Abstract

The superradiant Rayleigh scattering using a pump laser incident along the short axis of a Bose-Einstein condensate with a density distortion is studied, where the distortion is formed by shocking the condensate utilizing the residual magnetic force after the switching-off of the trapping potential. We find that very small variation of the atomic density distribution would induce remarkable asymmetrically populated scattering modes by the matter-wave superradiance with long time pulse. The optical field in the diluter region of the atomic cloud is more greatly amplified, which is not an ordinary mode amplification with the previous cognition. Our numerical simulations with the density envelop distortion are consistent with the experimental results. This supplies a useful method to reflect the geometric symmetries of the atomic density profile by the superradiance scattering.

© 2013 OSA

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  1. 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,” Science285, 571–574 (1999).
    [CrossRef] [PubMed]
  2. D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, “The onset of matter-wave amplification in a superradiant Bose-Einstein condensate,” Science300, 475–478 (2003).
    [CrossRef] [PubMed]
  3. M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, “Phase-coherent amplipcation of matter waves,” Science286, 2309–2312 (1999).
    [CrossRef] [PubMed]
  4. Y. Yoshikawa, Y. Torii, and T. Kuga, “Superradiant light scattering from thermal atomic vapors,” Phys. Rev. Lett.94, 083602 (2005).
    [CrossRef] [PubMed]
  5. Y. Yoshikawa, K. Nakayama, Y. Torii, and T. Kuga, “Holographic storage of multiple coherence gratings in a Bose-Einstein condensate,” Phys. Rev. Lett.99, 220407 (2007).
    [CrossRef]
  6. 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]
  7. F. Yang, X. J. Zhou, J. T. Li, Y. K Chen, L. Xia, and X. Z. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A78, 043611 (2008).
    [CrossRef]
  8. L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010).
    [CrossRef]
  9. N. S. Kampel, A. Griesmaier, M. P. Hornbak Steenstrup, F. Kaminski, E. S. Polzik, and J. H. Müller, “The effect of light assisted collisions on matter wave coherence in superradiant Bose-Einstein condensates,” Phys. Rev. Lett.108, 090401 (2012).
    [CrossRef] [PubMed]
  10. A. Hilliard, F. Kaminski, R. le Targat, C. Olausson, E. S. Polzik, and J. H. Müller, “Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate,” Phys. Rev. A78, 051403(R) (2008).
    [CrossRef]
  11. L. Fallani, C. Fort, N. Piovella, M. Cola, F. S. Cataliotti, M. Inguscio, and R. Bonifacio, “Collective atomic recoil in a moving Bose-Einstein condensate: from superradiance to Bragg scattering,” Phys. Rev. A71, 033612 (2005).
    [CrossRef]
  12. N. Bar-Gill, E. E. Rowen, and N. Davidson, “Spectroscopy of strong-pulse superradiance in a Bose-Einstein condensate,” Phys. Rev. A76, 043603 (2007).
    [CrossRef]
  13. X. J. Zhou, F. Yang, X. G. Yue, T. Vogt, and X. Z. Chen, “Imprinting light phase on matter-wave gratings in superradiance scattering,” Phys. Rev. A81, 013615 (2010).
    [CrossRef]
  14. M. G. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. lett.83, 5202–5205 (1999).
    [CrossRef]
  15. H. Pu, W. Zhang, and P. Meystre, “Wave mixing of optical pulses and Bose-Einstein condensates,” Phys. Rev. lett.91, 150407 (2003).
    [CrossRef] [PubMed]
  16. O. Zobay and G. M. Nikolopoulos, “Spatial effects in superradiant Rayleigh scattering from Bose-Einstein condensates,” Phys. Rev. A73, 013620 (2006).
    [CrossRef]
  17. H. Uys and P. Meystre, “Cooperative scattering of light and atoms in ultracold atomic gases,” Laser Phys. Lett.5, 487 (2008).
    [CrossRef]
  18. L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature414, 413–418 (2001).
    [CrossRef] [PubMed]
  19. B. Lu, X. J. Zhou, T. Vogt, Z. Fang, and X. Z. Chen, “Laser driving of superradiant scattering from a Bose-Einstein condensate at variable incidence angle,” Phys. Rev. A83, 033620 (2011).
    [CrossRef]
  20. M. R. Andrews, M.-O. Mewes, N. J. Druten, and D. S. Durfee, Direct, “Nondestructive observation of a Bose condensate,” Science273, 84–87 (1996).
    [CrossRef] [PubMed]
  21. N. Gemelke, X. Zhang, C. L. Hung, and C. Chin, “In situ observation of incompressible Mott-insulating domains in ultracold atomic gases,” Nature460, 995–998 (2009).
    [CrossRef] [PubMed]
  22. N. Katz, J. Steinhauer, R. Ozeri, and N. Davidson, “Beliaev damping of quasiparticles in a Bose-Einstein condensate,” Phys. Rev. Lett.89, 220401 (2002).
    [CrossRef] [PubMed]
  23. P. R. Berman, “Comparison of recoil-induced resonances and the collective atomic recoil laser,” Phys. Rev. A59, 585 (1999).
    [CrossRef]

