Abstract

We derive the exact explicit analytical expressions of incident and diffracted atom lasers and their difference in phase from the Bragg diffraction of an atom laser from an optical standing wave in the presence of two-body atomic interactions. These expressions demonstrate that two-body atomic interactions may significantly affect the Bragg diffraction of an atom laser from an optical standing wave, and they provide a convenient basis for discussing and designing the future Bragg devices of strong atom lasers.

© 2006 Optical Society of America

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  1. A. F. Bernhardt and B. W. Shore, "Coherent atomic deflection by resonant standing waves," Phys. Rev. A 23, 1290-1301 (1981).
    [CrossRef]
  2. P. J. Martin, B. G. Oldaker, A. H. Miklich, and D. E. Pritchard, "Bragg scattering of atoms from a standing light wave," Phys. Rev. Lett. 60, 515-518 (1988).
    [CrossRef]
  3. W. Zhang and D. F. Walls, "Quantum field theory of interaction of ultracold atoms with a light wave: Bragg scattering in nonlinear atom optics," Phys. Rev. A 49, 3799-3813 (1994).
    [CrossRef] [PubMed]
  4. K. J. Schernthanner, G. Lenz, and P. Meystre, "Many-body effects in near-resonant Kapitza-Dirac diffraction: the nonlinear pendellösung," Phys. Rev. A 51, 3121-3127 (1995).
    [CrossRef] [PubMed]
  5. P. Meystre, Atom Optics (Springer, 2001).
  6. M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction," Phys. Rev. Lett. 82, 871-875 (1999).
    [CrossRef]
  7. J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, "Bragg spectroscopy of a Bose-Einstein condensate," Phys. Rev. Lett. 82, 4569-4573 (1999).
    [CrossRef]
  8. R. Ozeri, N. Katz, J. Steinhauer, and N. Davidson, "Bulk Bogoliubov excitations in a Bose-Einstein condensate," Rev. Mod. Phys. 77, 187-205 (2005).
    [CrossRef]
  9. M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, "Phase-coherent amplification of matter waves," Science 286, 2309-2312 (1999).
    [CrossRef] [PubMed]
  10. S. Inouye, T. Pfau, S. Gupta, A. P. Chikkatur, A. Gorlitz, D. E. Pritchard, and W. Ketterle, "Phase-coherent amplification of atomic matter waves," Nature 402, 641-644 (1999).
    [CrossRef]
  11. K. Bongs and K. Sengstock, "Physics with coherent matter waves," Rep. Prog. Phys. 67, 907-963 (2004).
    [CrossRef]
  12. D. Schneble, Y. Torri, M. Boyd, E. W. Streed, D. Prichard, andW. Ketterle, "The onset of matter-wave amplication in a superradiant Bose-Einstein condensates," Science 300, 475-478 (2003).
    [CrossRef] [PubMed]
  13. Ö. E. Müstecaplioglu and L. You, "Superradiant light scattering from trapped Bose-Einstein condensates," Phys. Rev. A 62, 063615/1-12 (2001).
  14. N. Piovella, R. Bonifacio, B. W. J. McNeil, and G. R. M. Robb, "Superrradiant light scattering and grating formation in cold atomic vapours," Opt. Commun. 187, 165-170 (2001).
    [CrossRef]
  15. M. G. Moore, O. Zobay, and P. Meystre, "Quantum optics of a Bose-Einstein condensate coupled to a quantized light field," Phys. Rev. A 60, 1491-1506 (1999).
    [CrossRef]
  16. 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. A 71, 033612/1-8 (2005).
    [CrossRef]
  17. Y. Wu and X. Yang, "Fully quantized theory of four-wave mixing with bosonic matter waves," Opt. Lett. 30, 311-313 (2005).
    [CrossRef] [PubMed]
  18. Y. Wu and X. Yang, "Eigenstates and eigenenergies of four-wave mixing models," Opt. Lett. 29, 839-841 (2004).
    [CrossRef] [PubMed]
  19. Y. Wu, X. Yang, C. P. Sun, X. J. Zhou, and Y. Q. Wang, "Theory of four-wave mixing with matter waves without the undepleted pump approximation," Phys. Rev. A 61, 043604/1-6 (2000).
    [CrossRef]
  20. B. Deb and G. S. Agarwal, "Tripartite entanglement in a Bose-Einstein condensate by stimulated Bragg scattering," Phys. Rev. A 65, 063618/1-5 (2002).
    [CrossRef]
  21. B. Deb and G. S. Agarwal, "Entangling two Bose-Einstein condensates by stimulated Bragg scattering," Phys. Rev. A 67, 023603/1-4 (2003).
    [CrossRef]
  22. N. Piovella, M. Cola, and R. Bonifacio, "Quantum fluctuations and entanglement in the collective atomic recoil laser using a Bose-Einstein condensate," Phys. Rev. A 67, 013817/1-11 (2003).
    [CrossRef]
  23. A. Kozhekin, G. Kurizki, and B. Sherman, "Quantum state control by a single conditional measurement: the periodically-switched model," Phys. Rev. A 54, 3535-3538 (1996).
    [CrossRef] [PubMed]
  24. A. E. Kozhekin and G. Kurizki, "Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances," Phys. Rev. Lett. 74, 5020-5023 (1995).
    [CrossRef] [PubMed]
  25. P. J. Bardroff, I. Bialynicki-Birula, D. S. Krahmer, G. Kurizki, E. Mayer, P. Stifter, and W. P. Schleich, "Dynamical localization in atomic momentum transfer," Phys. Rev. Lett. 74, 3959-3962 (1995).
    [CrossRef] [PubMed]
  26. E. W. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A well-collimated quasi-continuous atom laser," Science 283, 1706-1714 (1999).
    [CrossRef] [PubMed]
  27. I. Bloch, T. W. Hänsch, and T. Esslinger, "Atom laser with a cw output coupler," Phys. Rev. Lett. 82, 3008-3011 (1999).
    [CrossRef]
  28. Y. Wu and X. Yang, "Output rate of atom lasers in Raman-type output-coupling scheme," Phys. Rev. A 62, 013603/1-8 (2000).
    [CrossRef]
  29. M. Holland, K. Burnett, C. Gardiner, J. I. Cirac, and P. Zoller, "Theory of an atom laser," Phys. Rev. A 54, R1757-R1760 (1996).
    [CrossRef] [PubMed]
  30. S. A. Haine, A. J. Ferris, J. D. Close, and J. J. Hope, "Control of an atom laser using feedback," Phys. Rev. A 69, 013605/1-6 (2004).
    [CrossRef]
  31. C. P. Search, S. Pötting, W. Zhang, and P. Meystre, "Input-output theory for fermions in an atom cavity," Phys. Rev. A 66, 043616/1-10 (2002).
    [CrossRef]
  32. S. A. Haine, J. J. Hope, N. P. Robins, and C. M. Savage, "Stability of continuously pumped atom lasers," Phys. Rev. Lett. 88, 170403/1-4 (2002).
    [CrossRef]
  33. L. K. Thomsen and H. M. Wiseman, "Atom-laser coherence and its control via feedback," Phys. Rev. A 65, 063607/1-14 (2002).
    [CrossRef]
  34. N. Robins, C. Savage, and E. A. Ostrovskaya, "Atom-laser dynamics," Phys. Rev. A 64, 043605/1-4 (2001).
    [CrossRef]
  35. X.-J. Liu, H. Jing, X. Liu, and M.-L. Ge, "Generation of two-flavor vortex atom laser from a five-state medium," Eur. Phys. J. D37, 261-265 (2005).
  36. A. Öttl, S. Ritter, M. Köhl, and T. Esslinger, "Correlations and counting statistics of an atom laser," Phys. Rev. Lett. 95, 090404/1-4 (2005).
    [CrossRef]
  37. N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, J. D. Close, "Achieving peak brightness in an atom laser," cond-mat/0509462 (2005).
  38. K. Chandrasekharan, Elliptic Functions (Springer-Verlag, 1980) Chap. VII.

2005 (4)

R. Ozeri, N. Katz, J. Steinhauer, and N. Davidson, "Bulk Bogoliubov excitations in a Bose-Einstein condensate," Rev. Mod. Phys. 77, 187-205 (2005).
[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. A 71, 033612/1-8 (2005).
[CrossRef]

A. Öttl, S. Ritter, M. Köhl, and T. Esslinger, "Correlations and counting statistics of an atom laser," Phys. Rev. Lett. 95, 090404/1-4 (2005).
[CrossRef]

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

2004 (3)

Y. Wu and X. Yang, "Eigenstates and eigenenergies of four-wave mixing models," Opt. Lett. 29, 839-841 (2004).
[CrossRef] [PubMed]

S. A. Haine, A. J. Ferris, J. D. Close, and J. J. Hope, "Control of an atom laser using feedback," Phys. Rev. A 69, 013605/1-6 (2004).
[CrossRef]

K. Bongs and K. Sengstock, "Physics with coherent matter waves," Rep. Prog. Phys. 67, 907-963 (2004).
[CrossRef]

2003 (3)

D. Schneble, Y. Torri, M. Boyd, E. W. Streed, D. Prichard, andW. Ketterle, "The onset of matter-wave amplication in a superradiant Bose-Einstein condensates," Science 300, 475-478 (2003).
[CrossRef] [PubMed]

B. Deb and G. S. Agarwal, "Entangling two Bose-Einstein condensates by stimulated Bragg scattering," Phys. Rev. A 67, 023603/1-4 (2003).
[CrossRef]

N. Piovella, M. Cola, and R. Bonifacio, "Quantum fluctuations and entanglement in the collective atomic recoil laser using a Bose-Einstein condensate," Phys. Rev. A 67, 013817/1-11 (2003).
[CrossRef]

2002 (4)

C. P. Search, S. Pötting, W. Zhang, and P. Meystre, "Input-output theory for fermions in an atom cavity," Phys. Rev. A 66, 043616/1-10 (2002).
[CrossRef]

S. A. Haine, J. J. Hope, N. P. Robins, and C. M. Savage, "Stability of continuously pumped atom lasers," Phys. Rev. Lett. 88, 170403/1-4 (2002).
[CrossRef]

L. K. Thomsen and H. M. Wiseman, "Atom-laser coherence and its control via feedback," Phys. Rev. A 65, 063607/1-14 (2002).
[CrossRef]

B. Deb and G. S. Agarwal, "Tripartite entanglement in a Bose-Einstein condensate by stimulated Bragg scattering," Phys. Rev. A 65, 063618/1-5 (2002).
[CrossRef]

2001 (3)

N. Robins, C. Savage, and E. A. Ostrovskaya, "Atom-laser dynamics," Phys. Rev. A 64, 043605/1-4 (2001).
[CrossRef]

Ö. E. Müstecaplioglu and L. You, "Superradiant light scattering from trapped Bose-Einstein condensates," Phys. Rev. A 62, 063615/1-12 (2001).

N. Piovella, R. Bonifacio, B. W. J. McNeil, and G. R. M. Robb, "Superrradiant light scattering and grating formation in cold atomic vapours," Opt. Commun. 187, 165-170 (2001).
[CrossRef]

2000 (2)

Y. Wu, X. Yang, C. P. Sun, X. J. Zhou, and Y. Q. Wang, "Theory of four-wave mixing with matter waves without the undepleted pump approximation," Phys. Rev. A 61, 043604/1-6 (2000).
[CrossRef]

Y. Wu and X. Yang, "Output rate of atom lasers in Raman-type output-coupling scheme," Phys. Rev. A 62, 013603/1-8 (2000).
[CrossRef]

1999 (7)

E. W. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A well-collimated quasi-continuous atom laser," Science 283, 1706-1714 (1999).
[CrossRef] [PubMed]

I. Bloch, T. W. Hänsch, and T. Esslinger, "Atom laser with a cw output coupler," Phys. Rev. Lett. 82, 3008-3011 (1999).
[CrossRef]

M. G. Moore, O. Zobay, and P. Meystre, "Quantum optics of a Bose-Einstein condensate coupled to a quantized light field," Phys. Rev. A 60, 1491-1506 (1999).
[CrossRef]

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, "Phase-coherent amplification of matter waves," Science 286, 2309-2312 (1999).
[CrossRef] [PubMed]

S. Inouye, T. Pfau, S. Gupta, A. P. Chikkatur, A. Gorlitz, D. E. Pritchard, and W. Ketterle, "Phase-coherent amplification of atomic matter waves," Nature 402, 641-644 (1999).
[CrossRef]

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction," Phys. Rev. Lett. 82, 871-875 (1999).
[CrossRef]

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, "Bragg spectroscopy of a Bose-Einstein condensate," Phys. Rev. Lett. 82, 4569-4573 (1999).
[CrossRef]

1996 (2)

A. Kozhekin, G. Kurizki, and B. Sherman, "Quantum state control by a single conditional measurement: the periodically-switched model," Phys. Rev. A 54, 3535-3538 (1996).
[CrossRef] [PubMed]

M. Holland, K. Burnett, C. Gardiner, J. I. Cirac, and P. Zoller, "Theory of an atom laser," Phys. Rev. A 54, R1757-R1760 (1996).
[CrossRef] [PubMed]

1995 (3)

A. E. Kozhekin and G. Kurizki, "Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances," Phys. Rev. Lett. 74, 5020-5023 (1995).
[CrossRef] [PubMed]

P. J. Bardroff, I. Bialynicki-Birula, D. S. Krahmer, G. Kurizki, E. Mayer, P. Stifter, and W. P. Schleich, "Dynamical localization in atomic momentum transfer," Phys. Rev. Lett. 74, 3959-3962 (1995).
[CrossRef] [PubMed]

K. J. Schernthanner, G. Lenz, and P. Meystre, "Many-body effects in near-resonant Kapitza-Dirac diffraction: the nonlinear pendellösung," Phys. Rev. A 51, 3121-3127 (1995).
[CrossRef] [PubMed]

1994 (1)

W. Zhang and D. F. Walls, "Quantum field theory of interaction of ultracold atoms with a light wave: Bragg scattering in nonlinear atom optics," Phys. Rev. A 49, 3799-3813 (1994).
[CrossRef] [PubMed]

1988 (1)

P. J. Martin, B. G. Oldaker, A. H. Miklich, and D. E. Pritchard, "Bragg scattering of atoms from a standing light wave," Phys. Rev. Lett. 60, 515-518 (1988).
[CrossRef]

1981 (1)

A. F. Bernhardt and B. W. Shore, "Coherent atomic deflection by resonant standing waves," Phys. Rev. A 23, 1290-1301 (1981).
[CrossRef]

Agarwal, G. S.

B. Deb and G. S. Agarwal, "Entangling two Bose-Einstein condensates by stimulated Bragg scattering," Phys. Rev. A 67, 023603/1-4 (2003).
[CrossRef]

B. Deb and G. S. Agarwal, "Tripartite entanglement in a Bose-Einstein condensate by stimulated Bragg scattering," Phys. Rev. A 65, 063618/1-5 (2002).
[CrossRef]

Bardroff, P. J.

P. J. Bardroff, I. Bialynicki-Birula, D. S. Krahmer, G. Kurizki, E. Mayer, P. Stifter, and W. P. Schleich, "Dynamical localization in atomic momentum transfer," Phys. Rev. Lett. 74, 3959-3962 (1995).
[CrossRef] [PubMed]

Bernhardt, A. F.

A. F. Bernhardt and B. W. Shore, "Coherent atomic deflection by resonant standing waves," Phys. Rev. A 23, 1290-1301 (1981).
[CrossRef]

Bialynicki-Birula, I.

P. J. Bardroff, I. Bialynicki-Birula, D. S. Krahmer, G. Kurizki, E. Mayer, P. Stifter, and W. P. Schleich, "Dynamical localization in atomic momentum transfer," Phys. Rev. Lett. 74, 3959-3962 (1995).
[CrossRef] [PubMed]

Bloch, I.

I. Bloch, T. W. Hänsch, and T. Esslinger, "Atom laser with a cw output coupler," Phys. Rev. Lett. 82, 3008-3011 (1999).
[CrossRef]

Bongs, K.

K. Bongs and K. Sengstock, "Physics with coherent matter waves," Rep. Prog. Phys. 67, 907-963 (2004).
[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. A 71, 033612/1-8 (2005).
[CrossRef]

N. Piovella, M. Cola, and R. Bonifacio, "Quantum fluctuations and entanglement in the collective atomic recoil laser using a Bose-Einstein condensate," Phys. Rev. A 67, 013817/1-11 (2003).
[CrossRef]

N. Piovella, R. Bonifacio, B. W. J. McNeil, and G. R. M. Robb, "Superrradiant light scattering and grating formation in cold atomic vapours," Opt. Commun. 187, 165-170 (2001).
[CrossRef]

Boyd, M.

D. Schneble, Y. Torri, M. Boyd, E. W. Streed, D. Prichard, andW. Ketterle, "The onset of matter-wave amplication in a superradiant Bose-Einstein condensates," Science 300, 475-478 (2003).
[CrossRef] [PubMed]

Burnett, K.

M. Holland, K. Burnett, C. Gardiner, J. I. Cirac, and P. Zoller, "Theory of an atom laser," Phys. Rev. A 54, R1757-R1760 (1996).
[CrossRef] [PubMed]

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. A 71, 033612/1-8 (2005).
[CrossRef]

Chandrasekharan, K.

K. Chandrasekharan, Elliptic Functions (Springer-Verlag, 1980) Chap. VII.

Chikkatur, A. P.

S. Inouye, T. Pfau, S. Gupta, A. P. Chikkatur, A. Gorlitz, D. E. Pritchard, and W. Ketterle, "Phase-coherent amplification of atomic matter waves," Nature 402, 641-644 (1999).
[CrossRef]

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, "Bragg spectroscopy of a Bose-Einstein condensate," Phys. Rev. Lett. 82, 4569-4573 (1999).
[CrossRef]

Cirac, J. I.

M. Holland, K. Burnett, C. Gardiner, J. I. Cirac, and P. Zoller, "Theory of an atom laser," Phys. Rev. A 54, R1757-R1760 (1996).
[CrossRef] [PubMed]

Close, J. D.

