Abstract

We study Kapitza-Dirac diffraction of a Bose-Einstein condensate from a standing light wave for a square pulse with variable pulse length but constant pulse area. We find that for sufficiently weak pulses, the usual analytical short-pulse prediction for the Raman-Nath regime continues to hold for longer times, albeit with a reduction of the apparent modulation depth of the standing wave. We quantitatively relate this effect to the Fourier width of the pulse, and draw analogies to the Rabi dynamics of a coupled two-state system. Our findings, combined with numerical modeling for stronger pulses, are of practical interest for the calibration of optical lattices in ultracold atomic systems.

© 2009 Optical Society of America

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  1. C. Adams, M. Sigel, and J. Mlynek, "Atom Optics," Phys. Rep. 240, 143-210 (1994).
    [CrossRef]
  2. P. Meystre, Atom Optics (Springer-Verlag, New York, 2001).
  3. P. L. Kapitza and P. A. M. Dirac, "The reflection of electrons from standing light waves." Proc. Cambridge Phil. Soc. 29, 297-300 (1933).
    [CrossRef]
  4. D. L. Freimund and H. Batelaan, "Bragg Scattering of Free Electrons Using the Kapitza-Dirac Effect," Phys. Rev. Lett. 89, 283602 (2002).
    [CrossRef]
  5. P. L. Gould, G. A. Ruff, and D. E. Pritchard, "Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect," Phys. Rev. Lett. 56, 827-830 (1986).
    [CrossRef] [PubMed]
  6. S. B. Cahn, A. Kumarakrishnan, U. Shim, T. Sleator, P. R. Berman, and B. Dubetsky, "Time-Domain de Broglie Wave Interferometry," Phys. Rev. Lett. 79, 784-787 (1997).
    [CrossRef]
  7. P. Berman, Atom Interferometry (Academic Press, San Diego, 1997).
  8. M. Inguscio, S. Stringari, and C. Wieman, (eds.) Bose-Einstein Condensation in Atomic Gases, Proceedings of the International School of Physics "Enrico Fermi" Course CXL (IOS Press Amsterdam, 1999).
  9. Yu. B. Ovchinnikov, J. H. Muller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Diffraction of a Released Bose-Einstein Condensate by a Pulsed Standing Light Wave," Phys. Rev. Lett. 83, 284-287 (1999).
    [CrossRef]
  10. J. Hecker Denschlag, J. E. Simsarian, H. Haffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A Bose-Einstein condensate in an optical lattice," J. Phys. B: At. Mol. Opt. Phys. 35, 3095-3110 (2002).
    [CrossRef]
  11. J. H. Huckans, I. B. Spielman, B. Laburthe Tolra, W. D. Phillips, and J. V. Porto, "Quantum and Classical Dynamics of a BEC in a Large-Period Optical Lattice," http://arxiv.org/abs/0901.1386 (2009).
  12. 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]
  13. S. Gupta, K. Dieckmann, Z. Hadzibabic, and D. E. Pritchard, "Contrast Interferometry using Bose-Einstein Condensates to Measure h=m and a," Phys. Rev. Lett. 89, 140401 (2002).
    [CrossRef] [PubMed]
  14. G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E. W. Streed, W. Ketterle, and D. E. Pritchard, "Photon Recoil Momentum in Dispersive Media," Phys. Rev. Lett. 94, 170403 (2005).
    [CrossRef] [PubMed]
  15. S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, "Superradiant Rayleigh Scattering from a Bose-Einstein Condensate," Science 285, 571-574 (1999).
    [CrossRef] [PubMed]
  16. D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, "The Onset of Matter-Wave Amplification in a Superradiant Bose-Einstein Condensate," Science 300, 475-478 (2003).
    [CrossRef] [PubMed]
  17. 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]
  18. S. Gupta, A. E. Leanhardt, A. D. Cronin, and D. E. Pritchard, "Coherent Manipulation of Atoms with Standing Light Waves," C. R. Acad. Sci., Paris 2, 479-495 (2001).
  19. W. R. Klein and B. D. Cook, "Unified Approach to Ultrasonic Light Diffraction," IEEE Trans. Sonics Ultrasonics 14, 123-134 (1967).
  20. O. Morsch and M. Oberthaler, "Dynamics of Bose-Einstein condensates in optical lattices," Rev. Mod. Phys. 78, 179-215 (2006).
    [CrossRef]
  21. I. Bloch, J. Dalibard, and W. Zwerger, "Many-body physics with ultracold gases," Rev. Mod. Phys. 80, 885-964 (2008).
    [CrossRef]
  22. R. J. Cook and A. F. Bernhardt, "Deflection of atoms by a resonant standing electromagnetic wave," Phys. Rev. A 18, 2533-2537 (1978).
    [CrossRef]
  23. H. Batelaan, "Colloquium: Illuminating the Kapitza-Dirac effect with electron matter optics," Rev. Mod. Phys. 79, 929-941 (2007).
    [CrossRef]
  24. D. Pertot, D. Greif, S. Albert, B. Gadway, and D. Schneble, "Versatile transporter apparatus for experiments with optically trapped Bose-Einstein condensates," J. Phys. B: At. Mol. Opt. Phys. (to be published), http://arxiv.org/abs/0907.1323 (2009).
    [CrossRef]
  25. M. Cristiani, O. Morsch, J. H. Muller, D. Ciampini, and E. Arimondo, "Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects," Phys. Rev. A 65, 063612 (2002).
    [CrossRef]

