Abstract

A new sort of matter wave with the general astigmatism is proposed, whose orientation of the phase front and the density profile are crossed. A generalized ABCD law is developed to treat the evolution of the general astigmatic matter wave. It is revealed that two “cylindrical lens” pulses with oblique orientations can bring general astigmatism to the matter wave. The evolution characteristics of the general astigmatic matter wave in the gravitational field is discussed and illustrated numerically in detail. It is found that the orientations of the density profile and the phase front of the matter wave rotate continuously during evolution.

© 2008 Optical Society of America

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References

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  1. H. J. Metcalf and P. Van der Straten, Laser Cooling and Trapping (Springer-Verlag New York, 1999).
    [Crossref]
  2. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys,  71, 463–512 (1999).
    [Crossref]
  3. K. Bongs and K. Sengstock, “Physics with coherent matter waves,” Rep. Prog. Phys. 67, 907–963 (2004).
    [Crossref]
  4. Ch. J. Bordé, “Atomic clocks and inertial sensors,” Metrologia 39435–463 (2002).
    [Crossref]
  5. 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, 416–419 (1996).
    [Crossref] [PubMed]
  6. G. Roati, M. Zaccanti, C.D Errico, J. Catani, M. Modugno, A. Simoni, M. Inguscio, and G. Modugno, “39K Bose-Einstein Condensate with Tunerable Interations,” Phys. Rev. Lett.99, 010403(1)–(4) (2007).
    [Crossref]
  7. T. Lahaye, T. Koch, B. Fröhlich, M. Fattori, J. Metz, A. Griesmaier, S. Giovanazzi, and T. Pfau, “Strong dipolar effects in a quantum ferrofluid,” Nature 448, 672–675 (2007).
    [Crossref] [PubMed]
  8. J. A. Arnaud and H. Kogelnik, “Gaussian light beams with general astigmatism,” Appl. Opt,  8, 1687–1693 (1969).
    [Crossref] [PubMed]
  9. Q. Lin and Y. Cai, “Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams,” Opt. Lett. 27, 216–218 (2002).
    [Crossref]
  10. Ch. Antoine and Ch. J. Bordé, “Exact phase shifts for atom interferometry,” Phys. Lett. A 306, 277–284 (2003).
    [Crossref]
  11. 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(1)–(4) (2001).
    [Crossref]
  12. J. -F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam quality of a nonlineal atom laser,” Phys. Rev. Lett. 96, 070404(1)–(4) (2006).
    [Crossref]
  13. F. Impens, P. Bouyer, and Ch. J. Bordé, “Matter-wave cavity gravimeter,” Appl. Phys. B 84, 603–615 (2006).
    [Crossref]
  14. Ch. J. Bordé, “Theoretical tools for atom optics and interferometry,” C. R. Acad. Sci. Paris, t. 2, Série IV, 509–530 (2001).
  15. J. H. Van Vleck, “The correspondence principle in the statistical interpretation of quantum mechanics,” Pro. Natl. Acad. Sci. USA 14, 178–188 (1928).
    [Crossref]
  16. G. Whyte, P. Öhberg, and J. Courtial, “Transverse laser modes in Bose-Einstein condensates,” Phys. Rev. A 69, 053610(1)–(8) (2004).
    [Crossref]
  17. D. R. Murry and P. Öhberg, “Matter wave focusing,” J. Phys. B: At. Mol. Opt. Phys. 38, 1227–1234 (2005).
    [Crossref]

2007 (1)

T. Lahaye, T. Koch, B. Fröhlich, M. Fattori, J. Metz, A. Griesmaier, S. Giovanazzi, and T. Pfau, “Strong dipolar effects in a quantum ferrofluid,” Nature 448, 672–675 (2007).
[Crossref] [PubMed]

2006 (2)

J. -F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam quality of a nonlineal atom laser,” Phys. Rev. Lett. 96, 070404(1)–(4) (2006).
[Crossref]

F. Impens, P. Bouyer, and Ch. J. Bordé, “Matter-wave cavity gravimeter,” Appl. Phys. B 84, 603–615 (2006).
[Crossref]

2005 (1)

D. R. Murry and P. Öhberg, “Matter wave focusing,” J. Phys. B: At. Mol. Opt. Phys. 38, 1227–1234 (2005).
[Crossref]

2004 (2)