S. A. Haine, A. J. Ferris, J. D. Close, and J. J. Hope, "Control of an atom laser using feedback," Phys. Rev. A 69, 013605/1-6 (2004).
[CrossRef]

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, J. D. Close, "Achieving peak brightness in an atom laser," cond-mat/0509462 (2005).

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. A 71, 033612/1-8 (2005).
[CrossRef]

N. Piovella, M. Cola, and R. Bonifacio, "Quantum fluctuations and entanglement in the collective atomic recoil laser using a Bose-Einstein condensate," Phys. Rev. A 67, 013817/1-11 (2003).
[CrossRef]

Davidson, N.

R. Ozeri, N. Katz, J. Steinhauer, and N. Davidson, "Bulk Bogoliubov excitations in a Bose-Einstein condensate," Rev. Mod. Phys. 77, 187-205 (2005).
[CrossRef]

Deb, B.

B. Deb and G. S. Agarwal, "Entangling two Bose-Einstein condensates by stimulated Bragg scattering," Phys. Rev. A 67, 023603/1-4 (2003).
[CrossRef]

B. Deb and G. S. Agarwal, "Tripartite entanglement in a Bose-Einstein condensate by stimulated Bragg scattering," Phys. Rev. A 65, 063618/1-5 (2002).
[CrossRef]

Deng, L.

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction," Phys. Rev. Lett. 82, 871-875 (1999).
[CrossRef]

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, "Phase-coherent amplification of matter waves," Science 286, 2309-2312 (1999).
[CrossRef] [PubMed]

E. W. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A well-collimated quasi-continuous atom laser," Science 283, 1706-1714 (1999).
[CrossRef] [PubMed]

Esslinger, T.

A. Öttl, S. Ritter, M. Köhl, and T. Esslinger, "Correlations and counting statistics of an atom laser," Phys. Rev. Lett. 95, 090404/1-4 (2005).
[CrossRef]

I. Bloch, T. W. Hänsch, and T. Esslinger, "Atom laser with a cw output coupler," Phys. Rev. Lett. 82, 3008-3011 (1999).
[CrossRef]

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. A 71, 033612/1-8 (2005).
[CrossRef]

Ferris, A. J.

S. A. Haine, A. J. Ferris, J. D. Close, and J. J. Hope, "Control of an atom laser using feedback," Phys. Rev. A 69, 013605/1-6 (2004).
[CrossRef]

Figl, C.

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, J. D. Close, "Achieving peak brightness in an atom laser," cond-mat/0509462 (2005).

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. A 71, 033612/1-8 (2005).
[CrossRef]

Gardiner, C.

M. Holland, K. Burnett, C. Gardiner, J. I. Cirac, and P. Zoller, "Theory of an atom laser," Phys. Rev. A 54, R1757-R1760 (1996).
[CrossRef] [PubMed]

Ge, M.-L.

X.-J. Liu, H. Jing, X. Liu, and M.-L. Ge, "Generation of two-flavor vortex atom laser from a five-state medium," Eur. Phys. J. D37, 261-265 (2005).

Gorlitz, A.

S. Inouye, T. Pfau, S. Gupta, A. P. Chikkatur, A. Gorlitz, D. E. Pritchard, and W. Ketterle, "Phase-coherent amplification of atomic matter waves," Nature 402, 641-644 (1999).
[CrossRef]

Gupta, S.

S. Inouye, T. Pfau, S. Gupta, A. P. Chikkatur, A. Gorlitz, D. E. Pritchard, and W. Ketterle, "Phase-coherent amplification of atomic matter waves," Nature 402, 641-644 (1999).
[CrossRef]

Hagley, E. W.

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction," Phys. Rev. Lett. 82, 871-875 (1999).
[CrossRef]

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, "Phase-coherent amplification of matter waves," Science 286, 2309-2312 (1999).
[CrossRef] [PubMed]

E. W. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A well-collimated quasi-continuous atom laser," Science 283, 1706-1714 (1999).
[CrossRef] [PubMed]

Haine, S. A.

S. A. Haine, A. J. Ferris, J. D. Close, and J. J. Hope, "Control of an atom laser using feedback," Phys. Rev. A 69, 013605/1-6 (2004).
[CrossRef]

S. A. Haine, J. J. Hope, N. P. Robins, and C. M. Savage, "Stability of continuously pumped atom lasers," Phys. Rev. Lett. 88, 170403/1-4 (2002).
[CrossRef]

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, J. D. Close, "Achieving peak brightness in an atom laser," cond-mat/0509462 (2005).

Hänsch, T. W.

I. Bloch, T. W. Hänsch, and T. Esslinger, "Atom laser with a cw output coupler," Phys. Rev. Lett. 82, 3008-3011 (1999).
[CrossRef]

Helmerson, K.

E. W. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A well-collimated quasi-continuous atom laser," Science 283, 1706-1714 (1999).
[CrossRef] [PubMed]

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction," Phys. Rev. Lett. 82, 871-875 (1999).
[CrossRef]

Holland, M.

M. Holland, K. Burnett, C. Gardiner, J. I. Cirac, and P. Zoller, "Theory of an atom laser," Phys. Rev. A 54, R1757-R1760 (1996).
[CrossRef] [PubMed]

Hope, J. J.

S. A. Haine, A. J. Ferris, J. D. Close, and J. J. Hope, "Control of an atom laser using feedback," Phys. Rev. A 69, 013605/1-6 (2004).
[CrossRef]

S. A. Haine, J. J. Hope, N. P. Robins, and C. M. Savage, "Stability of continuously pumped atom lasers," Phys. Rev. Lett. 88, 170403/1-4 (2002).
[CrossRef]

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, J. D. Close, "Achieving peak brightness in an atom laser," cond-mat/0509462 (2005).

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. A 71, 033612/1-8 (2005).
[CrossRef]

Inouye, S.

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, "Bragg spectroscopy of a Bose-Einstein condensate," Phys. Rev. Lett. 82, 4569-4573 (1999).
[CrossRef]

S. Inouye, T. Pfau, S. Gupta, A. P. Chikkatur, A. Gorlitz, D. E. Pritchard, and W. Ketterle, "Phase-coherent amplification of atomic matter waves," Nature 402, 641-644 (1999).
[CrossRef]

Jeppesen, M.

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, J. D. Close, "Achieving peak brightness in an atom laser," cond-mat/0509462 (2005).