2012 (1)

N. S. Kampel, A. Griesmaier, M. P. Hornbak Steenstrup, F. Kaminski, E. S. Polzik, and J. H. Müller, “The effect of light assisted collisions on matter wave coherence in superradiant Bose-Einstein condensates,” Phys. Rev. Lett.108, 090401 (2012).
[CrossRef] [PubMed]

2011 (1)

B. Lu, X. J. Zhou, T. Vogt, Z. Fang, and X. Z. Chen, “Laser driving of superradiant scattering from a Bose-Einstein condensate at variable incidence angle,” Phys. Rev. A83, 033620 (2011).
[CrossRef]

2010 (2)

X. J. Zhou, F. Yang, X. G. Yue, T. Vogt, and X. Z. Chen, “Imprinting light phase on matter-wave gratings in superradiance scattering,” Phys. Rev. A81, 013615 (2010).
[CrossRef]

L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010).
[CrossRef]

2009 (1)

N. Gemelke, X. Zhang, C. L. Hung, and C. Chin, “In situ observation of incompressible Mott-insulating domains in ultracold atomic gases,” Nature460, 995–998 (2009).
[CrossRef] [PubMed]

2008 (3)

F. Yang, X. J. Zhou, J. T. Li, Y. K Chen, L. Xia, and X. Z. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A78, 043611 (2008).
[CrossRef]

A. Hilliard, F. Kaminski, R. le Targat, C. Olausson, E. S. Polzik, and J. H. Müller, “Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate,” Phys. Rev. A78, 051403(R) (2008).
[CrossRef]

H. Uys and P. Meystre, “Cooperative scattering of light and atoms in ultracold atomic gases,” Laser Phys. Lett.5, 487 (2008).
[CrossRef]

2007 (3)

N. Bar-Gill, E. E. Rowen, and N. Davidson, “Spectroscopy of strong-pulse superradiance in a Bose-Einstein condensate,” Phys. Rev. A76, 043603 (2007).
[CrossRef]

Y. Yoshikawa, K. Nakayama, Y. Torii, and T. Kuga, “Holographic storage of multiple coherence gratings in a Bose-Einstein condensate,” Phys. Rev. Lett.99, 220407 (2007).
[CrossRef]

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]

2006 (1)

O. Zobay and G. M. Nikolopoulos, “Spatial effects in superradiant Rayleigh scattering from Bose-Einstein condensates,” Phys. Rev. A73, 013620 (2006).
[CrossRef]

2005 (2)

Y. Yoshikawa, Y. Torii, and T. Kuga, “Superradiant light scattering from thermal atomic vapors,” Phys. Rev. Lett.94, 083602 (2005).
[CrossRef] [PubMed]

L. Fallani, C. Fort, N. Piovella, M. Cola, F. S. Cataliotti, M. Inguscio, and R. Bonifacio, “Collective atomic recoil in a moving Bose-Einstein condensate: from superradiance to Bragg scattering,” Phys. Rev. A71, 033612 (2005).
[CrossRef]

2003 (2)

H. Pu, W. Zhang, and P. Meystre, “Wave mixing of optical pulses and Bose-Einstein condensates,” Phys. Rev. lett.91, 150407 (2003).
[CrossRef] [PubMed]

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, “The onset of matter-wave amplification in a superradiant Bose-Einstein condensate,” Science300, 475–478 (2003).
[CrossRef] [PubMed]

2002 (1)

N. Katz, J. Steinhauer, R. Ozeri, and N. Davidson, “Beliaev damping of quasiparticles in a Bose-Einstein condensate,” Phys. Rev. Lett.89, 220401 (2002).
[CrossRef] [PubMed]

2001 (1)

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature414, 413–418 (2001).
[CrossRef] [PubMed]

1999 (4)

M. G. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. lett.83, 5202–5205 (1999).
[CrossRef]

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, “Phase-coherent amplipcation of matter waves,” Science286, 2309–2312 (1999).
[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,” Science285, 571–574 (1999).
[CrossRef] [PubMed]

P. R. Berman, “Comparison of recoil-induced resonances and the collective atomic recoil laser,” Phys. Rev. A59, 585 (1999).
[CrossRef]

1996 (1)

M. R. Andrews, M.-O. Mewes, N. J. Druten, and D. S. Durfee, Direct, “Nondestructive observation of a Bose condensate,” Science273, 84–87 (1996).
[CrossRef] [PubMed]

Andrews, M. R.

M. R. Andrews, M.-O. Mewes, N. J. Druten, and D. S. Durfee, Direct, “Nondestructive observation of a Bose condensate,” Science273, 84–87 (1996).
[CrossRef] [PubMed]

Bar-Gill, N.