G. Whyte, P. Öhberg, and J. Courtial, “Transverse laser modes in Bose-Einstein condensates,” Phys. Rev. A 69, 053610(1)–(8) (2004).
[Crossref]

K. Bongs and K. Sengstock, “Physics with coherent matter waves,” Rep. Prog. Phys. 67, 907–963 (2004).
[Crossref]

2003 (1)

Ch. Antoine and Ch. J. Bordé, “Exact phase shifts for atom interferometry,” Phys. Lett. A 306, 277–284 (2003).
[Crossref]

2002 (2)

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(1)–(4) (2001).
[Crossref]

1999 (1)

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys,  71, 463–512 (1999).
[Crossref]

1996 (1)

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, 416–419 (1996).
[Crossref] [PubMed]

1969 (1)

J. A. Arnaud and H. Kogelnik, “Gaussian light beams with general astigmatism,” Appl. Opt,  8, 1687–1693 (1969).
[Crossref] [PubMed]

1928 (1)

J. H. Van Vleck, “The correspondence principle in the statistical interpretation of quantum mechanics,” Pro. Natl. Acad. Sci. USA 14, 178–188 (1928).
[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, 416–419 (1996).
[Crossref] [PubMed]

Antoine, Ch.

Ch. Antoine and Ch. J. Bordé, “Exact phase shifts for atom interferometry,” Phys. Lett. A 306, 277–284 (2003).
[Crossref]

Arnaud, J. A.

J. A. Arnaud and H. Kogelnik, “Gaussian light beams with general astigmatism,” Appl. Opt,  8, 1687–1693 (1969).
[Crossref] [PubMed]

Aspect, A.

J. -F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam quality of a nonlineal atom laser,” Phys. Rev. Lett. 96, 070404(1)–(4) (2006).
[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(1)–(4) (2001).
[Crossref]

Bongs, K.

K. Bongs and K. Sengstock, “Physics with coherent matter waves,” Rep. Prog. Phys. 67, 907–963 (2004).
[Crossref]

Bordé, Ch. J.

F. Impens, P. Bouyer, and Ch. J. Bordé, “Matter-wave cavity gravimeter,” Appl. Phys. B 84, 603–615 (2006).
[Crossref]

Ch. Antoine and Ch. J. Bordé, “Exact phase shifts for atom interferometry,” Phys. Lett. A 306, 277–284 (2003).
[Crossref]

Ch. J. Bordé, “Atomic clocks and inertial sensors,” Metrologia 39435–463 (2002).
[Crossref]

Ch. J. Bordé, “Theoretical tools for atom optics and interferometry,” C. R. Acad. Sci. Paris, t. 2, Série IV, 509–530 (2001).

Bouyer, P.

F. Impens, P. Bouyer, and Ch. J. Bordé, “Matter-wave cavity gravimeter,” Appl. Phys. B 84, 603–615 (2006).
[Crossref]

J. -F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam quality of a nonlineal atom laser,” Phys. Rev. Lett. 96, 070404(1)–(4) (2006).
[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(1)–(4) (2001).
[Crossref]

Cai, Y.

Catani, J.

G. Roati, M. Zaccanti, C.D Errico, J. Catani, M. Modugno, A. Simoni, M. Inguscio, and G. Modugno, “39K Bose-Einstein Condensate with Tunerable Interations,” Phys. Rev. Lett.99, 010403(1)–(4) (2007).
[Crossref]

Courtial, J.

G. Whyte, P. Öhberg, and J. Courtial, “Transverse laser modes in Bose-Einstein condensates,” Phys. Rev. A 69, 053610(1)–(8) (2004).
[Crossref]

Dalfovo, F.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys,  71, 463–512 (1999).
[Crossref]

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(1)–(4) (2001).
[Crossref]

Durfee, D. S.

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, 416–419 (1996).
[Crossref] [PubMed]

Errico, C.D

G. Roati, M. Zaccanti, C.D Errico, J. Catani, M. Modugno, A. Simoni, M. Inguscio, and G. Modugno, “39K Bose-Einstein Condensate with Tunerable Interations,” Phys. Rev. Lett.99, 010403(1)–(4) (2007).
[Crossref]

Fattori, M.

T. Lahaye, T. Koch, B. Fröhlich, M. Fattori, J. Metz, A. Griesmaier, S. Giovanazzi, and T. Pfau, “Strong dipolar effects in a quantum ferrofluid,” Nature 448, 672–675 (2007).
[Crossref] [PubMed]

Fauqembergue, M.

J. -F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam quality of a nonlineal atom laser,” Phys. Rev. Lett. 96, 070404(1)–(4) (2006).
[Crossref]

Fröhlich, B.

T. Lahaye, T. Koch, B. Fröhlich, M. Fattori, J. Metz, A. Griesmaier, S. Giovanazzi, and T. Pfau, “Strong dipolar effects in a quantum ferrofluid,” Nature 448, 672–675 (2007).
[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(1)–(4) (2001).
[Crossref]

Giorgini, S.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys,  71, 463–512 (1999).
[Crossref]

Giovanazzi, S.

T. Lahaye, T. Koch, B. Fröhlich, M. Fattori, J. Metz, A. Griesmaier, S. Giovanazzi, and T. Pfau, “Strong dipolar effects in a quantum ferrofluid,” Nature 448, 672–675 (2007).
[Crossref] [PubMed]

Griesmaier, A.

T. Lahaye, T. Koch, B. Fröhlich, M. Fattori, J. Metz, A. Griesmaier, S. Giovanazzi, and T. Pfau, “Strong dipolar effects in a quantum ferrofluid,” Nature 448, 672–675 (2007).
[Crossref] [PubMed]

Guerin, W.

J. -F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam quality of a nonlineal atom laser,” Phys. Rev. Lett. 96, 070404(1)–(4) (2006).
[Crossref]

Impens, F.

F. Impens, P. Bouyer, and Ch. J. Bordé, “Matter-wave cavity gravimeter,” Appl. Phys. B 84, 603–615 (2006).
[Crossref]

Inguscio, M.

G. Roati, M. Zaccanti, C.D Errico, J. Catani, M. Modugno, A. Simoni, M. Inguscio, and G. Modugno, “39K Bose-Einstein Condensate with Tunerable Interations,” Phys. Rev. Lett.99, 010403(1)–(4) (2007).
[Crossref]

Josse, V.

J. -F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam quality of a nonlineal atom laser,” Phys. Rev. Lett. 96, 070404(1)–(4) (2006).
[Crossref]

Ketterle, W.

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, 416–419 (1996).
[Crossref] [PubMed]

Koch, T.

T. Lahaye, T. Koch, B. Fröhlich, M. Fattori, J. Metz, A. Griesmaier, S. Giovanazzi, and T. Pfau, “Strong dipolar effects in a quantum ferrofluid,” Nature 448, 672–675 (2007).
[Crossref] [PubMed]

Kogelnik, H.

J. A. Arnaud and H. Kogelnik, “Gaussian light beams with general astigmatism,” Appl. Opt,  8, 1687–1693 (1969).
[Crossref] [PubMed]

Kurn, D. M.

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, 416–419 (1996).
[Crossref] [PubMed]

Lahaye, T.

T. Lahaye, T. Koch, B. Fröhlich, M. Fattori, J. Metz, A. Griesmaier, S. Giovanazzi, and T. Pfau, “Strong dipolar effects in a quantum ferrofluid,” Nature 448, 672–675 (2007).
[Crossref] [PubMed]

Le Coq, Y.

J. -F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam quality of a nonlineal atom laser,” Phys. Rev. Lett. 96, 070404(1)–(4) (2006).
[Crossref]

Le. Coq, Y.

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(1)–(4) (2001).
[Crossref]

Lin, Q.

Metcalf, H. J.

H. J. Metcalf and P. Van der Straten, Laser Cooling and Trapping (Springer-Verlag New York, 1999).
[Crossref]

Metz, J.

T. Lahaye, T. Koch, B. Fröhlich, M. Fattori, J. Metz, A. Griesmaier, S. Giovanazzi, and T. Pfau, “Strong dipolar effects in a quantum ferrofluid,” Nature 448, 672–675 (2007).
[Crossref] [PubMed]

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, 416–419 (1996).
[Crossref] [PubMed]

Modugno, G.

G. Roati, M. Zaccanti, C.D Errico, J. Catani, M. Modugno, A. Simoni, M. Inguscio, and G. Modugno, “39K Bose-Einstein Condensate with Tunerable Interations,” Phys. Rev. Lett.99, 010403(1)–(4) (2007).
[Crossref]

Modugno, M.

G. Roati, M. Zaccanti, C.D Errico, J. Catani, M. Modugno, A. Simoni, M. Inguscio, and G. Modugno, “39K Bose-Einstein Condensate with Tunerable Interations,” Phys. Rev. Lett.99, 010403(1)–(4) (2007).
[Crossref]

Murry, D. R.

D. R. Murry and P. Öhberg, “Matter wave focusing,” J. Phys. B: At. Mol. Opt. Phys. 38, 1227–1234 (2005).
[Crossref]

Öhberg, P.

D. R. Murry and P. Öhberg, “Matter wave focusing,” J. Phys. B: At. Mol. Opt. Phys. 38, 1227–1234 (2005).
[Crossref]

G. Whyte, P. Öhberg, and J. Courtial, “Transverse laser modes in Bose-Einstein condensates,” Phys. Rev. A 69, 053610(1)–(8) (2004).
[Crossref]

Pfau, T.

T. Lahaye, T. Koch, B. Fröhlich, M. Fattori, J. Metz, A. Griesmaier, S. Giovanazzi, and T. Pfau, “Strong dipolar effects in a quantum ferrofluid,” Nature 448, 672–675 (2007).
[Crossref] [PubMed]

Pitaevskii, L. P.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys,  71, 463–512 (1999).
[Crossref]

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(1)–(4) (2001).
[Crossref]

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(1)–(4) (2001).
[Crossref]

Riou, J. -F.

J. -F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam quality of a nonlineal atom laser,” Phys. Rev. Lett. 96, 070404(1)–(4) (2006).
[Crossref]

Roati, G.

G. Roati, M. Zaccanti, C.D Errico, J. Catani, M. Modugno, A. Simoni, M. Inguscio, and G. Modugno, “39K Bose-Einstein Condensate with Tunerable Interations,” Phys. Rev. Lett.99, 010403(1)–(4) (2007).
[Crossref]

Sengstock, K.

K. Bongs and K. Sengstock, “Physics with coherent matter waves,” Rep. Prog. Phys. 67, 907–963 (2004).
[Crossref]

Simoni, A.

G. Roati, M. Zaccanti, C.D Errico, J. Catani, M. Modugno, A. Simoni, M. Inguscio, and G. Modugno, “39K Bose-Einstein Condensate with Tunerable Interations,” Phys. Rev. Lett.99, 010403(1)–(4) (2007).
[Crossref]

Stringari, S.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys,  71, 463–512 (1999).
[Crossref]

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(1)–(4) (2001).
[Crossref]

Van der Straten, P.

H. J. Metcalf and P. Van der Straten, Laser Cooling and Trapping (Springer-Verlag New York, 1999).
[Crossref]

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, 416–419 (1996).
[Crossref] [PubMed]

Van Vleck, J. H.

J. H. Van Vleck, “The correspondence principle in the statistical interpretation of quantum mechanics,” Pro. Natl. Acad. Sci. USA 14, 178–188 (1928).
[Crossref]

Whyte, G.

G. Whyte, P. Öhberg, and J. Courtial, “Transverse laser modes in Bose-Einstein condensates,” Phys. Rev. A 69, 053610(1)–(8) (2004).
[Crossref]

Zaccanti, M.

G. Roati, M. Zaccanti, C.D Errico, J. Catani, M. Modugno, A. Simoni, M. Inguscio, and G. Modugno, “39K Bose-Einstein Condensate with Tunerable Interations,” Phys. Rev. Lett.99, 010403(1)–(4) (2007).
[Crossref]

Appl. Opt (1)

J. A. Arnaud and H. Kogelnik, “Gaussian light beams with general astigmatism,” Appl. Opt,  8, 1687–1693 (1969).
[Crossref] [PubMed]

Appl. Phys. B (1)

F. Impens, P. Bouyer, and Ch. J. Bordé, “Matter-wave cavity gravimeter,” Appl. Phys. B 84, 603–615 (2006).
[Crossref]

J. Phys. B: At. Mol. Opt. Phys. (1)

D. R. Murry and P. Öhberg, “Matter wave focusing,” J. Phys. B: At. Mol. Opt. Phys. 38, 1227–1234 (2005).
[Crossref]

Metrologia (1)

Ch. J. Bordé, “Atomic clocks and inertial sensors,” Metrologia 39435–463 (2002).
[Crossref]

Nature (1)

T. Lahaye, T. Koch, B. Fröhlich, M. Fattori, J. Metz, A. Griesmaier, S. Giovanazzi, and T. Pfau, “Strong dipolar effects in a quantum ferrofluid,” Nature 448, 672–675 (2007).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Lett. A (1)

Ch. Antoine and Ch. J. Bordé, “Exact phase shifts for atom interferometry,” Phys. Lett. A 306, 277–284 (2003).
[Crossref]

Phys. Rev. A (1)

G. Whyte, P. Öhberg, and J. Courtial, “Transverse laser modes in Bose-Einstein condensates,” Phys. Rev. A 69, 053610(1)–(8) (2004).
[Crossref]

Phys. Rev. Lett. (2)

J. -F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect, “Beam quality of a nonlineal atom laser,” Phys. Rev. Lett. 96, 070404(1)–(4) (2006).
[Crossref]

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, 416–419 (1996).
[Crossref] [PubMed]

Phys. Rev.Lett. (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(1)–(4) (2001).
[Crossref]

Pro. Natl. Acad. Sci. USA (1)

J. H. Van Vleck, “The correspondence principle in the statistical interpretation of quantum mechanics,” Pro. Natl. Acad. Sci. USA 14, 178–188 (1928).
[Crossref]

Rep. Prog. Phys. (1)

K. Bongs and K. Sengstock, “Physics with coherent matter waves,” Rep. Prog. Phys. 67, 907–963 (2004).
[Crossref]

Rev. Mod. Phys (1)

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys,  71, 463–512 (1999).
[Crossref]

Other (3)

H. J. Metcalf and P. Van der Straten, Laser Cooling and Trapping (Springer-Verlag New York, 1999).
[Crossref]

G. Roati, M. Zaccanti, C.D Errico, J. Catani, M. Modugno, A. Simoni, M. Inguscio, and G. Modugno, “39K Bose-Einstein Condensate with Tunerable Interations,” Phys. Rev. Lett.99, 010403(1)–(4) (2007).
[Crossref]

Ch. J. Bordé, “Theoretical tools for atom optics and interferometry,” C. R. Acad. Sci. Paris, t. 2, Série IV, 509–530 (2001).

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Figures (2)

Fig. 1.
Fig. 1.

One EMWpulse with a “focus length” f 1, focuses the matter wave in the x-direction. After an interval time t 1, another EM pulse whose “focus length” is f 2, focuses the matter wave in a direction with an angle α to the x-direction in the x-y plane. The gravitational acceleration g goes in the z-direction.

Fig. 2.
Fig. 2.

The phase front (a)-(d) and the density distribution (e)-(f) of the atom cloud after the interaction with the second pulse: (a) and (e) t 2=0; (b) and (f) t 2=0.06; (c) and (g) t 2=0.2; (d) and (h) t 2=0.3, where t 2 is the evolution time. The horizontal axis of figs. (e)-(f) is the x-coordinate and the vertical axis is the y-coordinate. The origin of the coordinate system is the center of mass of the atom cloud. The initial trapping frequency ω is 100kHz, and the atoms are Rubidium 87.

Equations (39)