2009 (1)

D. Pertot, D. Greif, S. Albert, B. Gadway, and D. Schneble, "Versatile transporter apparatus for experiments with optically trapped Bose-Einstein condensates," J. Phys. B: At. Mol. Opt. Phys. (to be published), http://arxiv.org/abs/0907.1323 (2009).
[CrossRef]

2008 (1)

I. Bloch, J. Dalibard, and W. Zwerger, "Many-body physics with ultracold gases," Rev. Mod. Phys. 80, 885-964 (2008).
[CrossRef]

2007 (1)

H. Batelaan, "Colloquium: Illuminating the Kapitza-Dirac effect with electron matter optics," Rev. Mod. Phys. 79, 929-941 (2007).
[CrossRef]

2006 (1)

O. Morsch and M. Oberthaler, "Dynamics of Bose-Einstein condensates in optical lattices," Rev. Mod. Phys. 78, 179-215 (2006).
[CrossRef]

2005 (1)

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E. W. Streed, W. Ketterle, and D. E. Pritchard, "Photon Recoil Momentum in Dispersive Media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

2003 (1)

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, "The Onset of Matter-Wave Amplification in a Superradiant Bose-Einstein Condensate," Science 300, 475-478 (2003).
[CrossRef] [PubMed]

2002 (4)

S. Gupta, K. Dieckmann, Z. Hadzibabic, and D. E. Pritchard, "Contrast Interferometry using Bose-Einstein Condensates to Measure h=m and a," Phys. Rev. Lett. 89, 140401 (2002).
[CrossRef] [PubMed]

D. L. Freimund and H. Batelaan, "Bragg Scattering of Free Electrons Using the Kapitza-Dirac Effect," Phys. Rev. Lett. 89, 283602 (2002).
[CrossRef]

J. Hecker Denschlag, J. E. Simsarian, H. Haffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A Bose-Einstein condensate in an optical lattice," J. Phys. B: At. Mol. Opt. Phys. 35, 3095-3110 (2002).
[CrossRef]

M. Cristiani, O. Morsch, J. H. Muller, D. Ciampini, and E. Arimondo, "Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects," Phys. Rev. A 65, 063612 (2002).
[CrossRef]

2001 (1)

S. Gupta, A. E. Leanhardt, A. D. Cronin, and D. E. Pritchard, "Coherent Manipulation of Atoms with Standing Light Waves," C. R. Acad. Sci., Paris 2, 479-495 (2001).

