574 (1999).
[CrossRef] [PubMed]

Reichel, J.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

Ritsch, H.

H. Zoubi, and H. Ritsch, “Quantum phases of bosonic atoms with two levels coupled by a cavity field in an optical lattice,” Phys. Rev. A 80, 053608 (2009).
[CrossRef]

I. B. Mekhov, C. Maschler, and H. Ritsch, “Cavity-Enhanced Light Scattering in Optical Lattices to Probe Atomic Quantum Statistics,” Phys. Rev. Lett. 98, 100402 (2007).
[CrossRef] [PubMed]

I. B. Mekhov, C. Maschler, and H. Ritsch, “Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity quantum electrodynamics,” Nat. Phys. 3, 319–323 (2007).
[CrossRef]

Ritter, S.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose-Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

Rolston, S. L.

E. W. Hagley, L. Deng, M. Kozuma, M. Trippenbach, Y. B. Band, M. Edwards, M. Doery, P. S. Julienne, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Measurement of the Coherence of a Bose-Einstein Condensate,” Phys. Rev. Lett. 83, 3112 (1999).
[CrossRef]

Rom, T.

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Coherent Transport of Neutral Atoms in Spin-Dependent Optical Lattice Potentials,” Phys. Rev. Lett. 91, 010407 (2003).
[CrossRef] [PubMed]

Sadler, L. E.

L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, “Coherence-Enhanced Imaging of a Degenerate Bose-Einstein Gas,” Phys. Rev. Lett. 98, 110401 (2007).
[CrossRef] [PubMed]

Schellekens, M.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[CrossRef] [PubMed]

M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, A. Aspect, and C. I. Westbrook, “Hanbury Brown Twiss Effect for Ultracold Quantum Gases,” Science 310, 648–651 (2005).
[CrossRef] [PubMed]

Schori, C.

T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, “Transition from a Strongly Interacting 1D Superfluid to a Mott Insulator,” Phys. Rev. Lett. 92, 130403 (2004).
[CrossRef] [PubMed]

Stamper-Kurn, D. M.

L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, “Coherence-Enhanced Imaging of a Degenerate Bose-Einstein Gas,” Phys. Rev. Lett. 98, 110401 (2007).
[CrossRef] [PubMed]

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, “Superradiant Rayleigh Scattering from a Bose-Einstein Condensate,” Science 285, 571–574 (1999).
[CrossRef] [PubMed]

Steinmetz, T.

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

Stenger, J.

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, “Superradiant Rayleigh Scattering from a Bose-Einstein Condensate,” Science 285, 571–574 (1999).
[CrossRef] [PubMed]

Stöferle, T.

T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, “Transition from a Strongly Interacting 1D Superfluid to a Mott Insulator,” Phys. Rev. Lett. 92, 130403 (2004).
[CrossRef] [PubMed]

Trippenbach, M.

E. W. Hagley, L. Deng, M. Kozuma, M. Trippenbach, Y. B. Band, M. Edwards, M. Doery, P. S. Julienne, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Measurement of the Coherence of a Bose-Einstein Condensate,” Phys. Rev. Lett. 83, 3112 (1999).
[CrossRef]

Trived, N.

Y. Kato, Q. Zhou, N. Kawashima, and N. Trived, “Sharp peaks in the momentum distribution of bosons in optical lattices in the normal state,” Nat. Phys. 4, 617–621 (2008).
[CrossRef]

Vassen, W.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[CrossRef] [PubMed]

Vengalattore, M.

L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalattore, and D. M. Stamper-Kurn, “Coherence-Enhanced Imaging of a Degenerate Bose-Einstein Gas,” Phys. Rev. Lett. 98, 110401 (2007).
[CrossRef] [PubMed]

Viana Gomes, J.

M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, A. Aspect, and C. I. Westbrook, “Hanbury Brown Twiss Effect for Ultracold Quantum Gases,” Science 310, 648–651 (2005).
[CrossRef] [PubMed]

Westbrook, C. I.

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[CrossRef] [PubMed]

M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, A. Aspect, and C. I. Westbrook, “Hanbury Brown Twiss Effect for Ultracold Quantum Gases,” Science 310, 648–651 (2005).
[CrossRef] [PubMed]

Widera, A.

