Abstract

The nonlinear coupling term in the Gross-Pitiaevski equation which describes a Bose-Einstein condensate (BEC) can cause four-wave mixing (4WM) if three BEC wavepackets with momenta k 1, k 2, and k 3 interact. The interaction will produce a fourth wavepacket with momentum k 4 = k 1 + k 2 - k 3. We study this process using numerical models and suggest that experiments are feasible. Conservation of energy and momentum have different consequences for 4WM with massive particles than in the nonlinear optics case because of the different energy-momentum dispersion relations.

© 1998 Optical Society of America

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References

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  1. M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two Bose-Einstein condensates,” Science 275, 637 (1997).
    [Crossref] [PubMed]
  2. D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of relative phase in two-component Bose-Einstein condensates,” Phys. Rev. Lett. 81, 1543 (1998).
    [Crossref]
  3. H. Wallis, A. Rohrl, M. Naraschewski, and A. Schenzle, “Phase-space dynamics of Bose condensates: Interference versus interaction,” Phys. Rev. A55, 2109 (1997).
  4. A. Rohrl, M. Naraschewski, A. Schenzle, and H. Wallis, “Transition from phase locking to the interference of independent Bose condensates: Theory versus experiment,” Phys. Rev. Lett. 78, 4143 (1997).
    [Crossref]
  5. J. Javanainen and M. Wilkens, “Phase and phase diffusion of a split Bose-Einstein condensate,” Phys. Rev. Lett. 78, 4675 (1997).
    [Crossref]
  6. R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479 (1964).
    [Crossref]
  7. O. Svelto, “Self-focusing, self-trapping, and self-phase modulation of laser beams,” Prog. Opt. 12, 3 (1973).
  8. R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quant. Electr. 5, 1 (1977).
    [Crossref]
  9. M.-O. Mewes, M R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, “Bose-Einstein Condensation in a Tightly Confining dc Magnetic Trap,” Phys. Rev. Lett. 77, 416 (1996).
    [Crossref] [PubMed]
  10. E. Goldstein, K. Plättner, and P. Meystre, “Atomic phase conjugation,” Quantum Semiclass. Opt. 7, 743 (1995).
    [Crossref]
  11. E. Goldstein, K. Plättner, and P. Meystre, “Atomic phase conjugation from a Bose condensate,” J. Res. Nat. Inst. Stand. Technol. 101, 583 (1996).
    [Crossref]
  12. E. Goldstein and P. Meystre, “Phase conjugation of trapped Bose-Einstein condensates,” LANL Preprint Archive Cond-mat/9806165 (1998).
  13. C. K. Law, H. Pu, and N. P. Bigelow, “Quantum spins mixing of spinor Bose-Einstein condensates,” LANL Preprint Archive Cond-mat/9807258 (1998).
  14. M. Kozuma, L. Deng, E. 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., in press (1998).
  15. E. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A well-collimated quasi-continuous atom laser,” preprint (1998).
  16. P. D. Maker and R. W. Terhune, “Study of optical effects due to induced polarization third order in the electric field strength,” Phys. Rev. A137, 801 (1965).
    [Crossref]
  17. A. Yariv and D. M. Pepper, “Amplified reflection , phase-conjugate, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1, 16 (1977).
    [Crossref] [PubMed]
  18. P. Noziéres and D. Pines, The Theory of Quantum Liquids, Vol. II, (Addison-Wesley, Redwood City, 1990).
  19. M. Trippenbach and Y. B. Band, “Dynamics of short pulse splitting in dispersive nonlinear media,” Phys. Rev. A56, 4242 (1997)
  20. M. Trippenbach and Y. B. Band, “Effects of Self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A57, 4791 (1998).
  21. Y. Japha, S. Choi, K. Burnett, and Y. B. Band, “Coherent output, stimulated quantum evaporation and pair breaking in a trapped atomic Bose gas,” Phys. Rev. Lett. (in press).
  22. J. Stenger, S. Inouye, D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, and W. Ketterle, “Spin domains in ground-state Bose-Einstein condensates,” Nature 396, 345 (1998).
    [Crossref]

1998 (3)

D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of relative phase in two-component Bose-Einstein condensates,” Phys. Rev. Lett. 81, 1543 (1998).
[Crossref]

M. Trippenbach and Y. B. Band, “Effects of Self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A57, 4791 (1998).

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, and W. Ketterle, “Spin domains in ground-state Bose-Einstein condensates,” Nature 396, 345 (1998).
[Crossref]

1997 (5)

M. Trippenbach and Y. B. Band, “Dynamics of short pulse splitting in dispersive nonlinear media,” Phys. Rev. A56, 4242 (1997)

H. Wallis, A. Rohrl, M. Naraschewski, and A. Schenzle, “Phase-space dynamics of Bose condensates: Interference versus interaction,” Phys. Rev. A55, 2109 (1997).

