OSA's Digital Library

Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 3, Iss. 13 — Dec. 21, 1998
  • pp: 530–537

Four wave mixing in the scattering of Bose-Einstein condensates

Marek Trippenbach, Yehuda B. Band, and Paul S. Julienne  »View Author Affiliations

Optics Express, Vol. 3, Issue 13, pp. 530-537 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (872 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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 k1, k2, and k3 interact. The interaction will produce a fourth wavepacket with momentum k4 = k1 + k2 - k3. 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.

© Optical Society of America

OCIS Codes
(020.7010) Atomic and molecular physics : Laser trapping
(140.3320) Lasers and laser optics : Laser cooling
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

ToC Category:
Research Papers

Original Manuscript: November 24, 1998
Published: December 21, 1998

Marek Trippenbach, Yehuda Band, and Paul Julienne, "Four wave mixing in the scattering of Bose-Einstein condensates," Opt. Express 3, 530-537 (1998)

Sort:  Journal  |  Reset  


  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. Plattner and P. Meystre, "Atomic phase conjugation," Quantum Semiclass. Opt. 7, 743 (1995). [CrossRef]
  11. E. Goldstein, K. Pl"attner 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. Nozieres 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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited