Abstract

A pulsed atom laser derived from a Bose-Einstein condensate is used to probe a second target condensate. The target condensate scatters the incident atom laser pulse. From the spatial distribution of scattered atoms, one can infer important properties of the target condensate and its interaction with the probe pulse. As an example, we measure the s-wave scattering length that, in low energy collisions, describes the interaction between the |F=1,mF=-1〉 and |F=2,mF=0〉 hyperfine ground states in87Rb.

© 2008 Optical Society of America

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  1. M.-O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, “Output Coupler for Bose-Einstein Condensed Atoms,”Phys. Rev. Lett. 78,582–585(1997).
    [CrossRef]
  2. E. W. Hagley, L. Deng, M. Kozuma, K. Wen, S. L. Helmerson, W. D. Rolston, and Phillips, “A Well-Collimated Quasi-Continuous Atom Laser,”Science 283,1706–1709(1999).
    [CrossRef] [PubMed]
  3. Immanuel Bloch, Theodor W. Hänsch, and Tilman Esslinger, “Atom Laser with a cw Output Coupler,”Phys. Rev. Lett. 82,3008–3011(1999).
    [CrossRef]
  4. Y. Le Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom Laser Divergence,”Phys. Rev. Lett. 87,170403(2001).
    [CrossRef] [PubMed]
  5. N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, and J. D. Close, “Achieving Peak Brightness in an Atom Laser,”Phys. Rev. Lett. 96,140403(2006).
    [CrossRef] [PubMed]
  6. J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauquembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam Quality of a Nonideal Atom Laser,”Phys. Rev. Lett. 96,070404(2006).
    [CrossRef] [PubMed]
  7. Anton Öttl, Stephan Ritter, Michael Köhl, and Tilman Esslinger, “Correlations and Counting Statistics of an Atom Laser,”Phys. Rev. Lett. 95,090404(2005).
    [CrossRef] [PubMed]
  8. G. Scoles, ed., (Oxford University Press, New York,1992), Vol. 2.
  9. G. Brusdeylins, R. Bruce Doak, and J. Peter Toennies, “Measurement of the Dispersion Relation for Rayleigh Surface Phonons of LiF(001) by Inelastic Scattering of He Atoms,”Phys. Rev. Lett. 46,437–439(1981).
    [CrossRef]
  10. E. Hulpke, ed., Springer Series in Surface Sciences (Springer-Verlag, Heidelberg,1992), Vol. 27.
  11. D. Farias and K. H. Rieder, “Atomic beam diffraction from solid surfaces,”Rep. Prog. Phys. 61,1575–1664(1998).
    [CrossRef]
  12. L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Four-wave mixing with matter waves,”Nature(London) 398,218–220(1999).
    [CrossRef]
  13. A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, and C. I. Westbrook, “Observation of Atom Pairs in Spontaneous Four-Wave Mixing of Two Colliding Bose-Einstein Condensates,”Phys. Rev. Lett. 99,150405(2007).
    [CrossRef] [PubMed]
  14. J. M. Vogels, J. K. Chin, and W. Ketterle, “Coherent Collisions between Bose-Einstein Condensates,”Phys. Rev. Lett. 90,030403(2003).
    [CrossRef] [PubMed]
  15. Olaf Mandel, Markus Greiner, Artur Widera, Tim Rom, Theodor W. Hänsch, and Immanuel Bloch, “Controlled collisions for multiparticle entanglement of optically trapped atoms,”Nature(London) 425,937–940(2003).
    [CrossRef] [PubMed]
  16. C. Samuelis, E. Tiesinga, T. Laue, M. Elbs, H. Knöckel, and E. Tiemann, “Cold atomic collisions studied by molecular spectroscopy,”Phys. Rev. A 63,012710(2000).
  17. John Weiner, Vanderlei S. Bagnato, Sergio Zilio, and Paul S. Julienne, “Experiments and theory in cold and ultracold collisions,”Rev. Mod. Phys. 71,1–85(1999).
    [CrossRef]
  18. E. G. M. van Kempen, S. J. J. M. F. Kokkelmans, D. J. Heinzen, and B. J. Verhaar, “Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments,”Phys. Rev. Lett. 88,093201(2002).
    [CrossRef] [PubMed]
  19. Ch. Buggle, J. Léonard, W. von Klitzing, and J. T. M. Walraven, “Interferometric Determination of the s and d-Wave Scattering Amplitudes in 87Rb,”Phys. Rev. Lett. 93,173202(2004).
    [CrossRef] [PubMed]
  20. Nicholas R. Thomas, Niels Kjærgaard, Paul S. Julienne, and Andrew C. Wilson, “Imaging of s and d Partial-Wave Interference in Quantum Scattering of Identical Bosonic Atoms,”Phys. Rev. Lett. 93,173201(2004).
    [CrossRef] [PubMed]
  21. Angela S. Mellish, Niels Kjærgaard, Paul S. Julienne, and Andrew C. Wilson, “Quantum scattering of distinguishable bosons using an ultracold-atom collider,”Phys. Rev. A 75,020701(R)(2007).
  22. Due to the rf ouput-coupling process we cannot avoid a weak density cloud of atoms in the |2,1〉 state. In the numerical analysis, the position of these atoms during the scattering process is approximated to be identical to the position of the source condensate.
  23. Th. Busch, M. Köhl, T. Esslinger, and K. Mølmer, “Transverse mode of an atom laser,”Phys. Rev. A 65,043615(2002).
  24. M. J. Bijlsma and H. T. C. Stoof, “Coherently scattering atoms from an excited Bose-Einstein condensate,”Phys. Rev. A 62,013605(2000).
  25. Uffe V. Poulsen and Klaus Mølmer, “Scattering of atoms on a Bose-Einstein condensate,”Phys. Rev. A 67,013610(2003).