1999 (3)

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, "Superradiant Rayleigh Scattering from a Bose-Einstein Condensate," Science 285, 571-574 (1999).
[CrossRef] [PubMed]

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]

Yu. B. Ovchinnikov, J. H. Muller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Diffraction of a Released Bose-Einstein Condensate by a Pulsed Standing Light Wave," Phys. Rev. Lett. 83, 284-287 (1999).
[CrossRef]

1997 (1)

S. B. Cahn, A. Kumarakrishnan, U. Shim, T. Sleator, P. R. Berman, and B. Dubetsky, "Time-Domain de Broglie Wave Interferometry," Phys. Rev. Lett. 79, 784-787 (1997).
[CrossRef]

1994 (1)

C. Adams, M. Sigel, and J. Mlynek, "Atom Optics," Phys. Rep. 240, 143-210 (1994).
[CrossRef]

1988 (1)

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]

1986 (1)

P. L. Gould, G. A. Ruff, and D. E. Pritchard, "Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect," Phys. Rev. Lett. 56, 827-830 (1986).
[CrossRef] [PubMed]

1978 (1)

R. J. Cook and A. F. Bernhardt, "Deflection of atoms by a resonant standing electromagnetic wave," Phys. Rev. A 18, 2533-2537 (1978).
[CrossRef]

1967 (1)

W. R. Klein and B. D. Cook, "Unified Approach to Ultrasonic Light Diffraction," IEEE Trans. Sonics Ultrasonics 14, 123-134 (1967).

1933 (1)

P. L. Kapitza and P. A. M. Dirac, "The reflection of electrons from standing light waves." Proc. Cambridge Phil. Soc. 29, 297-300 (1933).
[CrossRef]

Adams, C.

C. Adams, M. Sigel, and J. Mlynek, "Atom Optics," Phys. Rep. 240, 143-210 (1994).
[CrossRef]

Albert, S.

D. Pertot, D. Greif, S. Albert, B. Gadway, and D. Schneble, "Versatile transporter apparatus for experiments with optically trapped Bose-Einstein condensates," J. Phys. B: At. Mol. Opt. Phys. (to be published), http://arxiv.org/abs/0907.1323 (2009).
[CrossRef]

Arimondo, E.

M. Cristiani, O. Morsch, J. H. Muller, D. Ciampini, and E. Arimondo, "Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects," Phys. Rev. A 65, 063612 (2002).
[CrossRef]

Batelaan, H.

H. Batelaan, "Colloquium: Illuminating the Kapitza-Dirac effect with electron matter optics," Rev. Mod. Phys. 79, 929-941 (2007).
[CrossRef]

D. L. Freimund and H. Batelaan, "Bragg Scattering of Free Electrons Using the Kapitza-Dirac Effect," Phys. Rev. Lett. 89, 283602 (2002).
[CrossRef]

Berman, P. R.

S. B. Cahn, A. Kumarakrishnan, U. Shim, T. Sleator, P. R. Berman, and B. Dubetsky, "Time-Domain de Broglie Wave Interferometry," Phys. Rev. Lett. 79, 784-787 (1997).
[CrossRef]

Bernhardt, A. F.

R. J. Cook and A. F. Bernhardt, "Deflection of atoms by a resonant standing electromagnetic wave," Phys. Rev. A 18, 2533-2537 (1978).
[CrossRef]

Bloch, I.

I. Bloch, J. Dalibard, and W. Zwerger, "Many-body physics with ultracold gases," Rev. Mod. Phys. 80, 885-964 (2008).
[CrossRef]

Boyd, M.

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E. W. Streed, W. Ketterle, and D. E. Pritchard, "Photon Recoil Momentum in Dispersive Media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, "The Onset of Matter-Wave Amplification in a Superradiant Bose-Einstein Condensate," Science 300, 475-478 (2003).
[CrossRef] [PubMed]

Browaeys, A.