S. Fölling, F. Gerbier, A. Widera, O. Mandel, T. Gericke, and I. Bloch, “Spatial quantum noise interferometry in expanding ultracold atom clouds,” Nature 434, 481–484 (2005).
[CrossRef] [PubMed]

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Coherent Transport of Neutral Atoms in Spin-Dependent Optical Lattice Potentials,” Phys. Rev. Lett. 91, 010407 (2003).
[CrossRef] [PubMed]

Wu, Y.

Wu, Y. S.

G. H. Chen, and Y. S. Wu, “Quantum phase transition in a multicomponent Bose-Einstein condensate in optical lattices,” Phys. Rev. A 67, 013606 (2003).
[CrossRef]

Xia, L.

F. Yang, X. Zhou, J. Li, Y. Chen, L. Xia, and X. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A 78, 043611 (2008).
[CrossRef]

Xu, X.

X. Xu, X. J. Zhou, and X. Z. Chen, “Spectroscopy of superradiant scattering from an array of Bose-Einstein condensates,” Phys. Rev. A 79, 033605 (2009).
[CrossRef]

Yan, Y.-J.

J. Cheng, and Y.-J. Yan, “Quantum dynamics of a molecular matter-wave amplifier,” Phys. Rev. A 75, 033614 (2007).
[CrossRef]

Yang, F.

F. Yang, X. Zhou, J. Li, Y. Chen, L. Xia, and X. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A 78, 043611 (2008).
[CrossRef]

Yang, X.

Zhai, H.

R. B. Diener, Q. Zhou, H. Zhai, and T.-L. Ho, “Criterion for Bosonic Superfluidity in an Optical Lattice,” Phys. Rev. Lett. 98, 180404 (2007).
[CrossRef] [PubMed]

Zhou, Q.

Y. Kato, Q. Zhou, N. Kawashima, and N. Trived, “Sharp peaks in the momentum distribution of bosons in optical lattices in the normal state,” Nat. Phys. 4, 617–621 (2008).
[CrossRef]

R. B. Diener, Q. Zhou, H. Zhai, and T.-L. Ho, “Criterion for Bosonic Superfluidity in an Optical Lattice,” Phys. Rev. Lett. 98, 180404 (2007).
[CrossRef] [PubMed]

Zhou, X.

F. Yang, X. Zhou, J. Li, Y. Chen, L. Xia, and X. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A 78, 043611 (2008).
[CrossRef]

Zhou, X. J.

X. Xu, X. J. Zhou, and X. Z. Chen, “Spectroscopy of superradiant scattering from an array of Bose-Einstein condensates,” Phys. Rev. A 79, 033605 (2009).
[CrossRef]

Zoubi, H.

H. Zoubi, and H. Ritsch, “Quantum phases of bosonic atoms with two levels coupled by a cavity field in an optical lattice,” Phys. Rev. A 80, 053608 (2009).
[CrossRef]

Nat. Phys. (2)

I. B. Mekhov, C. Maschler, and H. Ritsch, “Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity quantum electrodynamics,” Nat. Phys. 3, 319–323 (2007).
[CrossRef]

Y. Kato, Q. Zhou, N. Kawashima, and N. Trived, “Sharp peaks in the momentum distribution of bosons in optical lattices in the normal state,” Nat. Phys. 4, 617–621 (2008).
[CrossRef]

Nature (7)

Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature 450, 272–276 (2007).
[CrossRef] [PubMed]

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 atom,” Nature 415, 39–44 (2002).
[CrossRef] [PubMed]

I. Bloch, “Quantum coherence and entanglement with ultracold atoms in optical lattices,” Nature 453, 1016–1022 (2008).
[CrossRef] [PubMed]

I. Bloch, T. W. Hänsch, and T. Esslinger, “Measurement of the spatial coherence of a trapped Bose gas at the phase transition,” Nature 403, 166–170 (2000).
[CrossRef] [PubMed]

S. Fölling, F. Gerbier, A. Widera, O. Mandel, T. Gericke, and I. Bloch, “Spatial quantum noise interferometry in expanding ultracold atom clouds,” Nature 434, 481–484 (2005).
[CrossRef] [PubMed]

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect, and C. I. Westbrook, “Comparison of the Hanbury Brown-Twiss effect for bosons and fermions,” Nature 445, 402–405 (2007).
[CrossRef] [PubMed]