2007 (2)

A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, and C. I. Westbrook, “Observation of Atom Pairs in Spontaneous Four-Wave Mixing of Two Colliding Bose-Einstein Condensates,”Phys. Rev. Lett. 99,150405(2007).
[CrossRef] [PubMed]

Angela S. Mellish, Niels Kjærgaard, Paul S. Julienne, and Andrew C. Wilson, “Quantum scattering of distinguishable bosons using an ultracold-atom collider,”Phys. Rev. A 75,020701(R)(2007).

2006 (2)

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, and J. D. Close, “Achieving Peak Brightness in an Atom Laser,”Phys. Rev. Lett. 96,140403(2006).
[CrossRef] [PubMed]

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauquembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam Quality of a Nonideal Atom Laser,”Phys. Rev. Lett. 96,070404(2006).
[CrossRef] [PubMed]

2005 (1)

Anton Öttl, Stephan Ritter, Michael Köhl, and Tilman Esslinger, “Correlations and Counting Statistics of an Atom Laser,”Phys. Rev. Lett. 95,090404(2005).
[CrossRef] [PubMed]

2004 (2)

Ch. Buggle, J. Léonard, W. von Klitzing, and J. T. M. Walraven, “Interferometric Determination of the s and d-Wave Scattering Amplitudes in 87Rb,”Phys. Rev. Lett. 93,173202(2004).
[CrossRef] [PubMed]

Nicholas R. Thomas, Niels Kjærgaard, Paul S. Julienne, and Andrew C. Wilson, “Imaging of s and d Partial-Wave Interference in Quantum Scattering of Identical Bosonic Atoms,”Phys. Rev. Lett. 93,173201(2004).
[CrossRef] [PubMed]

2003 (3)

J. M. Vogels, J. K. Chin, and W. Ketterle, “Coherent Collisions between Bose-Einstein Condensates,”Phys. Rev. Lett. 90,030403(2003).
[CrossRef] [PubMed]

Olaf Mandel, Markus Greiner, Artur Widera, Tim Rom, Theodor W. Hänsch, and Immanuel Bloch, “Controlled collisions for multiparticle entanglement of optically trapped atoms,”Nature(London) 425,937–940(2003).
[CrossRef] [PubMed]

Uffe V. Poulsen and Klaus Mølmer, “Scattering of atoms on a Bose-Einstein condensate,”Phys. Rev. A 67,013610(2003).

2002 (2)

E. G. M. van Kempen, S. J. J. M. F. Kokkelmans, D. J. Heinzen, and B. J. Verhaar, “Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments,”Phys. Rev. Lett. 88,093201(2002).
[CrossRef] [PubMed]

Th. Busch, M. Köhl, T. Esslinger, and K. Mølmer, “Transverse mode of an atom laser,”Phys. Rev. A 65,043615(2002).

2001 (1)

Y. Le Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom Laser Divergence,”Phys. Rev. Lett. 87,170403(2001).
[CrossRef] [PubMed]

2000 (2)

C. Samuelis, E. Tiesinga, T. Laue, M. Elbs, H. Knöckel, and E. Tiemann, “Cold atomic collisions studied by molecular spectroscopy,”Phys. Rev. A 63,012710(2000).

M. J. Bijlsma and H. T. C. Stoof, “Coherently scattering atoms from an excited Bose-Einstein condensate,”Phys. Rev. A 62,013605(2000).

1999 (4)

John Weiner, Vanderlei S. Bagnato, Sergio Zilio, and Paul S. Julienne, “Experiments and theory in cold and ultracold collisions,”Rev. Mod. Phys. 71,1–85(1999).
[CrossRef]

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Four-wave mixing with matter waves,”Nature(London) 398,218–220(1999).
[CrossRef]

E. W. Hagley, L. Deng, M. Kozuma, K. Wen, S. L. Helmerson, W. D. Rolston, and Phillips, “A Well-Collimated Quasi-Continuous Atom Laser,”Science 283,1706–1709(1999).
[CrossRef] [PubMed]

Immanuel Bloch, Theodor W. Hänsch, and Tilman Esslinger, “Atom Laser with a cw Output Coupler,”Phys. Rev. Lett. 82,3008–3011(1999).
[CrossRef]

1998 (1)

D. Farias and K. H. Rieder, “Atomic beam diffraction from solid surfaces,”Rep. Prog. Phys. 61,1575–1664(1998).
[CrossRef]

1997 (1)

M.-O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, “Output Coupler for Bose-Einstein Condensed Atoms,”Phys. Rev. Lett. 78,582–585(1997).
[CrossRef]

1981 (1)

G. Brusdeylins, R. Bruce Doak, and J. Peter Toennies, “Measurement of the Dispersion Relation for Rayleigh Surface Phonons of LiF(001) by Inelastic Scattering of He Atoms,”Phys. Rev. Lett. 46,437–439(1981).
[CrossRef]

Andrews, M. R.