A. Rohrl, M. Naraschewski, A. Schenzle, and H. Wallis, “Transition from phase locking to the interference of independent Bose condensates: Theory versus experiment,” Phys. Rev. Lett. 78, 4143 (1997).
[Crossref]

J. Javanainen and M. Wilkens, “Phase and phase diffusion of a split Bose-Einstein condensate,” Phys. Rev. Lett. 78, 4675 (1997).
[Crossref]

M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two Bose-Einstein condensates,” Science 275, 637 (1997).
[Crossref] [PubMed]

1996 (2)

M.-O. Mewes, M R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, “Bose-Einstein Condensation in a Tightly Confining dc Magnetic Trap,” Phys. Rev. Lett. 77, 416 (1996).
[Crossref] [PubMed]

E. Goldstein, K. Plättner, and P. Meystre, “Atomic phase conjugation from a Bose condensate,” J. Res. Nat. Inst. Stand. Technol. 101, 583 (1996).
[Crossref]

1995 (1)

E. Goldstein, K. Plättner, and P. Meystre, “Atomic phase conjugation,” Quantum Semiclass. Opt. 7, 743 (1995).
[Crossref]

1977 (2)

R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quant. Electr. 5, 1 (1977).
[Crossref]

A. Yariv and D. M. Pepper, “Amplified reflection , phase-conjugate, and oscillation in degenerate four-wave mixing,” Opt. Lett. 1, 16 (1977).
[Crossref] [PubMed]

1973 (1)

O. Svelto, “Self-focusing, self-trapping, and self-phase modulation of laser beams,” Prog. Opt. 12, 3 (1973).

1965 (1)

P. D. Maker and R. W. Terhune, “Study of optical effects due to induced polarization third order in the electric field strength,” Phys. Rev. A137, 801 (1965).
[Crossref]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Andrews, M R.

M.-O. Mewes, M R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, “Bose-Einstein Condensation in a Tightly Confining dc Magnetic Trap,” Phys. Rev. Lett. 77, 416 (1996).
[Crossref] [PubMed]

Andrews, M. R.

M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two Bose-Einstein condensates,” Science 275, 637 (1997).
[Crossref] [PubMed]

Band, Y. B.

M. Trippenbach and Y. B. Band, “Effects of Self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A57, 4791 (1998).

M. Trippenbach and Y. B. Band, “Dynamics of short pulse splitting in dispersive nonlinear media,” Phys. Rev. A56, 4242 (1997)

Y. Japha, S. Choi, K. Burnett, and Y. B. Band, “Coherent output, stimulated quantum evaporation and pair breaking in a trapped atomic Bose gas,” Phys. Rev. Lett. (in press).

Bigelow, N. P.

C. K. Law, H. Pu, and N. P. Bigelow, “Quantum spins mixing of spinor Bose-Einstein condensates,” LANL Preprint Archive Cond-mat/9807258 (1998).

Burnett, K.

Y. Japha, S. Choi, K. Burnett, and Y. B. Band, “Coherent output, stimulated quantum evaporation and pair breaking in a trapped atomic Bose gas,” Phys. Rev. Lett. (in press).

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Chikkatur, A. P.

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, and W. Ketterle, “Spin domains in ground-state Bose-Einstein condensates,” Nature 396, 345 (1998).
[Crossref]

Choi, S.

Y. Japha, S. Choi, K. Burnett, and Y. B. Band, “Coherent output, stimulated quantum evaporation and pair breaking in a trapped atomic Bose gas,” Phys. Rev. Lett. (in press).

Cornell, E. A.

D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of relative phase in two-component Bose-Einstein condensates,” Phys. Rev. Lett. 81, 1543 (1998).
[Crossref]

Deng, L.

M. Kozuma, L. Deng, E. 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., in press (1998).

E. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A well-collimated quasi-continuous atom laser,” preprint (1998).

Durfee, D. S.