N. Bar-Gill, E. E. Rowen, and N. Davidson, “Spectroscopy of strong-pulse superradiance in a Bose-Einstein condensate,” Phys. Rev. A76, 043603 (2007).
[CrossRef]

Berman, P. R.

P. R. Berman, “Comparison of recoil-induced resonances and the collective atomic recoil laser,” Phys. Rev. A59, 585 (1999).
[CrossRef]

Bonifacio, R.

L. Fallani, C. Fort, N. Piovella, M. Cola, F. S. Cataliotti, M. Inguscio, and R. Bonifacio, “Collective atomic recoil in a moving Bose-Einstein condensate: from superradiance to Bragg scattering,” Phys. Rev. A71, 033612 (2005).
[CrossRef]

Boyd, M.

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, “The onset of matter-wave amplification in a superradiant Bose-Einstein condensate,” Science300, 475–478 (2003).
[CrossRef] [PubMed]

Cao, Q.

L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010).
[CrossRef]

Cataliotti, F. S.

L. Fallani, C. Fort, N. Piovella, M. Cola, F. S. Cataliotti, M. Inguscio, and R. Bonifacio, “Collective atomic recoil in a moving Bose-Einstein condensate: from superradiance to Bragg scattering,” Phys. Rev. A71, 033612 (2005).
[CrossRef]

Chen, X.

L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010).
[CrossRef]

Chen, X. Z.

B. Lu, X. J. Zhou, T. Vogt, Z. Fang, and X. Z. Chen, “Laser driving of superradiant scattering from a Bose-Einstein condensate at variable incidence angle,” Phys. Rev. A83, 033620 (2011).
[CrossRef]

X. J. Zhou, F. Yang, X. G. Yue, T. Vogt, and X. Z. Chen, “Imprinting light phase on matter-wave gratings in superradiance scattering,” Phys. Rev. A81, 013615 (2010).
[CrossRef]

F. Yang, X. J. Zhou, J. T. Li, Y. K Chen, L. Xia, and X. Z. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A78, 043611 (2008).
[CrossRef]

Chen, Y. K

F. Yang, X. J. Zhou, J. T. Li, Y. K Chen, L. Xia, and X. Z. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A78, 043611 (2008).
[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,” Science285, 571–574 (1999).
[CrossRef] [PubMed]

Chin, C.

N. Gemelke, X. Zhang, C. L. Hung, and C. Chin, “In situ observation of incompressible Mott-insulating domains in ultracold atomic gases,” Nature460, 995–998 (2009).
[CrossRef] [PubMed]

Cirac, J. I.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature414, 413–418 (2001).
[CrossRef] [PubMed]

Cola, M.

L. Fallani, C. Fort, N. Piovella, M. Cola, F. S. Cataliotti, M. Inguscio, and R. Bonifacio, “Collective atomic recoil in a moving Bose-Einstein condensate: from superradiance to Bragg scattering,” Phys. Rev. A71, 033612 (2005).
[CrossRef]

Davidson, N.

N. Bar-Gill, E. E. Rowen, and N. Davidson, “Spectroscopy of strong-pulse superradiance in a Bose-Einstein condensate,” Phys. Rev. A76, 043603 (2007).
[CrossRef]

N. Katz, J. Steinhauer, R. Ozeri, and N. Davidson, “Beliaev damping of quasiparticles in a Bose-Einstein condensate,” Phys. Rev. Lett.89, 220401 (2002).
[CrossRef] [PubMed]

Deng, L.

L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010).
[CrossRef]

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, “Phase-coherent amplipcation of matter waves,” Science286, 2309–2312 (1999).
[CrossRef] [PubMed]

Druten, N. J.

M. R. Andrews, M.-O. Mewes, N. J. Druten, and D. S. Durfee, Direct, “Nondestructive observation of a Bose condensate,” Science273, 84–87 (1996).
[CrossRef] [PubMed]

Duan, L.-M.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature414, 413–418 (2001).
[CrossRef] [PubMed]

Durfee, D. S.

M. R. Andrews, M.-O. Mewes, N. J. Druten, and D. S. Durfee, Direct, “Nondestructive observation of a Bose condensate,” Science273, 84–87 (1996).
[CrossRef] [PubMed]

Fallani, L.

L. Fallani, C. Fort, N. Piovella, M. Cola, F. S. Cataliotti, M. Inguscio, and R. Bonifacio, “Collective atomic recoil in a moving Bose-Einstein condensate: from superradiance to Bragg scattering,” Phys. Rev. A71, 033612 (2005).
[CrossRef]

Fang, Z.

B. Lu, X. J. Zhou, T. Vogt, Z. Fang, and X. Z. Chen, “Laser driving of superradiant scattering from a Bose-Einstein condensate at variable incidence angle,” Phys. Rev. A83, 033620 (2011).
[CrossRef]

Fort, C.