M.-O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, “Output Coupler for Bose-Einstein Condensed Atoms,”Phys. Rev. Lett. 78,582–585(1997).
[CrossRef]

Aspect, A.

A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, and C. I. Westbrook, “Observation of Atom Pairs in Spontaneous Four-Wave Mixing of Two Colliding Bose-Einstein Condensates,”Phys. Rev. Lett. 99,150405(2007).
[CrossRef] [PubMed]

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauquembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam Quality of a Nonideal Atom Laser,”Phys. Rev. Lett. 96,070404(2006).
[CrossRef] [PubMed]

Y. Le Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom Laser Divergence,”Phys. Rev. Lett. 87,170403(2001).
[CrossRef] [PubMed]

Bagnato, Vanderlei S.

John Weiner, Vanderlei S. Bagnato, Sergio Zilio, and Paul S. Julienne, “Experiments and theory in cold and ultracold collisions,”Rev. Mod. Phys. 71,1–85(1999).
[CrossRef]

Band, Y.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Four-wave mixing with matter waves,”Nature(London) 398,218–220(1999).
[CrossRef]

Bijlsma, M. J.

M. J. Bijlsma and H. T. C. Stoof, “Coherently scattering atoms from an excited Bose-Einstein condensate,”Phys. Rev. A 62,013605(2000).

Bloch, Immanuel

Olaf Mandel, Markus Greiner, Artur Widera, Tim Rom, Theodor W. Hänsch, and Immanuel Bloch, “Controlled collisions for multiparticle entanglement of optically trapped atoms,”Nature(London) 425,937–940(2003).
[CrossRef] [PubMed]

Immanuel Bloch, Theodor W. Hänsch, and Tilman Esslinger, “Atom Laser with a cw Output Coupler,”Phys. Rev. Lett. 82,3008–3011(1999).
[CrossRef]

Boiron, D.

A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, and C. I. Westbrook, “Observation of Atom Pairs in Spontaneous Four-Wave Mixing of Two Colliding Bose-Einstein Condensates,”Phys. Rev. Lett. 99,150405(2007).
[CrossRef] [PubMed]

Bouyer, P.

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauquembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam Quality of a Nonideal Atom Laser,”Phys. Rev. Lett. 96,070404(2006).
[CrossRef] [PubMed]

Y. Le Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom Laser Divergence,”Phys. Rev. Lett. 87,170403(2001).
[CrossRef] [PubMed]

Bruce Doak, R.

G. Brusdeylins, R. Bruce Doak, and J. Peter Toennies, “Measurement of the Dispersion Relation for Rayleigh Surface Phonons of LiF(001) by Inelastic Scattering of He Atoms,”Phys. Rev. Lett. 46,437–439(1981).
[CrossRef]

Brusdeylins, G.

G. Brusdeylins, R. Bruce Doak, and J. Peter Toennies, “Measurement of the Dispersion Relation for Rayleigh Surface Phonons of LiF(001) by Inelastic Scattering of He Atoms,”Phys. Rev. Lett. 46,437–439(1981).
[CrossRef]

Buggle, Ch.

Ch. Buggle, J. Léonard, W. von Klitzing, and J. T. M. Walraven, “Interferometric Determination of the s and d-Wave Scattering Amplitudes in 87Rb,”Phys. Rev. Lett. 93,173202(2004).
[CrossRef] [PubMed]

Busch, Th.

Th. Busch, M. Köhl, T. Esslinger, and K. Mølmer, “Transverse mode of an atom laser,”Phys. Rev. A 65,043615(2002).

Chang, H.

A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, and C. I. Westbrook, “Observation of Atom Pairs in Spontaneous Four-Wave Mixing of Two Colliding Bose-Einstein Condensates,”Phys. Rev. Lett. 99,150405(2007).
[CrossRef] [PubMed]

Chin, J. K.

J. M. Vogels, J. K. Chin, and W. Ketterle, “Coherent Collisions between Bose-Einstein Condensates,”Phys. Rev. Lett. 90,030403(2003).
[CrossRef] [PubMed]

Close, J. D.

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, and J. D. Close, “Achieving Peak Brightness in an Atom Laser,”Phys. Rev. Lett. 96,140403(2006).
[CrossRef] [PubMed]

Delannoy, G.

Y. Le Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom Laser Divergence,”Phys. Rev. Lett. 87,170403(2001).
[CrossRef] [PubMed]

Deng, L.

E. W. Hagley, L. Deng, M. Kozuma, K. Wen, S. L. Helmerson, W. D. Rolston, and Phillips, “A Well-Collimated Quasi-Continuous Atom Laser,”Science 283,1706–1709(1999).
[CrossRef] [PubMed]

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Four-wave mixing with matter waves,”Nature(London) 398,218–220(1999).
[CrossRef]

Durfee, D. S.

M.-O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, “Output Coupler for Bose-Einstein Condensed Atoms,”Phys. Rev. Lett. 78,582–585(1997).
[CrossRef]

Elbs, M.

C. Samuelis, E. Tiesinga, T. Laue, M. Elbs, H. Knöckel, and E. Tiemann, “Cold atomic collisions studied by molecular spectroscopy,”Phys. Rev. A 63,012710(2000).