M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two Bose-Einstein condensates,” Science 275, 637 (1997).
[Crossref] [PubMed]

M.-O. Mewes, M R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, “Bose-Einstein Condensation in a Tightly Confining dc Magnetic Trap,” Phys. Rev. Lett. 77, 416 (1996).
[Crossref] [PubMed]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Goldstein, E.

E. Goldstein, K. Plättner, and P. Meystre, “Atomic phase conjugation from a Bose condensate,” J. Res. Nat. Inst. Stand. Technol. 101, 583 (1996).
[Crossref]

E. Goldstein, K. Plättner, and P. Meystre, “Atomic phase conjugation,” Quantum Semiclass. Opt. 7, 743 (1995).
[Crossref]

E. Goldstein and P. Meystre, “Phase conjugation of trapped Bose-Einstein condensates,” LANL Preprint Archive Cond-mat/9806165 (1998).

Hagley, E.

M. Kozuma, L. Deng, E. 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., in press (1998).

E. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A well-collimated quasi-continuous atom laser,” preprint (1998).

Hall, D. S.

D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of relative phase in two-component Bose-Einstein condensates,” Phys. Rev. Lett. 81, 1543 (1998).
[Crossref]

Hellwarth, R. W.

R. W. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quant. Electr. 5, 1 (1977).
[Crossref]

Helmerson, K.

E. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A well-collimated quasi-continuous atom laser,” preprint (1998).

M. Kozuma, L. Deng, E. 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., in press (1998).

Inouye, S.

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, and W. Ketterle, “Spin domains in ground-state Bose-Einstein condensates,” Nature 396, 345 (1998).
[Crossref]

Japha, Y.

Y. Japha, S. Choi, K. Burnett, and Y. B. Band, “Coherent output, stimulated quantum evaporation and pair breaking in a trapped atomic Bose gas,” Phys. Rev. Lett. (in press).

Javanainen, J.

J. Javanainen and M. Wilkens, “Phase and phase diffusion of a split Bose-Einstein condensate,” Phys. Rev. Lett. 78, 4675 (1997).
[Crossref]

Ketterle, W.

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, and W. Ketterle, “Spin domains in ground-state Bose-Einstein condensates,” Nature 396, 345 (1998).
[Crossref]

M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two Bose-Einstein condensates,” Science 275, 637 (1997).
[Crossref] [PubMed]

M.-O. Mewes, M R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, “Bose-Einstein Condensation in a Tightly Confining dc Magnetic Trap,” Phys. Rev. Lett. 77, 416 (1996).
[Crossref] [PubMed]

Kozuma, M.

E. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A well-collimated quasi-continuous atom laser,” preprint (1998).

M. Kozuma, L. Deng, E. 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., in press (1998).

Kurn, D. M.

M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two Bose-Einstein condensates,” Science 275, 637 (1997).
[Crossref] [PubMed]

M.-O. Mewes, M R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, “Bose-Einstein Condensation in a Tightly Confining dc Magnetic Trap,” Phys. Rev. Lett. 77, 416 (1996).
[Crossref] [PubMed]

Law, C. K.

C. K. Law, H. Pu, and N. P. Bigelow, “Quantum spins mixing of spinor Bose-Einstein condensates,” LANL Preprint Archive Cond-mat/9807258 (1998).

Lutwak, R.

M. Kozuma, L. Deng, E. 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., in press (1998).

Maker, P. D.

P. D. Maker and R. W. Terhune, “Study of optical effects due to induced polarization third order in the electric field strength,” Phys. Rev. A137, 801 (1965).
[Crossref]

Matthews, M. R.

D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of relative phase in two-component Bose-Einstein condensates,” Phys. Rev. Lett. 81, 1543 (1998).
[Crossref]

Mewes, M.-O.

M.-O. Mewes, M R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, “Bose-Einstein Condensation in a Tightly Confining dc Magnetic Trap,” Phys. Rev. Lett. 77, 416 (1996).
[Crossref] [PubMed]

Meystre, P.

E. Goldstein, K. Plättner, and P. Meystre, “Atomic phase conjugation from a Bose condensate,” J. Res. Nat. Inst. Stand. Technol. 101, 583 (1996).
[Crossref]

E. Goldstein, K. Plättner, and P. Meystre, “Atomic phase conjugation,” Quantum Semiclass. Opt. 7, 743 (1995).
[Crossref]

E. Goldstein and P. Meystre, “Phase conjugation of trapped Bose-Einstein condensates,” LANL Preprint Archive Cond-mat/9806165 (1998).

Miesner, H. J.

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, and W. Ketterle, “Spin domains in ground-state Bose-Einstein condensates,” Nature 396, 345 (1998).
[Crossref]

Miesner, H.-J.

M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two Bose-Einstein condensates,” Science 275, 637 (1997).
[Crossref] [PubMed]

Naraschewski, M.

H. Wallis, A. Rohrl, M. Naraschewski, and A. Schenzle, “Phase-space dynamics of Bose condensates: Interference versus interaction,” Phys. Rev. A55, 2109 (1997).

A. Rohrl, M. Naraschewski, A. Schenzle, and H. Wallis, “Transition from phase locking to the interference of independent Bose condensates: Theory versus experiment,” Phys. Rev. Lett. 78, 4143 (1997).
[Crossref]

Noziéres, P.

P. Noziéres and D. Pines, The Theory of Quantum Liquids, Vol. II, (Addison-Wesley, Redwood City, 1990).

Pepper, D. M.

Phillips, W. D.

E. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A well-collimated quasi-continuous atom laser,” preprint (1998).

M. Kozuma, L. Deng, E. 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., in press (1998).

Pines, D.

P. Noziéres and D. Pines, The Theory of Quantum Liquids, Vol. II, (Addison-Wesley, Redwood City, 1990).

Plättner, K.

E. Goldstein, K. Plättner, and P. Meystre, “Atomic phase conjugation from a Bose condensate,” J. Res. Nat. Inst. Stand. Technol. 101, 583 (1996).
[Crossref]

E. Goldstein, K. Plättner, and P. Meystre, “Atomic phase conjugation,” Quantum Semiclass. Opt. 7, 743 (1995).
[Crossref]

Pu, H.

C. K. Law, H. Pu, and N. P. Bigelow, “Quantum spins mixing of spinor Bose-Einstein condensates,” LANL Preprint Archive Cond-mat/9807258 (1998).

Rohrl, A.

H. Wallis, A. Rohrl, M. Naraschewski, and A. Schenzle, “Phase-space dynamics of Bose condensates: Interference versus interaction,” Phys. Rev. A55, 2109 (1997).

A. Rohrl, M. Naraschewski, A. Schenzle, and H. Wallis, “Transition from phase locking to the interference of independent Bose condensates: Theory versus experiment,” Phys. Rev. Lett. 78, 4143 (1997).
[Crossref]

Rolston, S. L.

M. Kozuma, L. Deng, E. 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., in press (1998).

E. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A well-collimated quasi-continuous atom laser,” preprint (1998).

Schenzle, A.

A. Rohrl, M. Naraschewski, A. Schenzle, and H. Wallis, “Transition from phase locking to the interference of independent Bose condensates: Theory versus experiment,” Phys. Rev. Lett. 78, 4143 (1997).
[Crossref]

H. Wallis, A. Rohrl, M. Naraschewski, and A. Schenzle, “Phase-space dynamics of Bose condensates: Interference versus interaction,” Phys. Rev. A55, 2109 (1997).

Stamper-Kurn, D. M.

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, and W. Ketterle, “Spin domains in ground-state Bose-Einstein condensates,” Nature 396, 345 (1998).
[Crossref]

Stenger, J.

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, and W. Ketterle, “Spin domains in ground-state Bose-Einstein condensates,” Nature 396, 345 (1998).
[Crossref]

Svelto, O.

O. Svelto, “Self-focusing, self-trapping, and self-phase modulation of laser beams,” Prog. Opt. 12, 3 (1973).

Terhune, R. W.

P. D. Maker and R. W. Terhune, “Study of optical effects due to induced polarization third order in the electric field strength,” Phys. Rev. A137, 801 (1965).
[Crossref]

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Townsend, C. G.

M. R. Andrews, C. G. Townsend, H.-J. Miesner, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Observation of interference between two Bose-Einstein condensates,” Science 275, 637 (1997).
[Crossref] [PubMed]

Trippenbach, M.

M. Trippenbach and Y. B. Band, “Effects of Self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A57, 4791 (1998).

M. Trippenbach and Y. B. Band, “Dynamics of short pulse splitting in dispersive nonlinear media,” Phys. Rev. A56, 4242 (1997)

van Druten, N. J.