L. Fallani, C. Fort, N. Piovella, M. Cola, F. S. Cataliotti, M. Inguscio, and R. Bonifacio, “Collective atomic recoil in a moving Bose-Einstein condensate: from superradiance to Bragg scattering,” Phys. Rev. A71, 033612 (2005).
[CrossRef]

Gemelke, N.

N. Gemelke, X. Zhang, C. L. Hung, and C. Chin, “In situ observation of incompressible Mott-insulating domains in ultracold atomic gases,” Nature460, 995–998 (2009).
[CrossRef] [PubMed]

Griesmaier, A.

N. S. Kampel, A. Griesmaier, M. P. Hornbak Steenstrup, F. Kaminski, E. S. Polzik, and J. H. Müller, “The effect of light assisted collisions on matter wave coherence in superradiant Bose-Einstein condensates,” Phys. Rev. Lett.108, 090401 (2012).
[CrossRef] [PubMed]

Hagley, E. W.

L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010).
[CrossRef]

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, “Phase-coherent amplipcation of matter waves,” Science286, 2309–2312 (1999).
[CrossRef] [PubMed]

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]

Hilliard, A.

A. Hilliard, F. Kaminski, R. le Targat, C. Olausson, E. S. Polzik, and J. H. Müller, “Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate,” Phys. Rev. A78, 051403(R) (2008).
[CrossRef]

Hornbak Steenstrup, M. P.

N. S. Kampel, A. Griesmaier, M. P. Hornbak Steenstrup, F. Kaminski, E. S. Polzik, and J. H. Müller, “The effect of light assisted collisions on matter wave coherence in superradiant Bose-Einstein condensates,” Phys. Rev. Lett.108, 090401 (2012).
[CrossRef] [PubMed]

Hung, C. L.

N. Gemelke, X. Zhang, C. L. Hung, and C. Chin, “In situ observation of incompressible Mott-insulating domains in ultracold atomic gases,” Nature460, 995–998 (2009).
[CrossRef] [PubMed]

Inguscio, M.

L. Fallani, C. Fort, N. Piovella, M. Cola, F. S. Cataliotti, M. Inguscio, and R. Bonifacio, “Collective atomic recoil in a moving Bose-Einstein condensate: from superradiance to Bragg scattering,” Phys. Rev. A71, 033612 (2005).
[CrossRef]

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,” Science285, 571–574 (1999).
[CrossRef] [PubMed]

Kaminski, F.

N. S. Kampel, A. Griesmaier, M. P. Hornbak Steenstrup, F. Kaminski, E. S. Polzik, and J. H. Müller, “The effect of light assisted collisions on matter wave coherence in superradiant Bose-Einstein condensates,” Phys. Rev. Lett.108, 090401 (2012).
[CrossRef] [PubMed]

A. Hilliard, F. Kaminski, R. le Targat, C. Olausson, E. S. Polzik, and J. H. Müller, “Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate,” Phys. Rev. A78, 051403(R) (2008).
[CrossRef]

Kampel, N. S.

N. S. Kampel, A. Griesmaier, M. P. Hornbak Steenstrup, F. Kaminski, E. S. Polzik, and J. H. Müller, “The effect of light assisted collisions on matter wave coherence in superradiant Bose-Einstein condensates,” Phys. Rev. Lett.108, 090401 (2012).
[CrossRef] [PubMed]

Katz, N.

N. Katz, J. Steinhauer, R. Ozeri, and N. Davidson, “Beliaev damping of quasiparticles in a Bose-Einstein condensate,” Phys. Rev. Lett.89, 220401 (2002).
[CrossRef] [PubMed]

Ketterle, W.

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, “The onset of matter-wave amplification in a superradiant Bose-Einstein condensate,” Science300, 475–478 (2003).
[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,” Science285, 571–574 (1999).
[CrossRef] [PubMed]

Kozuma, M.

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, “Phase-coherent amplipcation of matter waves,” Science286, 2309–2312 (1999).
[CrossRef] [PubMed]

Kuga, T.

Y. Yoshikawa, K. Nakayama, Y. Torii, and T. Kuga, “Holographic storage of multiple coherence gratings in a Bose-Einstein condensate,” Phys. Rev. Lett.99, 220407 (2007).
[CrossRef]

Y. Yoshikawa, Y. Torii, and T. Kuga, “Superradiant light scattering from thermal atomic vapors,” Phys. Rev. Lett.94, 083602 (2005).
[CrossRef] [PubMed]

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, “Phase-coherent amplipcation of matter waves,” Science286, 2309–2312 (1999).
[CrossRef] [PubMed]

le Targat, R.

A. Hilliard, F. Kaminski, R. le Targat, C. Olausson, E. S. Polzik, and J. H. Müller, “Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate,” Phys. Rev. A78, 051403(R) (2008).
[CrossRef]

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]

Li, J. T.

F. Yang, X. J. Zhou, J. T. Li, Y. K Chen, L. Xia, and X. Z. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A78, 043611 (2008).
[CrossRef]

Lu, B.