J. Hecker Denschlag, J. E. Simsarian, H. Haffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A Bose-Einstein condensate in an optical lattice," J. Phys. B: At. Mol. Opt. Phys. 35, 3095-3110 (2002).
[CrossRef]

Cahn, S. B.

S. B. Cahn, A. Kumarakrishnan, U. Shim, T. Sleator, P. R. Berman, and B. Dubetsky, "Time-Domain de Broglie Wave Interferometry," Phys. Rev. Lett. 79, 784-787 (1997).
[CrossRef]

Campbell, G. K.

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E. W. Streed, W. Ketterle, and D. E. Pritchard, "Photon Recoil Momentum in Dispersive Media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

Chikkatur, A. P.

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]

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, "Superradiant Rayleigh Scattering from a Bose-Einstein Condensate," Science 285, 571-574 (1999).
[CrossRef] [PubMed]

Cho, D.

J. Hecker Denschlag, J. E. Simsarian, H. Haffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A Bose-Einstein condensate in an optical lattice," J. Phys. B: At. Mol. Opt. Phys. 35, 3095-3110 (2002).
[CrossRef]

Ciampini, D.

M. Cristiani, O. Morsch, J. H. Muller, D. Ciampini, and E. Arimondo, "Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects," Phys. Rev. A 65, 063612 (2002).
[CrossRef]

Cook, B. D.

W. R. Klein and B. D. Cook, "Unified Approach to Ultrasonic Light Diffraction," IEEE Trans. Sonics Ultrasonics 14, 123-134 (1967).

Cook, R. J.

R. J. Cook and A. F. Bernhardt, "Deflection of atoms by a resonant standing electromagnetic wave," Phys. Rev. A 18, 2533-2537 (1978).
[CrossRef]

Cristiani, M.

M. Cristiani, O. Morsch, J. H. Muller, D. Ciampini, and E. Arimondo, "Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects," Phys. Rev. A 65, 063612 (2002).
[CrossRef]

Cronin, A. D.

S. Gupta, A. E. Leanhardt, A. D. Cronin, and D. E. Pritchard, "Coherent Manipulation of Atoms with Standing Light Waves," C. R. Acad. Sci., Paris 2, 479-495 (2001).

Dalibard, J.

I. Bloch, J. Dalibard, and W. Zwerger, "Many-body physics with ultracold gases," Rev. Mod. Phys. 80, 885-964 (2008).
[CrossRef]

Dieckmann, K.

S. Gupta, K. Dieckmann, Z. Hadzibabic, and D. E. Pritchard, "Contrast Interferometry using Bose-Einstein Condensates to Measure h=m and a," Phys. Rev. Lett. 89, 140401 (2002).
[CrossRef] [PubMed]

Dirac, P. A. M.

P. L. Kapitza and P. A. M. Dirac, "The reflection of electrons from standing light waves." Proc. Cambridge Phil. Soc. 29, 297-300 (1933).
[CrossRef]

Doery, M. R.

Yu. B. Ovchinnikov, J. H. Muller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Diffraction of a Released Bose-Einstein Condensate by a Pulsed Standing Light Wave," Phys. Rev. Lett. 83, 284-287 (1999).
[CrossRef]

Dubetsky, B.

S. B. Cahn, A. Kumarakrishnan, U. Shim, T. Sleator, P. R. Berman, and B. Dubetsky, "Time-Domain de Broglie Wave Interferometry," Phys. Rev. Lett. 79, 784-787 (1997).
[CrossRef]

Freimund, D. L.

D. L. Freimund and H. Batelaan, "Bragg Scattering of Free Electrons Using the Kapitza-Dirac Effect," Phys. Rev. Lett. 89, 283602 (2002).
[CrossRef]

Gadway, B.

D. Pertot, D. Greif, S. Albert, B. Gadway, and D. Schneble, "Versatile transporter apparatus for experiments with optically trapped Bose-Einstein condensates," J. Phys. B: At. Mol. Opt. Phys. (to be published), http://arxiv.org/abs/0907.1323 (2009).
[CrossRef]

Gould, P. L.