Jing, H.

X.-J. Liu, H. Jing, X. Liu, and M.-L. Ge, "Generation of two-flavor vortex atom laser from a five-state medium," Eur. Phys. J. D37, 261-265 (2005).

Katz, N.

R. Ozeri, N. Katz, J. Steinhauer, and N. Davidson, "Bulk Bogoliubov excitations in a Bose-Einstein condensate," Rev. Mod. Phys. 77, 187-205 (2005).
[CrossRef]

Ketterle, W.

D. Schneble, Y. Torri, M. Boyd, E. W. Streed, D. Prichard, andW. Ketterle, "The onset of matter-wave amplication in a superradiant Bose-Einstein condensates," Science 300, 475-478 (2003).
[CrossRef] [PubMed]

S. Inouye, T. Pfau, S. Gupta, A. P. Chikkatur, A. Gorlitz, D. E. Pritchard, and W. Ketterle, "Phase-coherent amplification of atomic matter waves," Nature 402, 641-644 (1999).
[CrossRef]

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, "Bragg spectroscopy of a Bose-Einstein condensate," Phys. Rev. Lett. 82, 4569-4573 (1999).
[CrossRef]

Köhl, M.

A. Öttl, S. Ritter, M. Köhl, and T. Esslinger, "Correlations and counting statistics of an atom laser," Phys. Rev. Lett. 95, 090404/1-4 (2005).
[CrossRef]

Kozhekin, A.

A. Kozhekin, G. Kurizki, and B. Sherman, "Quantum state control by a single conditional measurement: the periodically-switched model," Phys. Rev. A 54, 3535-3538 (1996).
[CrossRef] [PubMed]

Kozhekin, A. E.

A. E. Kozhekin and G. Kurizki, "Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances," Phys. Rev. Lett. 74, 5020-5023 (1995).
[CrossRef] [PubMed]

Kozuma, M.

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction," Phys. Rev. Lett. 82, 871-875 (1999).
[CrossRef]

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, "Phase-coherent amplification of matter waves," Science 286, 2309-2312 (1999).
[CrossRef] [PubMed]

E. W. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A well-collimated quasi-continuous atom laser," Science 283, 1706-1714 (1999).
[CrossRef] [PubMed]

Krahmer, D. S.

P. J. Bardroff, I. Bialynicki-Birula, D. S. Krahmer, G. Kurizki, E. Mayer, P. Stifter, and W. P. Schleich, "Dynamical localization in atomic momentum transfer," Phys. Rev. Lett. 74, 3959-3962 (1995).
[CrossRef] [PubMed]

Kuga, T.

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, "Phase-coherent amplification of matter waves," Science 286, 2309-2312 (1999).
[CrossRef] [PubMed]

Kurizki, G.

A. Kozhekin, G. Kurizki, and B. Sherman, "Quantum state control by a single conditional measurement: the periodically-switched model," Phys. Rev. A 54, 3535-3538 (1996).
[CrossRef] [PubMed]

P. J. Bardroff, I. Bialynicki-Birula, D. S. Krahmer, G. Kurizki, E. Mayer, P. Stifter, and W. P. Schleich, "Dynamical localization in atomic momentum transfer," Phys. Rev. Lett. 74, 3959-3962 (1995).
[CrossRef] [PubMed]

A. E. Kozhekin and G. Kurizki, "Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances," Phys. Rev. Lett. 74, 5020-5023 (1995).
[CrossRef] [PubMed]

Lenz, G.

K. J. Schernthanner, G. Lenz, and P. Meystre, "Many-body effects in near-resonant Kapitza-Dirac diffraction: the nonlinear pendellösung," Phys. Rev. A 51, 3121-3127 (1995).
[CrossRef] [PubMed]

Liu, X.

X.-J. Liu, H. Jing, X. Liu, and M.-L. Ge, "Generation of two-flavor vortex atom laser from a five-state medium," Eur. Phys. J. D37, 261-265 (2005).

Liu, X.-J.

X.-J. Liu, H. Jing, X. Liu, and M.-L. Ge, "Generation of two-flavor vortex atom laser from a five-state medium," Eur. Phys. J. D37, 261-265 (2005).

Lutwak, R.

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction," Phys. Rev. Lett. 82, 871-875 (1999).
[CrossRef]

Martin, P. J.

P. J. Martin, B. G. Oldaker, A. H. Miklich, and D. E. Pritchard, "Bragg scattering of atoms from a standing light wave," Phys. Rev. Lett. 60, 515-518 (1988).
[CrossRef]

Mayer, E.

P. J. Bardroff, I. Bialynicki-Birula, D. S. Krahmer, G. Kurizki, E. Mayer, P. Stifter, and W. P. Schleich, "Dynamical localization in atomic momentum transfer," Phys. Rev. Lett. 74, 3959-3962 (1995).
[CrossRef] [PubMed]

McNeil, B. W. J.

N. Piovella, R. Bonifacio, B. W. J. McNeil, and G. R. M. Robb, "Superrradiant light scattering and grating formation in cold atomic vapours," Opt. Commun. 187, 165-170 (2001).
[CrossRef]

Meystre, P.

C. P. Search, S. Pötting, W. Zhang, and P. Meystre, "Input-output theory for fermions in an atom cavity," Phys. Rev. A 66, 043616/1-10 (2002).
[CrossRef]

M. G. Moore, O. Zobay, and P. Meystre, "Quantum optics of a Bose-Einstein condensate coupled to a quantized light field," Phys. Rev. A 60, 1491-1506 (1999).
[CrossRef]

K. J. Schernthanner, G. Lenz, and P. Meystre, "Many-body effects in near-resonant Kapitza-Dirac diffraction: the nonlinear pendellösung," Phys. Rev. A 51, 3121-3127 (1995).
[CrossRef] [PubMed]

P. Meystre, Atom Optics (Springer, 2001).

Miklich, A. H.

P. J. Martin, B. G. Oldaker, A. H. Miklich, and D. E. Pritchard, "Bragg scattering of atoms from a standing light wave," Phys. Rev. Lett. 60, 515-518 (1988).
[CrossRef]

Moore, M. G.