B. Lu, X. J. Zhou, T. Vogt, Z. Fang, and X. Z. Chen, “Laser driving of superradiant scattering from a Bose-Einstein condensate at variable incidence angle,” Phys. Rev. A83, 033620 (2011).
[CrossRef]

Lukin, M. D.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature414, 413–418 (2001).
[CrossRef] [PubMed]

Luo, X.

L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010).
[CrossRef]

Mewes, M.-O.

M. R. Andrews, M.-O. Mewes, N. J. Druten, and D. S. Durfee, Direct, “Nondestructive observation of a Bose condensate,” Science273, 84–87 (1996).
[CrossRef] [PubMed]

Meystre, P.

H. Uys and P. Meystre, “Cooperative scattering of light and atoms in ultracold atomic gases,” Laser Phys. Lett.5, 487 (2008).
[CrossRef]

H. Pu, W. Zhang, and P. Meystre, “Wave mixing of optical pulses and Bose-Einstein condensates,” Phys. Rev. lett.91, 150407 (2003).
[CrossRef] [PubMed]

M. G. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. lett.83, 5202–5205 (1999).
[CrossRef]

Moore, M. G.

M. G. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. lett.83, 5202–5205 (1999).
[CrossRef]

Müller, J. H.

N. S. Kampel, A. Griesmaier, M. P. Hornbak Steenstrup, F. Kaminski, E. S. Polzik, and J. H. Müller, “The effect of light assisted collisions on matter wave coherence in superradiant Bose-Einstein condensates,” Phys. Rev. Lett.108, 090401 (2012).
[CrossRef] [PubMed]

A. Hilliard, F. Kaminski, R. le Targat, C. Olausson, E. S. Polzik, and J. H. Müller, “Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate,” Phys. Rev. A78, 051403(R) (2008).
[CrossRef]

Nakayama, K.

Y. Yoshikawa, K. Nakayama, Y. Torii, and T. Kuga, “Holographic storage of multiple coherence gratings in a Bose-Einstein condensate,” Phys. Rev. Lett.99, 220407 (2007).
[CrossRef]

Nikolopoulos, G. M.

O. Zobay and G. M. Nikolopoulos, “Spatial effects in superradiant Rayleigh scattering from Bose-Einstein condensates,” Phys. Rev. A73, 013620 (2006).
[CrossRef]

Olausson, C.

A. Hilliard, F. Kaminski, R. le Targat, C. Olausson, E. S. Polzik, and J. H. Müller, “Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate,” Phys. Rev. A78, 051403(R) (2008).
[CrossRef]

Ozeri, R.

N. Katz, J. Steinhauer, R. Ozeri, and N. Davidson, “Beliaev damping of quasiparticles in a Bose-Einstein condensate,” Phys. Rev. Lett.89, 220401 (2002).
[CrossRef] [PubMed]

Payne, M. G.

L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010).
[CrossRef]

Piovella, N.

L. Fallani, C. Fort, N. Piovella, M. Cola, F. S. Cataliotti, M. Inguscio, and R. Bonifacio, “Collective atomic recoil in a moving Bose-Einstein condensate: from superradiance to Bragg scattering,” Phys. Rev. A71, 033612 (2005).
[CrossRef]

Polzik, E. S.

N. S. Kampel, A. Griesmaier, M. P. Hornbak Steenstrup, F. Kaminski, E. S. Polzik, and J. H. Müller, “The effect of light assisted collisions on matter wave coherence in superradiant Bose-Einstein condensates,” Phys. Rev. Lett.108, 090401 (2012).
[CrossRef] [PubMed]

A. Hilliard, F. Kaminski, R. le Targat, C. Olausson, E. S. Polzik, and J. H. Müller, “Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate,” Phys. Rev. A78, 051403(R) (2008).
[CrossRef]

Pritchard, D. E.

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, “The onset of matter-wave amplification in a superradiant Bose-Einstein condensate,” Science300, 475–478 (2003).
[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,” Science285, 571–574 (1999).
[CrossRef] [PubMed]

Pu, H.

H. Pu, W. Zhang, and P. Meystre, “Wave mixing of optical pulses and Bose-Einstein condensates,” Phys. Rev. lett.91, 150407 (2003).
[CrossRef] [PubMed]

Rowen, E. E.

N. Bar-Gill, E. E. Rowen, and N. Davidson, “Spectroscopy of strong-pulse superradiance in a Bose-Einstein condensate,” Phys. Rev. A76, 043603 (2007).
[CrossRef]

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]

Schneble, D.

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, “The onset of matter-wave amplification in a superradiant Bose-Einstein condensate,” Science300, 475–478 (2003).
[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,” Science285, 571–574 (1999).
[CrossRef] [PubMed]

Steinhauer, J.

N. Katz, J. Steinhauer, R. Ozeri, and N. Davidson, “Beliaev damping of quasiparticles in a Bose-Einstein condensate,” Phys. Rev. Lett.89, 220401 (2002).
[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,” Science285, 571–574 (1999).
[CrossRef] [PubMed]

Streed, E. W.

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, “The onset of matter-wave amplification in a superradiant Bose-Einstein condensate,” Science300, 475–478 (2003).
[CrossRef] [PubMed]

Sugiura, T.

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, “Phase-coherent amplipcation of matter waves,” Science286, 2309–2312 (1999).
[CrossRef] [PubMed]

Suzuki, Y.

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, “Phase-coherent amplipcation of matter waves,” Science286, 2309–2312 (1999).
[CrossRef] [PubMed]

Torii, Y.

Y. Yoshikawa, K. Nakayama, Y. Torii, and T. Kuga, “Holographic storage of multiple coherence gratings in a Bose-Einstein condensate,” Phys. Rev. Lett.99, 220407 (2007).
[CrossRef]

Y. Yoshikawa, Y. Torii, and T. Kuga, “Superradiant light scattering from thermal atomic vapors,” Phys. Rev. Lett.94, 083602 (2005).
[CrossRef] [PubMed]

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, “The onset of matter-wave amplification in a superradiant Bose-Einstein condensate,” Science300, 475–478 (2003).
[CrossRef] [PubMed]

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, “Phase-coherent amplipcation of matter waves,” Science286, 2309–2312 (1999).
[CrossRef] [PubMed]

Uys, H.

H. Uys and P. Meystre, “Cooperative scattering of light and atoms in ultracold atomic gases,” Laser Phys. Lett.5, 487 (2008).
[CrossRef]

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]

Vogt, T.

B. Lu, X. J. Zhou, T. Vogt, Z. Fang, and X. Z. Chen, “Laser driving of superradiant scattering from a Bose-Einstein condensate at variable incidence angle,” Phys. Rev. A83, 033620 (2011).
[CrossRef]

X. J. Zhou, F. Yang, X. G. Yue, T. Vogt, and X. Z. Chen, “Imprinting light phase on matter-wave gratings in superradiance scattering,” Phys. Rev. A81, 013615 (2010).
[CrossRef]

Wang, R.

L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010).
[CrossRef]

Wang, X.

L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010).
[CrossRef]

Xia, L.

F. Yang, X. J. Zhou, J. T. Li, Y. K Chen, L. Xia, and X. Z. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A78, 043611 (2008).
[CrossRef]

Yang, F.

L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010).
[CrossRef]

X. J. Zhou, F. Yang, X. G. Yue, T. Vogt, and X. Z. Chen, “Imprinting light phase on matter-wave gratings in superradiance scattering,” Phys. Rev. A81, 013615 (2010).
[CrossRef]

F. Yang, X. J. Zhou, J. T. Li, Y. K Chen, L. Xia, and X. Z. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A78, 043611 (2008).
[CrossRef]

Yoshikawa, Y.

Y. Yoshikawa, K. Nakayama, Y. Torii, and T. Kuga, “Holographic storage of multiple coherence gratings in a Bose-Einstein condensate,” Phys. Rev. Lett.99, 220407 (2007).
[CrossRef]

Y. Yoshikawa, Y. Torii, and T. Kuga, “Superradiant light scattering from thermal atomic vapors,” Phys. Rev. Lett.94, 083602 (2005).
[CrossRef] [PubMed]

Yue, X. G.

X. J. Zhou, F. Yang, X. G. Yue, T. Vogt, and X. Z. Chen, “Imprinting light phase on matter-wave gratings in superradiance scattering,” Phys. Rev. A81, 013615 (2010).
[CrossRef]

Zhan, M.

L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010).
[CrossRef]

Zhang, W.

H. Pu, W. Zhang, and P. Meystre, “Wave mixing of optical pulses and Bose-Einstein condensates,” Phys. Rev. lett.91, 150407 (2003).
[CrossRef] [PubMed]

Zhang, X.

N. Gemelke, X. Zhang, C. L. Hung, and C. Chin, “In situ observation of incompressible Mott-insulating domains in ultracold atomic gases,” Nature460, 995–998 (2009).
[CrossRef] [PubMed]

Zhou, X.

L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010).
[CrossRef]

Zhou, X. J.

B. Lu, X. J. Zhou, T. Vogt, Z. Fang, and X. Z. Chen, “Laser driving of superradiant scattering from a Bose-Einstein condensate at variable incidence angle,” Phys. Rev. A83, 033620 (2011).
[CrossRef]

X. J. Zhou, F. Yang, X. G. Yue, T. Vogt, and X. Z. Chen, “Imprinting light phase on matter-wave gratings in superradiance scattering,” Phys. Rev. A81, 013615 (2010).
[CrossRef]

F. Yang, X. J. Zhou, J. T. Li, Y. K Chen, L. Xia, and X. Z. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A78, 043611 (2008).
[CrossRef]

Zobay, O.