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity QED with a Bose-Einstein condensate,” Nature 450, 268–271 (2007).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (7)

H. Zoubi, and H. Ritsch, “Quantum phases of bosonic atoms with two levels coupled by a cavity field in an optical lattice,” Phys. Rev. A 80, 053608 (2009).
[CrossRef]

G. H. Chen, and Y. S. Wu, “Quantum phase transition in a multicomponent Bose-Einstein condensate in optical lattices,” Phys. Rev. A 67, 013606 (2003).
[CrossRef]

J. Cheng, and Y.-J. Yan, “Quantum dynamics of a molecular matter-wave amplifier,” Phys. Rev. A 75, 033614 (2007).
[CrossRef]

F. Yang, X. Zhou, J. Li, Y. Chen, L. Xia, and X. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A 78, 043611 (2008).
[CrossRef]

Y. Wu, and X. Yang, “Algebraic method for solving a class of coupled-channel cavity QED models,” Phys. Rev. A 63, 043816 (2001).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

(a) Sketch of the system. Atoms with two spin components are held in a 1D optical lattice along the x axis. A pump laser incidents along the y axis, and the cavity mode is along the x axis. (b) Atomic levels picture. Atoms with two internal states |1〉, |2〉 and one excited state |e〉. The laser with frequency ωp pumps atoms transversely, and couples states |e〉 and |1〉. The cavity mode with frequency ωc is resonant to the transition between |e〉 and |2〉.

Fig. 2.
Fig. 2.

Steps to measure the coherence length. (a) First, all the atoms are prepared in |1〉 state, and then a π/2 pulse is used to transfer half atoms to |2〉. (b) Secondly, we vary the phase of one optical lattice and perform the displacement action to the atoms in state |2〉. (c) Thirdly, the probe laser is used to detect the intensity of scattering light leaking from the cavity mode.

Fig. 3.
Fig. 3.

The scattering light intensity of cavity mode versus the scaled displacement (d/a 0) for the ηk = η 0 case, with M = 100 and n = 100. These atoms are initially prepared in the SF state (dashed line), MI state (dotted line), or the PC state with coherence length L = 60 sites (solid line).

Fig. 4.
Fig. 4.

Occupation number (s) q (a) or product (1) q (2) q (b) in momentum space versus the scaled momentum for atoms with one (a) or two (b) internal states, M=10, assuming the Wannier function is approximated as Gaussian. (a)With one internal state, occupation number for the SF state (solid line), and MI state (dotted line). (b) With two internal states, the product of two occupation numbers in the SF-SF state (dotted line), SF-MI or MI-SF states (dashed line), and MI-MI state (solid line), and the inset is enlarged picture for SF-MI or MI-SF states, and MI-MI state.

Equations (10)

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H ̂ = Σ k Σ s = 1 2 [ ε 0 n ̂ k ( s ) + ε 1 j ̂ k ( s ) + ε 1 * j ̂ k ( s ) ] + H ̂ aa Δ a ̂ a ̂
+ Σ k [ ( u 0 n ̂ k ( 1 ) + u 1 j ̂ k ( 1 ) + u 1 * j ̂ k ( 1 ) ) a ̂ a ̂
+ η k ( b ̂ k ( 1 ) a ̂ b ̂ k ( 2 ) + b ̂ k ( 1 ) a ̂ b ̂ k ( 2 ) ) ] ,
a ̂ = i Σ k η k b ̂ k ( 1 ) b ̂ k ( 2 ) i [ Δ Σ k ( u 0 n ̂ k ( 1 ) + u 1 j ̂ k ( 1 ) + u 1 * j ̂ k ( 1 ) ) ] κ .
I ̂ γ [ Σ k k η k * η k b ̂ k ( 1 ) b ̂ k ( 2 ) b ̂ k ( 2 ) b ̂ k ( 1 ) + Σ k η k 2 b ̂ k ( 2 ) b ̂ k ( 2 ) ] ,
I SF = γ η 0 2 N ( N 1 ) γ η 0 2 M 2 n 2 ,
I MI = γ η 0 2 Mn 2 .
I PC { γ η 0 2 ( L d ) Mn 2 , d < L , γ η 0 2 Mn 2 , d L .
I MI MI = I MI SF = I SF MI = γ η 0 2 Mn 2 ;
I SF SF = γ η 0 2 M 2 n 2 .

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