M. G. Moore, O. Zobay, and P. Meystre, "Quantum optics of a Bose-Einstein condensate coupled to a quantized light field," Phys. Rev. A 60, 1491-1506 (1999).
[CrossRef]

Morrison, A. K.

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, J. D. Close, "Achieving peak brightness in an atom laser," cond-mat/0509462 (2005).

Müstecaplioglu, Ö. E.

Ö. E. Müstecaplioglu and L. You, "Superradiant light scattering from trapped Bose-Einstein condensates," Phys. Rev. A 62, 063615/1-12 (2001).

Oldaker, B. G.

P. J. Martin, B. G. Oldaker, A. H. Miklich, and D. E. Pritchard, "Bragg scattering of atoms from a standing light wave," Phys. Rev. Lett. 60, 515-518 (1988).
[CrossRef]

Ostrovskaya, E. A.

N. Robins, C. Savage, and E. A. Ostrovskaya, "Atom-laser dynamics," Phys. Rev. A 64, 043605/1-4 (2001).
[CrossRef]

Öttl, A.

A. Öttl, S. Ritter, M. Köhl, and T. Esslinger, "Correlations and counting statistics of an atom laser," Phys. Rev. Lett. 95, 090404/1-4 (2005).
[CrossRef]

Ozeri, R.

R. Ozeri, N. Katz, J. Steinhauer, and N. Davidson, "Bulk Bogoliubov excitations in a Bose-Einstein condensate," Rev. Mod. Phys. 77, 187-205 (2005).
[CrossRef]

Pfau, T.

S. Inouye, T. Pfau, S. Gupta, A. P. Chikkatur, A. Gorlitz, D. E. Pritchard, and W. Ketterle, "Phase-coherent amplification of atomic matter waves," Nature 402, 641-644 (1999).
[CrossRef]

Phillips, W. D.

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction," Phys. Rev. Lett. 82, 871-875 (1999).
[CrossRef]

E. W. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A well-collimated quasi-continuous atom laser," Science 283, 1706-1714 (1999).
[CrossRef] [PubMed]

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. A 71, 033612/1-8 (2005).
[CrossRef]

N. Piovella, M. Cola, and R. Bonifacio, "Quantum fluctuations and entanglement in the collective atomic recoil laser using a Bose-Einstein condensate," Phys. Rev. A 67, 013817/1-11 (2003).
[CrossRef]

N. Piovella, R. Bonifacio, B. W. J. McNeil, and G. R. M. Robb, "Superrradiant light scattering and grating formation in cold atomic vapours," Opt. Commun. 187, 165-170 (2001).
[CrossRef]

Pötting, S.

C. P. Search, S. Pötting, W. Zhang, and P. Meystre, "Input-output theory for fermions in an atom cavity," Phys. Rev. A 66, 043616/1-10 (2002).
[CrossRef]

Prichard, D.

D. Schneble, Y. Torri, M. Boyd, E. W. Streed, D. Prichard, andW. Ketterle, "The onset of matter-wave amplication in a superradiant Bose-Einstein condensates," Science 300, 475-478 (2003).
[CrossRef] [PubMed]

Pritchard, D. E.

S. Inouye, T. Pfau, S. Gupta, A. P. Chikkatur, A. Gorlitz, D. E. Pritchard, and W. Ketterle, "Phase-coherent amplification of atomic matter waves," Nature 402, 641-644 (1999).
[CrossRef]

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, "Bragg spectroscopy of a Bose-Einstein condensate," Phys. Rev. Lett. 82, 4569-4573 (1999).
[CrossRef]

P. J. Martin, B. G. Oldaker, A. H. Miklich, and D. E. Pritchard, "Bragg scattering of atoms from a standing light wave," Phys. Rev. Lett. 60, 515-518 (1988).
[CrossRef]

Ritter, S.

A. Öttl, S. Ritter, M. Köhl, and T. Esslinger, "Correlations and counting statistics of an atom laser," Phys. Rev. Lett. 95, 090404/1-4 (2005).
[CrossRef]

Robb, G. R. M.

N. Piovella, R. Bonifacio, B. W. J. McNeil, and G. R. M. Robb, "Superrradiant light scattering and grating formation in cold atomic vapours," Opt. Commun. 187, 165-170 (2001).
[CrossRef]

Robins, N.

N. Robins, C. Savage, and E. A. Ostrovskaya, "Atom-laser dynamics," Phys. Rev. A 64, 043605/1-4 (2001).
[CrossRef]

Robins, N. P.

S. A. Haine, J. J. Hope, N. P. Robins, and C. M. Savage, "Stability of continuously pumped atom lasers," Phys. Rev. Lett. 88, 170403/1-4 (2002).
[CrossRef]

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, J. D. Close, "Achieving peak brightness in an atom laser," cond-mat/0509462 (2005).

Rolston, S. L.

E. W. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A well-collimated quasi-continuous atom laser," Science 283, 1706-1714 (1999).
[CrossRef] [PubMed]

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction," Phys. Rev. Lett. 82, 871-875 (1999).
[CrossRef]

Savage, C.

N. Robins, C. Savage, and E. A. Ostrovskaya, "Atom-laser dynamics," Phys. Rev. A 64, 043605/1-4 (2001).
[CrossRef]

Savage, C. M.

S. A. Haine, J. J. Hope, N. P. Robins, and C. M. Savage, "Stability of continuously pumped atom lasers," Phys. Rev. Lett. 88, 170403/1-4 (2002).
[CrossRef]

Schernthanner, K. J.

K. J. Schernthanner, G. Lenz, and P. Meystre, "Many-body effects in near-resonant Kapitza-Dirac diffraction: the nonlinear pendellösung," Phys. Rev. A 51, 3121-3127 (1995).
[CrossRef] [PubMed]

Schleich, W. P.

P. J. Bardroff, I. Bialynicki-Birula, D. S. Krahmer, G. Kurizki, E. Mayer, P. Stifter, and W. P. Schleich, "Dynamical localization in atomic momentum transfer," Phys. Rev. Lett. 74, 3959-3962 (1995).
[CrossRef] [PubMed]

Schneble, D.

D. Schneble, Y. Torri, M. Boyd, E. W. Streed, D. Prichard, andW. Ketterle, "The onset of matter-wave amplication in a superradiant Bose-Einstein condensates," Science 300, 475-478 (2003).
[CrossRef] [PubMed]

Search, C. P.