O. Zobay and G. M. Nikolopoulos, “Spatial effects in superradiant Rayleigh scattering from Bose-Einstein condensates,” Phys. Rev. A73, 013620 (2006).
[CrossRef]

Zoller, P.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature414, 413–418 (2001).
[CrossRef] [PubMed]

Laser Phys. Lett. (1)

H. Uys and P. Meystre, “Cooperative scattering of light and atoms in ultracold atomic gases,” Laser Phys. Lett.5, 487 (2008).
[CrossRef]

Nature (2)

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature414, 413–418 (2001).
[CrossRef] [PubMed]

N. Gemelke, X. Zhang, C. L. Hung, and C. Chin, “In situ observation of incompressible Mott-insulating domains in ultracold atomic gases,” Nature460, 995–998 (2009).
[CrossRef] [PubMed]

Phys. Rev. A (8)

F. Yang, X. J. Zhou, J. T. Li, Y. K Chen, L. Xia, and X. Z. Chen, “Resonant sequential scattering in two-frequency-pumping superradiance from a Bose-Einstein condensate,” Phys. Rev. A78, 043611 (2008).
[CrossRef]

B. Lu, X. J. Zhou, T. Vogt, Z. Fang, and X. Z. Chen, “Laser driving of superradiant scattering from a Bose-Einstein condensate at variable incidence angle,” Phys. Rev. A83, 033620 (2011).
[CrossRef]

A. Hilliard, F. Kaminski, R. le Targat, C. Olausson, E. S. Polzik, and J. H. Müller, “Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate,” Phys. Rev. A78, 051403(R) (2008).
[CrossRef]

L. Fallani, C. Fort, N. Piovella, M. Cola, F. S. Cataliotti, M. Inguscio, and R. Bonifacio, “Collective atomic recoil in a moving Bose-Einstein condensate: from superradiance to Bragg scattering,” Phys. Rev. A71, 033612 (2005).
[CrossRef]

N. Bar-Gill, E. E. Rowen, and N. Davidson, “Spectroscopy of strong-pulse superradiance in a Bose-Einstein condensate,” Phys. Rev. A76, 043603 (2007).
[CrossRef]

X. J. Zhou, F. Yang, X. G. Yue, T. Vogt, and X. Z. Chen, “Imprinting light phase on matter-wave gratings in superradiance scattering,” Phys. Rev. A81, 013615 (2010).
[CrossRef]

O. Zobay and G. M. Nikolopoulos, “Spatial effects in superradiant Rayleigh scattering from Bose-Einstein condensates,” Phys. Rev. A73, 013620 (2006).
[CrossRef]

P. R. Berman, “Comparison of recoil-induced resonances and the collective atomic recoil laser,” Phys. Rev. A59, 585 (1999).
[CrossRef]

Phys. Rev. lett. (2)

M. G. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. lett.83, 5202–5205 (1999).
[CrossRef]

H. Pu, W. Zhang, and P. Meystre, “Wave mixing of optical pulses and Bose-Einstein condensates,” Phys. Rev. lett.91, 150407 (2003).
[CrossRef] [PubMed]

Y. Yoshikawa, Y. Torii, and T. Kuga, “Superradiant light scattering from thermal atomic vapors,” Phys. Rev. Lett.94, 083602 (2005).
[CrossRef] [PubMed]

Y. Yoshikawa, K. Nakayama, Y. Torii, and T. Kuga, “Holographic storage of multiple coherence gratings in a Bose-Einstein condensate,” Phys. Rev. Lett.99, 220407 (2007).
[CrossRef]

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]

L. Deng, E. W. Hagley, Q. Cao, X. Wang, X. Luo, R. Wang, M. G. Payne, F. Yang, X. Zhou, X. Chen, and M. Zhan, “Observation of a red-blue detuning asymmetry in matter-wave superradiance,” Phys. Rev. Lett.105, 220404 (2010).
[CrossRef]

N. S. Kampel, A. Griesmaier, M. P. Hornbak Steenstrup, F. Kaminski, E. S. Polzik, and J. H. Müller, “The effect of light assisted collisions on matter wave coherence in superradiant Bose-Einstein condensates,” Phys. Rev. Lett.108, 090401 (2012).
[CrossRef] [PubMed]

N. Katz, J. Steinhauer, R. Ozeri, and N. Davidson, “Beliaev damping of quasiparticles in a Bose-Einstein condensate,” Phys. Rev. Lett.89, 220401 (2002).
[CrossRef] [PubMed]

Science (4)

M. R. Andrews, M.-O. Mewes, N. J. Druten, and D. S. Durfee, Direct, “Nondestructive observation of a Bose condensate,” Science273, 84–87 (1996).
[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,” Science285, 571–574 (1999).
[CrossRef] [PubMed]

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, “The onset of matter-wave amplification in a superradiant Bose-Einstein condensate,” Science300, 475–478 (2003).
[CrossRef] [PubMed]

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, “Phase-coherent amplipcation of matter waves,” Science286, 2309–2312 (1999).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) An elongated condensate is pumped by a single off-resonant laser beam (ωl, kl). The beam is collectively scattered to two end-fire modes and the atoms get recoiled to the discrete side-modes (m, n). (b) The time sequence of our experiment. When the magnetic trap is turned off, there is a residual magnetic fields generated, resulted from the different decay rates of the quadrupole and Ioffe trap. Then after a delay Δt, a pump field with duration t and intensity I is incident upon the BEC along the short axis of the condensate to initiate the superradiant scattering. Finally, after a 22ms time-of-flight, a probing beam is applied to the system to get the absorption images of the scattered side-modes.