Esslinger, T.

Th. Busch, M. Köhl, T. Esslinger, and K. Mølmer, “Transverse mode of an atom laser,”Phys. Rev. A 65,043615(2002).

Esslinger, Tilman

Anton Öttl, Stephan Ritter, Michael Köhl, and Tilman Esslinger, “Correlations and Counting Statistics of an Atom Laser,”Phys. Rev. Lett. 95,090404(2005).
[CrossRef] [PubMed]

Immanuel Bloch, Theodor W. Hänsch, and Tilman Esslinger, “Atom Laser with a cw Output Coupler,”Phys. Rev. Lett. 82,3008–3011(1999).
[CrossRef]

Farias, D.

D. Farias and K. H. Rieder, “Atomic beam diffraction from solid surfaces,”Rep. Prog. Phys. 61,1575–1664(1998).
[CrossRef]

Fauquembergue, M.

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauquembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam Quality of a Nonideal Atom Laser,”Phys. Rev. Lett. 96,070404(2006).
[CrossRef] [PubMed]

Figl, C.

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, and J. D. Close, “Achieving Peak Brightness in an Atom Laser,”Phys. Rev. Lett. 96,140403(2006).
[CrossRef] [PubMed]

Gerbier, F.

Y. Le Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom Laser Divergence,”Phys. Rev. Lett. 87,170403(2001).
[CrossRef] [PubMed]

Greiner, Markus

Olaf Mandel, Markus Greiner, Artur Widera, Tim Rom, Theodor W. Hänsch, and Immanuel Bloch, “Controlled collisions for multiparticle entanglement of optically trapped atoms,”Nature(London) 425,937–940(2003).
[CrossRef] [PubMed]

Guerin, W.

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauquembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam Quality of a Nonideal Atom Laser,”Phys. Rev. Lett. 96,070404(2006).
[CrossRef] [PubMed]

Hagley, E. W.

E. W. Hagley, L. Deng, M. Kozuma, K. Wen, S. L. Helmerson, W. D. Rolston, and Phillips, “A Well-Collimated Quasi-Continuous Atom Laser,”Science 283,1706–1709(1999).
[CrossRef] [PubMed]

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Four-wave mixing with matter waves,”Nature(London) 398,218–220(1999).
[CrossRef]

Haine, S. A.

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, and J. D. Close, “Achieving Peak Brightness in an Atom Laser,”Phys. Rev. Lett. 96,140403(2006).
[CrossRef] [PubMed]

Hänsch, Theodor W.

Olaf Mandel, Markus Greiner, Artur Widera, Tim Rom, Theodor W. Hänsch, and Immanuel Bloch, “Controlled collisions for multiparticle entanglement of optically trapped atoms,”Nature(London) 425,937–940(2003).
[CrossRef] [PubMed]

Immanuel Bloch, Theodor W. Hänsch, and Tilman Esslinger, “Atom Laser with a cw Output Coupler,”Phys. Rev. Lett. 82,3008–3011(1999).
[CrossRef]

Heinzen, D. J.

E. G. M. van Kempen, S. J. J. M. F. Kokkelmans, D. J. Heinzen, and B. J. Verhaar, “Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments,”Phys. Rev. Lett. 88,093201(2002).
[CrossRef] [PubMed]

Helmerson, K.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Four-wave mixing with matter waves,”Nature(London) 398,218–220(1999).
[CrossRef]

Helmerson, S. L.

E. W. Hagley, L. Deng, M. Kozuma, K. Wen, S. L. Helmerson, W. D. Rolston, and Phillips, “A Well-Collimated Quasi-Continuous Atom Laser,”Science 283,1706–1709(1999).
[CrossRef] [PubMed]

Hope, J. J.

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, and J. D. Close, “Achieving Peak Brightness in an Atom Laser,”Phys. Rev. Lett. 96,140403(2006).
[CrossRef] [PubMed]

Hulpke, E.

E. Hulpke, ed., Springer Series in Surface Sciences (Springer-Verlag, Heidelberg,1992), Vol. 27.

Jeppesen, M.

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, and J. D. Close, “Achieving Peak Brightness in an Atom Laser,”Phys. Rev. Lett. 96,140403(2006).
[CrossRef] [PubMed]

Josse, V.

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauquembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam Quality of a Nonideal Atom Laser,”Phys. Rev. Lett. 96,070404(2006).
[CrossRef] [PubMed]

Julienne, P. S.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Four-wave mixing with matter waves,”Nature(London) 398,218–220(1999).
[CrossRef]

Julienne, Paul S.

Angela S. Mellish, Niels Kjærgaard, Paul S. Julienne, and Andrew C. Wilson, “Quantum scattering of distinguishable bosons using an ultracold-atom collider,”Phys. Rev. A 75,020701(R)(2007).

Nicholas R. Thomas, Niels Kjærgaard, Paul S. Julienne, and Andrew C. Wilson, “Imaging of s and d Partial-Wave Interference in Quantum Scattering of Identical Bosonic Atoms,”Phys. Rev. Lett. 93,173201(2004).
[CrossRef] [PubMed]

John Weiner, Vanderlei S. Bagnato, Sergio Zilio, and Paul S. Julienne, “Experiments and theory in cold and ultracold collisions,”Rev. Mod. Phys. 71,1–85(1999).
[CrossRef]

Ketterle, W.