P. L. Gould, G. A. Ruff, and D. E. Pritchard, "Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect," Phys. Rev. Lett. 56, 827-830 (1986).
[CrossRef] [PubMed]

Greif, D.

D. Pertot, D. Greif, S. Albert, B. Gadway, and D. Schneble, "Versatile transporter apparatus for experiments with optically trapped Bose-Einstein condensates," J. Phys. B: At. Mol. Opt. Phys. (to be published), http://arxiv.org/abs/0907.1323 (2009).
[CrossRef]

Gupta, S.

S. Gupta, K. Dieckmann, Z. Hadzibabic, and D. E. Pritchard, "Contrast Interferometry using Bose-Einstein Condensates to Measure h=m and a," Phys. Rev. Lett. 89, 140401 (2002).
[CrossRef] [PubMed]

S. Gupta, A. E. Leanhardt, A. D. Cronin, and D. E. Pritchard, "Coherent Manipulation of Atoms with Standing Light Waves," C. R. Acad. Sci., Paris 2, 479-495 (2001).

Hadzibabic, Z.

S. Gupta, K. Dieckmann, Z. Hadzibabic, and D. E. Pritchard, "Contrast Interferometry using Bose-Einstein Condensates to Measure h=m and a," Phys. Rev. Lett. 89, 140401 (2002).
[CrossRef] [PubMed]

Haffner, H.

J. Hecker Denschlag, J. E. Simsarian, H. Haffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A Bose-Einstein condensate in an optical lattice," J. Phys. B: At. Mol. Opt. Phys. 35, 3095-3110 (2002).
[CrossRef]

Hecker Denschlag, J.

J. Hecker Denschlag, J. E. Simsarian, H. Haffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A Bose-Einstein condensate in an optical lattice," J. Phys. B: At. Mol. Opt. Phys. 35, 3095-3110 (2002).
[CrossRef]

Helmerson, K.

J. Hecker Denschlag, J. E. Simsarian, H. Haffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A Bose-Einstein condensate in an optical lattice," J. Phys. B: At. Mol. Opt. Phys. 35, 3095-3110 (2002).
[CrossRef]

Yu. B. Ovchinnikov, J. H. Muller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Diffraction of a Released Bose-Einstein Condensate by a Pulsed Standing Light Wave," Phys. Rev. Lett. 83, 284-287 (1999).
[CrossRef]

Inouye, S.

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]

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, "Superradiant Rayleigh Scattering from a Bose-Einstein Condensate," Science 285, 571-574 (1999).
[CrossRef] [PubMed]

Kapitza, P. L.

P. L. Kapitza and P. A. M. Dirac, "The reflection of electrons from standing light waves." Proc. Cambridge Phil. Soc. 29, 297-300 (1933).
[CrossRef]

Ketterle, W.

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E. W. Streed, W. Ketterle, and D. E. Pritchard, "Photon Recoil Momentum in Dispersive Media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, "The Onset of Matter-Wave Amplification in a Superradiant Bose-Einstein Condensate," Science 300, 475-478 (2003).
[CrossRef] [PubMed]

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, "Superradiant Rayleigh Scattering from a Bose-Einstein Condensate," Science 285, 571-574 (1999).
[CrossRef] [PubMed]

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]

Klein, W. R.

W. R. Klein and B. D. Cook, "Unified Approach to Ultrasonic Light Diffraction," IEEE Trans. Sonics Ultrasonics 14, 123-134 (1967).

Kumarakrishnan, A.

S. B. Cahn, A. Kumarakrishnan, U. Shim, T. Sleator, P. R. Berman, and B. Dubetsky, "Time-Domain de Broglie Wave Interferometry," Phys. Rev. Lett. 79, 784-787 (1997).
[CrossRef]

Leanhardt, A. E.

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E. W. Streed, W. Ketterle, and D. E. Pritchard, "Photon Recoil Momentum in Dispersive Media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

S. Gupta, A. E. Leanhardt, A. D. Cronin, and D. E. Pritchard, "Coherent Manipulation of Atoms with Standing Light Waves," C. R. Acad. Sci., Paris 2, 479-495 (2001).

Martin, P. J.

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]

McKenzie, C.

J. Hecker Denschlag, J. E. Simsarian, H. Haffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A Bose-Einstein condensate in an optical lattice," J. Phys. B: At. Mol. Opt. Phys. 35, 3095-3110 (2002).
[CrossRef]

Miklich, A. H.

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]

Mlynek, J.

C. Adams, M. Sigel, and J. Mlynek, "Atom Optics," Phys. Rep. 240, 143-210 (1994).
[CrossRef]

Morsch, O.

O. Morsch and M. Oberthaler, "Dynamics of Bose-Einstein condensates in optical lattices," Rev. Mod. Phys. 78, 179-215 (2006).
[CrossRef]

M. Cristiani, O. Morsch, J. H. Muller, D. Ciampini, and E. Arimondo, "Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects," Phys. Rev. A 65, 063612 (2002).
[CrossRef]

Muller, J. H.

M. Cristiani, O. Morsch, J. H. Muller, D. Ciampini, and E. Arimondo, "Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects," Phys. Rev. A 65, 063612 (2002).
[CrossRef]

Yu. B. Ovchinnikov, J. H. Muller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Diffraction of a Released Bose-Einstein Condensate by a Pulsed Standing Light Wave," Phys. Rev. Lett. 83, 284-287 (1999).
[CrossRef]

Mun, J.

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E. W. Streed, W. Ketterle, and D. E. Pritchard, "Photon Recoil Momentum in Dispersive Media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

Oberthaler, M.

O. Morsch and M. Oberthaler, "Dynamics of Bose-Einstein condensates in optical lattices," Rev. Mod. Phys. 78, 179-215 (2006).
[CrossRef]

Oldaker, B. G.

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]

Ovchinnikov, Yu. B.

Yu. B. Ovchinnikov, J. H. Muller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Diffraction of a Released Bose-Einstein Condensate by a Pulsed Standing Light Wave," Phys. Rev. Lett. 83, 284-287 (1999).
[CrossRef]

Pertot, D.

D. Pertot, D. Greif, S. Albert, B. Gadway, and D. Schneble, "Versatile transporter apparatus for experiments with optically trapped Bose-Einstein condensates," J. Phys. B: At. Mol. Opt. Phys. (to be published), http://arxiv.org/abs/0907.1323 (2009).
[CrossRef]

Phillips, W. D.

J. Hecker Denschlag, J. E. Simsarian, H. Haffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A Bose-Einstein condensate in an optical lattice," J. Phys. B: At. Mol. Opt. Phys. 35, 3095-3110 (2002).
[CrossRef]

Yu. B. Ovchinnikov, J. H. Muller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Diffraction of a Released Bose-Einstein Condensate by a Pulsed Standing Light Wave," Phys. Rev. Lett. 83, 284-287 (1999).
[CrossRef]

Pritchard, D. E.

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E. W. Streed, W. Ketterle, and D. E. Pritchard, "Photon Recoil Momentum in Dispersive Media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, "The Onset of Matter-Wave Amplification in a Superradiant Bose-Einstein Condensate," Science 300, 475-478 (2003).
[CrossRef] [PubMed]

S. Gupta, K. Dieckmann, Z. Hadzibabic, and D. E. Pritchard, "Contrast Interferometry using Bose-Einstein Condensates to Measure h=m and a," Phys. Rev. Lett. 89, 140401 (2002).
[CrossRef] [PubMed]

S. Gupta, A. E. Leanhardt, A. D. Cronin, and D. E. Pritchard, "Coherent Manipulation of Atoms with Standing Light Waves," C. R. Acad. Sci., Paris 2, 479-495 (2001).

