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]

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

[CrossRef]
[PubMed]

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]

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]

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

[CrossRef]
[PubMed]

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

[CrossRef]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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

[CrossRef]

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]

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

[CrossRef]

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]

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

[CrossRef]

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

[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]

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]

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]

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]

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]

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

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]

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]

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).

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]

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]

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]

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]

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]

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]

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]

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).

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]

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]

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).

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]

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, 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]

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]

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).

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

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. 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]

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).

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]

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]

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).

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).

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]

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]

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]

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]

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]

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, 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]

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]

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]

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]

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]

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]

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).

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).

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]

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]

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]

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]

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).

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]

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]

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).

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

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]

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

[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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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

[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).

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]

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

[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]

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. 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]

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]

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]

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

[CrossRef]

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]

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

[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]

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]

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. 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]

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]

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]

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]

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]

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

[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]

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]

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]

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]

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]

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

[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]

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

[CrossRef]
[PubMed]

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]

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

[CrossRef]

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]

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

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]

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]

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. 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. 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]

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]

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]

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]

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]

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]

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

[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]

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]

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]

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]

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

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]

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

[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]

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]

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]

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]

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

[CrossRef]

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]

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]

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]

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).

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

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).

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