Fig. 2
Fig. 2

(a) The experimentally measured atomic number distribution (in arbitrary unit) along the axis of the condensate, obtained by using the time-of-flight absorption imaging method. The blue dash-dotted curve is the mirror image of the atomic distribution of the right half of the BEC, implying a higher atomic density on the left side. Absorption images of the condensate after the matter-wave superradiance process are presented in (b) for symmetric BEC, and (c) for distorted BEC in which the experimental data is chosen as Δt = 500μs; both images are obtained by absorption imaging after 22ms of free expansion and averaged over four experiments at t = 100μs.

Fig. 3
Fig. 3

(a) The profile of the wave function used in our simulation. It is a linearly distorted wave function in Thomas-Fermi approximation. dz measures the displacement of the peak density point of the condensate from the geometric center. (b) Experimentally measured atomic populations of (1, 1) (red circle) and (1, −1) (blue square) side-modes in comparison to the simulated results for (1, 1) (red dashed line) and (1, −1) (blue dash-dotted line), in the matter-wave superradiant experiment. The light-atom coupling constant is chosen g = 3.6 × 106s−1 according to the experiment, with the fitted parameter l = −500μm. The numerical results at t = 80μs and t = 120μs are presented in (c) and (d), respectively. The density profile |ψ0,0|2(z) of the (0,0) mode is in black solid curve, |ψ1,−1|2(z) in blue dashed curve, |ψ1,1|2(z) in red dashed curve and |ψ2,0|2(z) in green solid curve; the strength of the end-fire mode ε+ is in blue dotted curve, and ε is in red dotted curve.

Fig. 4
Fig. 4

Schematic of matter-wave superradiance of a condensate moving at a velocity v0. There are two moving optical lattices (with wave vector q±) formed by the superposition the pump pulse and the light field in each of the end-fire modes, moving with velocity v± along z direction, respectively.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

N ˙ n , m = ( G n , m Γ n , m ) N n , m ,
i h ¯ t ψ ( r , t ) = h ¯ 2 2 M Δ ψ ( r , t ) + ( d E ( + ) ) ( d E ( ) ) h ¯ δ ψ ( r , t ) ,
2 E ( ± ) t 2 = c 2 Δ E ( ± ) 1 ε 0 2 P ( ± ) t 2 ,
ψ ( r , t ) = n , m ψ n , m ( z , t ) A e i ( ω n , m t n k x m k z ) ,
N n , m = | ψ n , m | 2 d z .
E ( ± ) ( r , t ) = ε l e y e ± i ( ω l t k x ) / 2 + ε + ( z , t ) e y e ± i ( ω + t k z ) + ε ( z , t ) e y e ± i ( ω t + k z ) ,
i ψ n , m ( ξ , τ ) τ = 1 2 2 ψ n , m ( ξ , τ ) ξ 2 i m ψ n , m ( ξ , τ ) ξ + κ [ e + * ( ξ , τ ) ψ n 1 , m + 1 ( ξ , τ ) e i ( n m + 2 ) τ + e * ( ξ , τ ) ψ n 1 , m 1 ( ξ , τ ) e i ( n + m 2 ) τ + e + ( ξ , τ ) ψ n + 1 , m 1 ( ξ , τ ) e i ( n m ) τ + e ( ξ , τ ) ψ n + 1 , m + 1 ( ξ , τ ) e i ( n + m ) τ ] ,
e ± ( ξ , τ ) = i κ χ d ξ n , m e i ( n ± m ) τ × ψ n , m ( ξ , τ ) ψ n + 1 , m 1 * ( ξ , τ ) ,
i ψ 1 , ± 1 τ = 1 2 2 ψ 1 , ± 1 ξ 2 i ψ 1 , ± 1 ξ + κ e ± * S 2 ψ 0 , 0 ,
e ± ( ξ , τ ) = i κ S ( ξ ) χ d ξ ψ 00 ( ξ ) ψ 1 , 1 * ( ξ , τ ) S 2 ,
N 1 , ± 1 ( τ ) = N 1 , ± 1 ( 0 ) e G 1 , ± 1 τ ,
G 1 , 1 = N κ 2 χ d ξ ψ s * ψ s S 2 ξ d ξ ψ s * ψ s S 2 ,
G 1 , 1 = N κ 2 χ d ξ ψ s * ψ s S 2 ξ d ξ ψ s * ψ s S 2 .
Δ ω ± Δ ω ± = 2 ω r ( 1 ± m ) ,

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