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( r 1 v 1 ) = ( ξ ξ ˙ ) + M ( r 0 v 0 ) ,
M = ( A B C D ) .
S = m ξ ˙ ˜ ( r 1 ξ ) + t 0 t 1 L ( t ) d t t 0 t 1 V ( t ) d t
+ m 2 [ ( r ˜ 1 ξ ˜ ) D B 1 ( r 1 ξ ) 2 ( r ˜ 1 ξ ˜ ) ( B 1 ) T r 0 + r ˜ 0 B 1 A r 0 ] ,
S ( r 1 , t 1 , r 0 , t 0 ) = m ξ ˙ ˜ ( r 1 ξ ) + S 0 + m 2 ( r 0 r 1 ξ ) T U ( r 0 r 1 ξ ) ,
S 0 = t 0 t 1 L ( t ) d t t 0 t 1 V ( t ) d t
U = [ B 1 A B 1 ( C D B 1 A ) D B 1 ] .
{ ( B 1 A ) T = B 1 A , ( B 1 ) T = C D B 1 A , ( D B 1 ) T = D B 1 .
ψ ( r 1 , t 1 ) = K ( q 1 , t 1 , r 0 , t 0 ) ψ ( r 0 , t 0 ) d r 0 .
K ( r 1 , t 1 , r 0 , t 0 ) = ( m 2 π i h ¯ ) 3 2 det B 1 2 exp [ iS h ¯ ] ,
ψ ( r 0 , t 0 ) = exp [ im 2 h ¯ ( r 0 r 0 c ) T Q 0 1 ( r 0 r 0 c ) ] exp [ im v ˜ 0 ( r 0 r 0 c ) h ¯ ] ,
Q 0 1 = R 0 1 + 2 i h ¯ m W 0 2 ,
ψ ( r 1 , t 1 )
= ( m 2 π i h ¯ ) 3 2 det B 1 2 exp [ iS 0 h ¯ ] exp [ im ξ ˙ ˜ ( r 1 ξ ) h ]
exp { im 2 h ¯ [ r 0 r 1 ξ T U r 0 r 1 ξ + r ˜ 0 Q 0 1 r 0 + 2 v ˜ 0 r 0 ] } d r 0
= ( m 2 π i h ¯ ) 3 2 det B 1 2 exp [ iS c h ¯ ]
exp [ im 2 h ¯ ( r 1 r c ) T Q 1 1 ( r 1 r c ) ] exp [ im v ˜ c ( r 1 r c ) h ¯ ]
exp [ im 2 h ¯ ( B 1 A + Q 0 1 ) 1 2 r 0 ( B 1 A + Q 0 1 ) 1 2 B 1 ( r 1 r c ) 2 ] d r 0
= A + BQ 0 1 1 2 exp [ iS c h ¯ ]
exp [ im 2 h ¯ ( r 1 r c ) T Q 1 1 ( r 1 r c ) ] exp [ im v ˜ c ( r 1 r c ) h ¯ ]
Q 1 1 = ( C + D Q 0 1 ) ( A + B Q 0 1 ) 1 ,
S c = m 2 v ˜ 0 DBv 0 + m ξ ˙ ˜ Bv 0 + m 2 t 0 t 1 ( ξ ˙ 2 + ξ ˜ γ ξ + 2 g ˜ ξ ) dt t 0 t 1 V ( t ) dt .
r c = Bv 0 + ξ , v c = Dv 0 + ξ ˙ .
E ( x ) = E 0 ( 1 x 2 w x 2 ) u ,
Ω ac ( x ) = Ω ac 0 ( 1 2 x 2 w x 2 ) .
ψ ( t 0 + τ ) = ρ 1 exp [ i 2 Ω ac 0 τ w x 2 x 2 ] ψ ( t 0 ; v 0 + h ¯ k eff m , Q 0 1 ) .
ψ ( t 0 + τ ) = ρ 1 ψ ( t 0 ; v 0 + h ¯ k eff m , Q 1 1 ) ,
M = ( A B C D ) = ( I 0 F I ) ,
F = 1 f ( 1 0 0 0 0 0 0 0 0 ) ,
f = mw x 2 4 h ¯ Ω ac 0 τ .
M = M 2 M t 1 M 1 .
M 1 , 2 = ( I 0 F 1 , 2 I ) ,
F 1 = 1 f 1 ( 1 0 0 0 0 0 0 0 0 ) ,
F 2 = 1 f 2 ( cos 2 α sin α cos α 0 sin α cos α sin 2 α 0 0 0 0 ) .
M t 1 = ( I t 1 I 0 I ) .
Q 0 1 = ( q 1 0 0 0 q 1 0 0 0 q 1 ) ,
Q 2 1 = ( q 1 1 f 1 1 t 1 f 1 + t 1 q 1 cos 2 α f 2 sin α cos α f 2 0 sin α cos α f 2 q 1 1 + t 1 q 1 sin 2 α f 2 0 0 0 q 1 1 + t 1 q 1 ) .
M t = M t 2 M ,
M t 2 = ( I t 2 I 0 I )

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