J. M. Vogels, J. K. Chin, and W. Ketterle, “Coherent Collisions between Bose-Einstein Condensates,”Phys. Rev. Lett. 90,030403(2003).
[CrossRef] [PubMed]

M.-O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, “Output Coupler for Bose-Einstein Condensed Atoms,”Phys. Rev. Lett. 78,582–585(1997).
[CrossRef]

Kjærgaard, Niels

Angela S. Mellish, Niels Kjærgaard, Paul S. Julienne, and Andrew C. Wilson, “Quantum scattering of distinguishable bosons using an ultracold-atom collider,”Phys. Rev. A 75,020701(R)(2007).

Nicholas R. Thomas, Niels Kjærgaard, Paul S. Julienne, and Andrew C. Wilson, “Imaging of s and d Partial-Wave Interference in Quantum Scattering of Identical Bosonic Atoms,”Phys. Rev. Lett. 93,173201(2004).
[CrossRef] [PubMed]

Knöckel, H.

C. Samuelis, E. Tiesinga, T. Laue, M. Elbs, H. Knöckel, and E. Tiemann, “Cold atomic collisions studied by molecular spectroscopy,”Phys. Rev. A 63,012710(2000).

Köhl, M.

Th. Busch, M. Köhl, T. Esslinger, and K. Mølmer, “Transverse mode of an atom laser,”Phys. Rev. A 65,043615(2002).

Köhl, Michael

Anton Öttl, Stephan Ritter, Michael Köhl, and Tilman Esslinger, “Correlations and Counting Statistics of an Atom Laser,”Phys. Rev. Lett. 95,090404(2005).
[CrossRef] [PubMed]

Kokkelmans, S. J. J. M. F.

E. G. M. van Kempen, S. J. J. M. F. Kokkelmans, D. J. Heinzen, and B. J. Verhaar, “Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments,”Phys. Rev. Lett. 88,093201(2002).
[CrossRef] [PubMed]

Kozuma, M.

E. W. Hagley, L. Deng, M. Kozuma, K. Wen, S. L. Helmerson, W. D. Rolston, and Phillips, “A Well-Collimated Quasi-Continuous Atom Laser,”Science 283,1706–1709(1999).
[CrossRef] [PubMed]

Krachmalnicoff, V.

A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, and C. I. Westbrook, “Observation of Atom Pairs in Spontaneous Four-Wave Mixing of Two Colliding Bose-Einstein Condensates,”Phys. Rev. Lett. 99,150405(2007).
[CrossRef] [PubMed]

Kurn, D. M.

M.-O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, “Output Coupler for Bose-Einstein Condensed Atoms,”Phys. Rev. Lett. 78,582–585(1997).
[CrossRef]

Laue, T.

C. Samuelis, E. Tiesinga, T. Laue, M. Elbs, H. Knöckel, and E. Tiemann, “Cold atomic collisions studied by molecular spectroscopy,”Phys. Rev. A 63,012710(2000).

Le Coq, Y.

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauquembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam Quality of a Nonideal Atom Laser,”Phys. Rev. Lett. 96,070404(2006).
[CrossRef] [PubMed]

Y. Le Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom Laser Divergence,”Phys. Rev. Lett. 87,170403(2001).
[CrossRef] [PubMed]

Léonard, J.

Ch. Buggle, J. Léonard, W. von Klitzing, and J. T. M. Walraven, “Interferometric Determination of the s and d-Wave Scattering Amplitudes in 87Rb,”Phys. Rev. Lett. 93,173202(2004).
[CrossRef] [PubMed]

Mandel, Olaf

Olaf Mandel, Markus Greiner, Artur Widera, Tim Rom, Theodor W. Hänsch, and Immanuel Bloch, “Controlled collisions for multiparticle entanglement of optically trapped atoms,”Nature(London) 425,937–940(2003).
[CrossRef] [PubMed]

Mellish, Angela S.

Angela S. Mellish, Niels Kjærgaard, Paul S. Julienne, and Andrew C. Wilson, “Quantum scattering of distinguishable bosons using an ultracold-atom collider,”Phys. Rev. A 75,020701(R)(2007).

Mewes, M.-O.

M.-O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, “Output Coupler for Bose-Einstein Condensed Atoms,”Phys. Rev. Lett. 78,582–585(1997).
[CrossRef]

Mølmer, K.

Th. Busch, M. Köhl, T. Esslinger, and K. Mølmer, “Transverse mode of an atom laser,”Phys. Rev. A 65,043615(2002).

Mølmer, Klaus

Uffe V. Poulsen and Klaus Mølmer, “Scattering of atoms on a Bose-Einstein condensate,”Phys. Rev. A 67,013610(2003).

Morrison, A. K.

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, and J. D. Close, “Achieving Peak Brightness in an Atom Laser,”Phys. Rev. Lett. 96,140403(2006).
[CrossRef] [PubMed]

Öttl, Anton

Anton Öttl, Stephan Ritter, Michael Köhl, and Tilman Esslinger, “Correlations and Counting Statistics of an Atom Laser,”Phys. Rev. Lett. 95,090404(2005).
[CrossRef] [PubMed]

Perrin, A.