C. P. Search, S. Pötting, W. Zhang, and P. Meystre, "Input-output theory for fermions in an atom cavity," Phys. Rev. A 66, 043616/1-10 (2002).
[CrossRef]

Sengstock, K.

K. Bongs and K. Sengstock, "Physics with coherent matter waves," Rep. Prog. Phys. 67, 907-963 (2004).
[CrossRef]

Sherman, B.

A. Kozhekin, G. Kurizki, and B. Sherman, "Quantum state control by a single conditional measurement: the periodically-switched model," Phys. Rev. A 54, 3535-3538 (1996).
[CrossRef] [PubMed]

Shore, B. W.

A. F. Bernhardt and B. W. Shore, "Coherent atomic deflection by resonant standing waves," Phys. Rev. A 23, 1290-1301 (1981).
[CrossRef]

Stamper-Kurn, D. M.

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, "Bragg spectroscopy of a Bose-Einstein condensate," Phys. Rev. Lett. 82, 4569-4573 (1999).
[CrossRef]

Steinhauer, J.

R. Ozeri, N. Katz, J. Steinhauer, and N. Davidson, "Bulk Bogoliubov excitations in a Bose-Einstein condensate," Rev. Mod. Phys. 77, 187-205 (2005).
[CrossRef]

Stenger, J.

J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, "Bragg spectroscopy of a Bose-Einstein condensate," Phys. Rev. Lett. 82, 4569-4573 (1999).
[CrossRef]

Stifter, P.

P. J. Bardroff, I. Bialynicki-Birula, D. S. Krahmer, G. Kurizki, E. Mayer, P. Stifter, and W. P. Schleich, "Dynamical localization in atomic momentum transfer," Phys. Rev. Lett. 74, 3959-3962 (1995).
[CrossRef] [PubMed]

Streed, E. W.

D. Schneble, Y. Torri, M. Boyd, E. W. Streed, D. Prichard, andW. Ketterle, "The onset of matter-wave amplication in a superradiant Bose-Einstein condensates," Science 300, 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 amplification of matter waves," Science 286, 2309-2312 (1999).
[CrossRef] [PubMed]

Sun, C. P.

Y. Wu, X. Yang, C. P. Sun, X. J. Zhou, and Y. Q. Wang, "Theory of four-wave mixing with matter waves without the undepleted pump approximation," Phys. Rev. A 61, 043604/1-6 (2000).
[CrossRef]

Suzuki, Y.

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, "Phase-coherent amplification of matter waves," Science 286, 2309-2312 (1999).
[CrossRef] [PubMed]

Thomsen, L. K.

L. K. Thomsen and H. M. Wiseman, "Atom-laser coherence and its control via feedback," Phys. Rev. A 65, 063607/1-14 (2002).
[CrossRef]

Torii, Y.

M. Kozuma, Y. Suzuki, Y. Torii, T. Sugiura, T. Kuga, E. W. Hagley, and L. Deng, "Phase-coherent amplification of matter waves," Science 286, 2309-2312 (1999).
[CrossRef] [PubMed]

Torri, Y.

D. Schneble, Y. Torri, M. Boyd, E. W. Streed, D. Prichard, andW. Ketterle, "The onset of matter-wave amplication in a superradiant Bose-Einstein condensates," Science 300, 475-478 (2003).
[CrossRef] [PubMed]

Walls, D. F.

W. Zhang and D. F. Walls, "Quantum field theory of interaction of ultracold atoms with a light wave: Bragg scattering in nonlinear atom optics," Phys. Rev. A 49, 3799-3813 (1994).
[CrossRef] [PubMed]

Wang, Y. Q.

Y. Wu, X. Yang, C. P. Sun, X. J. Zhou, and Y. Q. Wang, "Theory of four-wave mixing with matter waves without the undepleted pump approximation," Phys. Rev. A 61, 043604/1-6 (2000).
[CrossRef]

Wen, J.

E. W. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A well-collimated quasi-continuous atom laser," Science 283, 1706-1714 (1999).
[CrossRef] [PubMed]

M. Kozuma, L. Deng, E. W. Hagley, J. Wen, R. Lutwak, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction," Phys. Rev. Lett. 82, 871-875 (1999).
[CrossRef]

Wiseman, H. M.

L. K. Thomsen and H. M. Wiseman, "Atom-laser coherence and its control via feedback," Phys. Rev. A 65, 063607/1-14 (2002).
[CrossRef]

Wu, Y.

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

Y. Wu and X. Yang, "Eigenstates and eigenenergies of four-wave mixing models," Opt. Lett. 29, 839-841 (2004).
[CrossRef] [PubMed]

Y. Wu, X. Yang, C. P. Sun, X. J. Zhou, and Y. Q. Wang, "Theory of four-wave mixing with matter waves without the undepleted pump approximation," Phys. Rev. A 61, 043604/1-6 (2000).
[CrossRef]

Y. Wu and X. Yang, "Output rate of atom lasers in Raman-type output-coupling scheme," Phys. Rev. A 62, 013603/1-8 (2000).
[CrossRef]

Yang, X.

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

Y. Wu and X. Yang, "Eigenstates and eigenenergies of four-wave mixing models," Opt. Lett. 29, 839-841 (2004).
[CrossRef] [PubMed]

Y. Wu, X. Yang, C. P. Sun, X. J. Zhou, and Y. Q. Wang, "Theory of four-wave mixing with matter waves without the undepleted pump approximation," Phys. Rev. A 61, 043604/1-6 (2000).
[CrossRef]

Y. Wu and X. Yang, "Output rate of atom lasers in Raman-type output-coupling scheme," Phys. Rev. A 62, 013603/1-8 (2000).
[CrossRef]

You, L.

Ö. E. Müstecaplioglu and L. You, "Superradiant light scattering from trapped Bose-Einstein condensates," Phys. Rev. A 62, 063615/1-12 (2001).

Zhang, W.

C. P. Search, S. Pötting, W. Zhang, and P. Meystre, "Input-output theory for fermions in an atom cavity," Phys. Rev. A 66, 043616/1-10 (2002).
[CrossRef]

W. Zhang and D. F. Walls, "Quantum field theory of interaction of ultracold atoms with a light wave: Bragg scattering in nonlinear atom optics," Phys. Rev. A 49, 3799-3813 (1994).
[CrossRef] [PubMed]

Zhou, X. J.

Y. Wu, X. Yang, C. P. Sun, X. J. Zhou, and Y. Q. Wang, "Theory of four-wave mixing with matter waves without the undepleted pump approximation," Phys. Rev. A 61, 043604/1-6 (2000).
[CrossRef]

Zobay, O.

M. G. Moore, O. Zobay, and P. Meystre, "Quantum optics of a Bose-Einstein condensate coupled to a quantized light field," Phys. Rev. A 60, 1491-1506 (1999).
[CrossRef]

Zoller, P.

M. Holland, K. Burnett, C. Gardiner, J. I. Cirac, and P. Zoller, "Theory of an atom laser," Phys. Rev. A 54, R1757-R1760 (1996).
[CrossRef] [PubMed]

Nature (1)

S. Inouye, T. Pfau, S. Gupta, A. P. Chikkatur, A. Gorlitz, D. E. Pritchard, and W. Ketterle, "Phase-coherent amplification of atomic matter waves," Nature 402, 641-644 (1999).
[CrossRef]

Opt. Commun. (1)

N. Piovella, R. Bonifacio, B. W. J. McNeil, and G. R. M. Robb, "Superrradiant light scattering and grating formation in cold atomic vapours," Opt. Commun. 187, 165-170 (2001).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (17)

L. K. Thomsen and H. M. Wiseman, "Atom-laser coherence and its control via feedback," Phys. Rev. A 65, 063607/1-14 (2002).
[CrossRef]

N. Robins, C. Savage, and E. A. Ostrovskaya, "Atom-laser dynamics," Phys. Rev. A 64, 043605/1-4 (2001).
[CrossRef]

Ö. E. Müstecaplioglu and L. You, "Superradiant light scattering from trapped Bose-Einstein condensates," Phys. Rev. A 62, 063615/1-12 (2001).

Y. Wu and X. Yang, "Output rate of atom lasers in Raman-type output-coupling scheme," Phys. Rev. A 62, 013603/1-8 (2000).
[CrossRef]

M. Holland, K. Burnett, C. Gardiner, J. I. Cirac, and P. Zoller, "Theory of an atom laser," Phys. Rev. A 54, R1757-R1760 (1996).
[CrossRef] [PubMed]

S. A. Haine, A. J. Ferris, J. D. Close, and J. J. Hope, "Control of an atom laser using feedback," Phys. Rev. A 69, 013605/1-6 (2004).
[CrossRef]

C. P. Search, S. Pötting, W. Zhang, and P. Meystre, "Input-output theory for fermions in an atom cavity," Phys. Rev. A 66, 043616/1-10 (2002).
[CrossRef]

M. G. Moore, O. Zobay, and P. Meystre, "Quantum optics of a Bose-Einstein condensate coupled to a quantized light field," Phys. Rev. A 60, 1491-1506 (1999).
[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. A 71, 033612/1-8 (2005).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematic of the Bragg diffraction. Atom laser A is incident onto an optical standing wave existing within the region x [ 0 , L ] to produce a diffracted atom laser B.

Fig. 2
Fig. 2

Diffraction efficiency η (left) and the phase difference ϕ B A (right) versus L ̃ = v L Ω 2 R , the dimensionless width of the diffraction region, for u = 0.8 . The superimposed dashed curves are the results in the absence of the two-body atomic interactions ( u = 0 ) .

Fig. 3
Fig. 3

Same as Fig. 2 except for u = 1.5 .

Fig. 4
Fig. 4

Same as Fig. 2 except for u = 1 .

Fig. 5
Fig. 5

Same as Fig. 2 except for u = 3 .

Fig. 6
Fig. 6

Same as Fig. 2 except for u = 0.99 .

Equations (15)

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i Ψ t = ( 2 2 M 2 + 4 π 2 σ M Ψ 2 + Ω 2 R cos θ ) Ψ ,
d A d x ̃ = i 1 2 B i 2 u n ( A 2 + 2 B 2 ) A ,
d B d x ̃ = i 1 2 A i 2 u n ( B 2 + 2 A 2 ) B ,
1 2 n A d n A d x ̃ + i d ϕ A d x ̃ = d ln A d x ̃ = i n B 2 n A exp [ i ( ϕ B ϕ A ) ] i 2 u n ( n A + 2 n B ) ,
1 2 n B d n B d x ̃ + i d ϕ B d x ̃ = d ln B d x ̃ = i n A 2 n B exp [ i ( ϕ B ϕ A ) ] i 2 u n ( n B + 2 n A ) .
d n A d x ̃ = n A n B cos ϕ ,
d ϕ d x ̃ = d ( ϕ B ϕ A ) d x ̃ = 1 2 ( n A n B n B n A ) sin ϕ + 2 u n ( n B n A ) .
d f d x ̃ = f ( 1 f ) cos ϕ H ϕ ,
d ϕ d x ̃ = 2 f 1 2 f ( 1 f ) sin ϕ + 2 u ( 1 2 f ) H f ,
( d G d x ̃ ) 2 = ( 1 G 2 ) [ ( 1 u 2 ) + u 2 G 2 ] ,
( d G d ξ ) 2 = ( 1 G 2 ) [ ( u 2 1 ) + G 2 ] ,
n B ( x ) n = 1 c n ( x l , u 2 ) 2 , sin ϕ ( x ) = u s n ( x l , u 2 ) , as u = 2 π n σ M Ω 2 R 1 ,
n B ( x ) n = 1 d n ( x l 1 , u 2 ) 2 , sin ϕ ( x ) = 1 u s n ( x l 1 , u 2 ) , as u = 2 π n σ M Ω 2 R 1 ,
η = 1 c n ( L ̃ , u 2 ) 2 , ϕ B A = cos 1 [ u s n ( L ̃ , u 2 ) ] ,
η = 1 d n ( L ̃ 1 , u 2 ) 2 , ϕ B A = cos 1 [ s n ( L ̃ 1 , u 2 ) u ] ,

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