M.-O. Mewes, M R. Andrews, N. J. van Druten, D. M. Kurn, D. S. Durfee, and W. Ketterle, “Bose-Einstein Condensation in a Tightly Confining dc Magnetic Trap,” Phys. Rev. Lett. 77, 416 (1996).
[Crossref] [PubMed]

Wallis, H.

H. Wallis, A. Rohrl, M. Naraschewski, and A. Schenzle, “Phase-space dynamics of Bose condensates: Interference versus interaction,” Phys. Rev. A55, 2109 (1997).

A. Rohrl, M. Naraschewski, A. Schenzle, and H. Wallis, “Transition from phase locking to the interference of independent Bose condensates: Theory versus experiment,” Phys. Rev. Lett. 78, 4143 (1997).
[Crossref]

Wen, J.

M. Kozuma, L. Deng, E. 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., in press (1998).

E. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S. L. Rolston, and W. D. Phillips, “A well-collimated quasi-continuous atom laser,” preprint (1998).

Wieman, C. E.

D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of relative phase in two-component Bose-Einstein condensates,” Phys. Rev. Lett. 81, 1543 (1998).
[Crossref]

Wilkens, M.

J. Javanainen and M. Wilkens, “Phase and phase diffusion of a split Bose-Einstein condensate,” Phys. Rev. Lett. 78, 4675 (1997).
[Crossref]

Yariv, A.

J. Res. Nat. Inst. Stand. Technol. (1)

E. Goldstein, K. Plättner, and P. Meystre, “Atomic phase conjugation from a Bose condensate,” J. Res. Nat. Inst. Stand. Technol. 101, 583 (1996).
[Crossref]

Nature (1)

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H. J. Miesner, A. P. Chikkatur, and W. Ketterle, “Spin domains in ground-state Bose-Einstein condensates,” Nature 396, 345 (1998).
[Crossref]

Opt. Lett. (1)

Phys. Rev. (4)

M. Trippenbach and Y. B. Band, “Dynamics of short pulse splitting in dispersive nonlinear media,” Phys. Rev. A56, 4242 (1997)

M. Trippenbach and Y. B. Band, “Effects of Self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A57, 4791 (1998).

H. Wallis, A. Rohrl, M. Naraschewski, and A. Schenzle, “Phase-space dynamics of Bose condensates: Interference versus interaction,” Phys. Rev. A55, 2109 (1997).

P. D. Maker and R. W. Terhune, “Study of optical effects due to induced polarization third order in the electric field strength,” Phys. Rev. A137, 801 (1965).
[Crossref]

Phys. Rev. Lett. (5)

A. Rohrl, M. Naraschewski, A. Schenzle, and H. Wallis, “Transition from phase locking to the interference of independent Bose condensates: Theory versus experiment,” Phys. Rev. Lett. 78, 4143 (1997).
[Crossref]

J. Javanainen and M. Wilkens, “Phase and phase diffusion of a split Bose-Einstein condensate,” Phys. Rev. Lett. 78, 4675 (1997).
[Crossref]

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Figures (3)

Figure 1.
Figure 1.

Schematic view of the initial positions and momenta of the three BECs wavepackets. The inset shows the momentum of the additional wavepacket formed by the 4WM process.

Figure 2.
Figure 2.

Probability distribution |Φ(x,y,t)|2 versus x and y in length units of x 0 = 10 μm. Panels (a), (b), and (c) are for respective times t = -1, 0, and 1 t 0 before, during, and after the collision, where t 0 = 36.2 ms. The initial wavepacket started at t = -2t 0, and expanded about 8-fold by the time of panel (a). Panels (d), (e), and (f) show the corresponding momentum distribution |Φ(kx, ky, t)|2 versus kx and ky in x01 units.

Figure 3.
Figure 3.

Blowup of the probability distribution |Ψ(x, y, t)|2 of panel (c) in Fig. 2.

Equations (4)

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Ψ t = ( T x + V x t + U 0 Ψ 2 ) Ψ ,
Ψ ( x , t = 0 ) = N i = 1 3 Ψ ( x x i ) exp ( i k i · x )
Ψ t = i w 0 2 t DF ( 2 Ψ x 2 + 2 Ψ y 2 + 2 Ψ z 2 ) i 1 t NL Ψ 2 Ψ m 2 Ψ .
dz Ψ ( x , y , z , t ) 2 ,

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