A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, and C. I. Westbrook, “Observation of Atom Pairs in Spontaneous Four-Wave Mixing of Two Colliding Bose-Einstein Condensates,”Phys. Rev. Lett. 99,150405(2007).
[CrossRef] [PubMed]

Peter Toennies, J.

G. Brusdeylins, R. Bruce Doak, and J. Peter Toennies, “Measurement of the Dispersion Relation for Rayleigh Surface Phonons of LiF(001) by Inelastic Scattering of He Atoms,”Phys. Rev. Lett. 46,437–439(1981).
[CrossRef]

Phillips,

E. W. Hagley, L. Deng, M. Kozuma, K. Wen, S. L. Helmerson, W. D. Rolston, and Phillips, “A Well-Collimated Quasi-Continuous Atom Laser,”Science 283,1706–1709(1999).
[CrossRef] [PubMed]

Phillips, W. D.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Four-wave mixing with matter waves,”Nature(London) 398,218–220(1999).
[CrossRef]

Poulsen, Uffe V.

Uffe V. Poulsen and Klaus Mølmer, “Scattering of atoms on a Bose-Einstein condensate,”Phys. Rev. A 67,013610(2003).

Rangwala, S. A.

Y. Le Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom Laser Divergence,”Phys. Rev. Lett. 87,170403(2001).
[CrossRef] [PubMed]

Richard, S.

Y. Le Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom Laser Divergence,”Phys. Rev. Lett. 87,170403(2001).
[CrossRef] [PubMed]

Rieder, K. H.

D. Farias and K. H. Rieder, “Atomic beam diffraction from solid surfaces,”Rep. Prog. Phys. 61,1575–1664(1998).
[CrossRef]

Riou, J.-F.

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauquembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam Quality of a Nonideal Atom Laser,”Phys. Rev. Lett. 96,070404(2006).
[CrossRef] [PubMed]

Ritter, Stephan

Anton Öttl, Stephan Ritter, Michael Köhl, and Tilman Esslinger, “Correlations and Counting Statistics of an Atom Laser,”Phys. Rev. Lett. 95,090404(2005).
[CrossRef] [PubMed]

Robins, N. P.

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, and J. D. Close, “Achieving Peak Brightness in an Atom Laser,”Phys. Rev. Lett. 96,140403(2006).
[CrossRef] [PubMed]

Rolston, S. L.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Four-wave mixing with matter waves,”Nature(London) 398,218–220(1999).
[CrossRef]

Rolston, W. D.

E. W. Hagley, L. Deng, M. Kozuma, K. Wen, S. L. Helmerson, W. D. Rolston, and Phillips, “A Well-Collimated Quasi-Continuous Atom Laser,”Science 283,1706–1709(1999).
[CrossRef] [PubMed]

Rom, Tim

Olaf Mandel, Markus Greiner, Artur Widera, Tim Rom, Theodor W. Hänsch, and Immanuel Bloch, “Controlled collisions for multiparticle entanglement of optically trapped atoms,”Nature(London) 425,937–940(2003).
[CrossRef] [PubMed]

Samuelis, C.

C. Samuelis, E. Tiesinga, T. Laue, M. Elbs, H. Knöckel, and E. Tiemann, “Cold atomic collisions studied by molecular spectroscopy,”Phys. Rev. A 63,012710(2000).

Schellekens, M.

A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, and C. I. Westbrook, “Observation of Atom Pairs in Spontaneous Four-Wave Mixing of Two Colliding Bose-Einstein Condensates,”Phys. Rev. Lett. 99,150405(2007).
[CrossRef] [PubMed]

Scoles, G.

G. Scoles, ed., (Oxford University Press, New York,1992), Vol. 2.

Simsarian, J. E.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Four-wave mixing with matter waves,”Nature(London) 398,218–220(1999).
[CrossRef]

Stoof, H. T. C.

M. J. Bijlsma and H. T. C. Stoof, “Coherently scattering atoms from an excited Bose-Einstein condensate,”Phys. Rev. A 62,013605(2000).

Thomas, Nicholas R.

Nicholas R. Thomas, Niels Kjærgaard, Paul S. Julienne, and Andrew C. Wilson, “Imaging of s and d Partial-Wave Interference in Quantum Scattering of Identical Bosonic Atoms,”Phys. Rev. Lett. 93,173201(2004).
[CrossRef] [PubMed]

Thywissen, J. H.

Y. Le Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom Laser Divergence,”Phys. Rev. Lett. 87,170403(2001).
[CrossRef] [PubMed]

Tiemann, E.

C. Samuelis, E. Tiesinga, T. Laue, M. Elbs, H. Knöckel, and E. Tiemann, “Cold atomic collisions studied by molecular spectroscopy,”Phys. Rev. A 63,012710(2000).

Tiesinga, E.

C. Samuelis, E. Tiesinga, T. Laue, M. Elbs, H. Knöckel, and E. Tiemann, “Cold atomic collisions studied by molecular spectroscopy,”Phys. Rev. A 63,012710(2000).

Townsend, C. G.

M.-O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, “Output Coupler for Bose-Einstein Condensed Atoms,”Phys. Rev. Lett. 78,582–585(1997).
[CrossRef]

Trippenbach, M.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Four-wave mixing with matter waves,”Nature(London) 398,218–220(1999).
[CrossRef]

van Kempen, E. G. M.

E. G. M. van Kempen, S. J. J. M. F. Kokkelmans, D. J. Heinzen, and B. J. Verhaar, “Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments,”Phys. Rev. Lett. 88,093201(2002).
[CrossRef] [PubMed]

Verhaar, B. J.

E. G. M. van Kempen, S. J. J. M. F. Kokkelmans, D. J. Heinzen, and B. J. Verhaar, “Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments,”Phys. Rev. Lett. 88,093201(2002).
[CrossRef] [PubMed]

Vogels, J. M.

J. M. Vogels, J. K. Chin, and W. Ketterle, “Coherent Collisions between Bose-Einstein Condensates,”Phys. Rev. Lett. 90,030403(2003).
[CrossRef] [PubMed]

von Klitzing, W.

Ch. Buggle, J. Léonard, W. von Klitzing, and J. T. M. Walraven, “Interferometric Determination of the s and d-Wave Scattering Amplitudes in 87Rb,”Phys. Rev. Lett. 93,173202(2004).
[CrossRef] [PubMed]

Walraven, J. T. M.

Ch. Buggle, J. Léonard, W. von Klitzing, and J. T. M. Walraven, “Interferometric Determination of the s and d-Wave Scattering Amplitudes in 87Rb,”Phys. Rev. Lett. 93,173202(2004).
[CrossRef] [PubMed]

Weiner, John

John Weiner, Vanderlei S. Bagnato, Sergio Zilio, and Paul S. Julienne, “Experiments and theory in cold and ultracold collisions,”Rev. Mod. Phys. 71,1–85(1999).
[CrossRef]

Wen, J.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Four-wave mixing with matter waves,”Nature(London) 398,218–220(1999).
[CrossRef]

Wen, K.

E. W. Hagley, L. Deng, M. Kozuma, K. Wen, S. L. Helmerson, W. D. Rolston, and Phillips, “A Well-Collimated Quasi-Continuous Atom Laser,”Science 283,1706–1709(1999).
[CrossRef] [PubMed]

Westbrook, C. I.

A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, and C. I. Westbrook, “Observation of Atom Pairs in Spontaneous Four-Wave Mixing of Two Colliding Bose-Einstein Condensates,”Phys. Rev. Lett. 99,150405(2007).
[CrossRef] [PubMed]

Widera, Artur

Olaf Mandel, Markus Greiner, Artur Widera, Tim Rom, Theodor W. Hänsch, and Immanuel Bloch, “Controlled collisions for multiparticle entanglement of optically trapped atoms,”Nature(London) 425,937–940(2003).
[CrossRef] [PubMed]

Wilson, Andrew C.

Angela S. Mellish, Niels Kjærgaard, Paul S. Julienne, and Andrew C. Wilson, “Quantum scattering of distinguishable bosons using an ultracold-atom collider,”Phys. Rev. A 75,020701(R)(2007).

Nicholas R. Thomas, Niels Kjærgaard, Paul S. Julienne, and Andrew C. Wilson, “Imaging of s and d Partial-Wave Interference in Quantum Scattering of Identical Bosonic Atoms,”Phys. Rev. Lett. 93,173201(2004).
[CrossRef] [PubMed]

Zilio, Sergio

John Weiner, Vanderlei S. Bagnato, Sergio Zilio, and Paul S. Julienne, “Experiments and theory in cold and ultracold collisions,”Rev. Mod. Phys. 71,1–85(1999).
[CrossRef]

Nature (2)

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, and W. D. Phillips, “Four-wave mixing with matter waves,”Nature(London) 398,218–220(1999).
[CrossRef]

Olaf Mandel, Markus Greiner, Artur Widera, Tim Rom, Theodor W. Hänsch, and Immanuel Bloch, “Controlled collisions for multiparticle entanglement of optically trapped atoms,”Nature(London) 425,937–940(2003).
[CrossRef] [PubMed]

Phys. Rev (1)

M. J. Bijlsma and H. T. C. Stoof, “Coherently scattering atoms from an excited Bose-Einstein condensate,”Phys. Rev. A 62,013605(2000).

Phys. Rev. (4)

Uffe V. Poulsen and Klaus Mølmer, “Scattering of atoms on a Bose-Einstein condensate,”Phys. Rev. A 67,013610(2003).

Th. Busch, M. Köhl, T. Esslinger, and K. Mølmer, “Transverse mode of an atom laser,”Phys. Rev. A 65,043615(2002).

C. Samuelis, E. Tiesinga, T. Laue, M. Elbs, H. Knöckel, and E. Tiemann, “Cold atomic collisions studied by molecular spectroscopy,”Phys. Rev. A 63,012710(2000).

Angela S. Mellish, Niels Kjærgaard, Paul S. Julienne, and Andrew C. Wilson, “Quantum scattering of distinguishable bosons using an ultracold-atom collider,”Phys. Rev. A 75,020701(R)(2007).

Phys. Rev. Lett. (12)

E. G. M. van Kempen, S. J. J. M. F. Kokkelmans, D. J. Heinzen, and B. J. Verhaar, “Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments,”Phys. Rev. Lett. 88,093201(2002).
[CrossRef] [PubMed]

Ch. Buggle, J. Léonard, W. von Klitzing, and J. T. M. Walraven, “Interferometric Determination of the s and d-Wave Scattering Amplitudes in 87Rb,”Phys. Rev. Lett. 93,173202(2004).
[CrossRef] [PubMed]

Nicholas R. Thomas, Niels Kjærgaard, Paul S. Julienne, and Andrew C. Wilson, “Imaging of s and d Partial-Wave Interference in Quantum Scattering of Identical Bosonic Atoms,”Phys. Rev. Lett. 93,173201(2004).
[CrossRef] [PubMed]

A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect, and C. I. Westbrook, “Observation of Atom Pairs in Spontaneous Four-Wave Mixing of Two Colliding Bose-Einstein Condensates,”Phys. Rev. Lett. 99,150405(2007).
[CrossRef] [PubMed]

J. M. Vogels, J. K. Chin, and W. Ketterle, “Coherent Collisions between Bose-Einstein Condensates,”Phys. Rev. Lett. 90,030403(2003).
[CrossRef] [PubMed]

Immanuel Bloch, Theodor W. Hänsch, and Tilman Esslinger, “Atom Laser with a cw Output Coupler,”Phys. Rev. Lett. 82,3008–3011(1999).
[CrossRef]

Y. Le Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom Laser Divergence,”Phys. Rev. Lett. 87,170403(2001).
[CrossRef] [PubMed]

N. P. Robins, C. Figl, S. A. Haine, A. K. Morrison, M. Jeppesen, J. J. Hope, and J. D. Close, “Achieving Peak Brightness in an Atom Laser,”Phys. Rev. Lett. 96,140403(2006).
[CrossRef] [PubMed]

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauquembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam Quality of a Nonideal Atom Laser,”Phys. Rev. Lett. 96,070404(2006).
[CrossRef] [PubMed]

Anton Öttl, Stephan Ritter, Michael Köhl, and Tilman Esslinger, “Correlations and Counting Statistics of an Atom Laser,”Phys. Rev. Lett. 95,090404(2005).
[CrossRef] [PubMed]

M.-O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, “Output Coupler for Bose-Einstein Condensed Atoms,”Phys. Rev. Lett. 78,582–585(1997).
[CrossRef]

G. Brusdeylins, R. Bruce Doak, and J. Peter Toennies, “Measurement of the Dispersion Relation for Rayleigh Surface Phonons of LiF(001) by Inelastic Scattering of He Atoms,”Phys. Rev. Lett. 46,437–439(1981).
[CrossRef]

Rep. Prog. Phys. (1)

D. Farias and K. H. Rieder, “Atomic beam diffraction from solid surfaces,”Rep. Prog. Phys. 61,1575–1664(1998).
[CrossRef]

Rev. Mod. Phys. (1)

John Weiner, Vanderlei S. Bagnato, Sergio Zilio, and Paul S. Julienne, “Experiments and theory in cold and ultracold collisions,”Rev. Mod. Phys. 71,1–85(1999).
[CrossRef]

Science (1)

E. W. Hagley, L. Deng, M. Kozuma, K. Wen, S. L. Helmerson, W. D. Rolston, and Phillips, “A Well-Collimated Quasi-Continuous Atom Laser,”Science 283,1706–1709(1999).
[CrossRef] [PubMed]

Other (3)

E. Hulpke, ed., Springer Series in Surface Sciences (Springer-Verlag, Heidelberg,1992), Vol. 27.

G. Scoles, ed., (Oxford University Press, New York,1992), Vol. 2.

Due to the rf ouput-coupling process we cannot avoid a weak density cloud of atoms in the |2,1〉 state. In the numerical analysis, the position of these atoms during the scattering process is approximated to be identical to the position of the source condensate.

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Figures (3)

Fig. 1.
Fig. 1.

(Color online) Schematic setup of the experiment. The two condensates are situated at different vertical positions in the same magnetic trap. (a) The atom laser is outputcoupled from the source condensate and (b) scattered off the target condensate. (c) The scattered probe pulse falls under gravity and (d) is imaged by near-resonant light incident along the long axis of the condensates. The confining magnetic fields are switched off before the image is taken, letting the condensates expand for 5ms.

Fig. 2.
Fig. 2.

(Color online) Non-averaged absorption pictures of the scattered probe pulse and the two condensates for atom numbers of (a) 0.05×106, (b) 0.16×106, (c) 0.45×106, (d) 0.87×106, (e) 1.25×106, and (f) 1.38×106atoms in the target condensate. The three images in each section are taken 0ms, 9ms and 22ms after output-coupling the atom laser pulse. The ballistic expansion time for the two condensates is 5ms. The graphs below each section show the density profile of the probe pulse, integrated over the width of the pulse along the propagation (y-) direction.

Fig. 3.
Fig. 3.

(Color online) Width of the scattered atom laser pulse (FWHM) as a function of the atom number in the target condensate. The red dots indicate the results of the measurements, the blue circles show the best fit of the numerical simulations to the experimental data. The fall time of the atom pulse before measuring the pulse width is 22ms.

Equations (2)

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

U ( x , y ) = U t ( x , y ) + U s ( x , y ) + mgy ,
U t ( x , y ) = g 12 μ t g 11 ( 1 ( y y t ) 2 + x 2 r t 2 ) θ ( r t 2 ( ( y y t ) 2 + x 2 ) ) ,

Metrics