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, "Superradiant Rayleigh Scattering from a Bose-Einstein Condensate," Science 285, 571-574 (1999).
[CrossRef] [PubMed]

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]

P. L. Gould, G. A. Ruff, and D. E. Pritchard, "Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect," Phys. Rev. Lett. 56, 827-830 (1986).
[CrossRef] [PubMed]

Rolston, S. L.

J. Hecker Denschlag, J. E. Simsarian, H. Haffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A Bose-Einstein condensate in an optical lattice," J. Phys. B: At. Mol. Opt. Phys. 35, 3095-3110 (2002).
[CrossRef]

Yu. B. Ovchinnikov, J. H. Muller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Diffraction of a Released Bose-Einstein Condensate by a Pulsed Standing Light Wave," Phys. Rev. Lett. 83, 284-287 (1999).
[CrossRef]

Ruff, G. A.

P. L. Gould, G. A. Ruff, and D. E. Pritchard, "Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect," Phys. Rev. Lett. 56, 827-830 (1986).
[CrossRef] [PubMed]

Schneble, D.

D. Pertot, D. Greif, S. Albert, B. Gadway, and D. Schneble, "Versatile transporter apparatus for experiments with optically trapped Bose-Einstein condensates," J. Phys. B: At. Mol. Opt. Phys. (to be published), http://arxiv.org/abs/0907.1323 (2009).
[CrossRef]

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, "The Onset of Matter-Wave Amplification in a Superradiant Bose-Einstein Condensate," Science 300, 475-478 (2003).
[CrossRef] [PubMed]

Shim, U.

S. B. Cahn, A. Kumarakrishnan, U. Shim, T. Sleator, P. R. Berman, and B. Dubetsky, "Time-Domain de Broglie Wave Interferometry," Phys. Rev. Lett. 79, 784-787 (1997).
[CrossRef]

Sigel, M.

C. Adams, M. Sigel, and J. Mlynek, "Atom Optics," Phys. Rep. 240, 143-210 (1994).
[CrossRef]

Simsarian, J. E.

J. Hecker Denschlag, J. E. Simsarian, H. Haffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A Bose-Einstein condensate in an optical lattice," J. Phys. B: At. Mol. Opt. Phys. 35, 3095-3110 (2002).
[CrossRef]

Sleator, T.

S. B. Cahn, A. Kumarakrishnan, U. Shim, T. Sleator, P. R. Berman, and B. Dubetsky, "Time-Domain de Broglie Wave Interferometry," Phys. Rev. Lett. 79, 784-787 (1997).
[CrossRef]

Stamper-Kurn, D. M.

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]

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, "Superradiant Rayleigh Scattering from a Bose-Einstein Condensate," Science 285, 571-574 (1999).
[CrossRef] [PubMed]

Stenger, J.

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, "Superradiant Rayleigh Scattering from a Bose-Einstein Condensate," Science 285, 571-574 (1999).
[CrossRef] [PubMed]

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]

Streed, E. W.

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E. W. Streed, W. Ketterle, and D. E. Pritchard, "Photon Recoil Momentum in Dispersive Media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, "The Onset of Matter-Wave Amplification in a Superradiant Bose-Einstein Condensate," Science 300, 475-478 (2003).
[CrossRef] [PubMed]

Torii, Y.

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, "The Onset of Matter-Wave Amplification in a Superradiant Bose-Einstein Condensate," Science 300, 475-478 (2003).
[CrossRef] [PubMed]

Vredenbregt, E. J. D.

Yu. B. Ovchinnikov, J. H. Muller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Diffraction of a Released Bose-Einstein Condensate by a Pulsed Standing Light Wave," Phys. Rev. Lett. 83, 284-287 (1999).
[CrossRef]

Zwerger, W.

I. Bloch, J. Dalibard, and W. Zwerger, "Many-body physics with ultracold gases," Rev. Mod. Phys. 80, 885-964 (2008).
[CrossRef]

C. R. Acad. Sci., Paris (1)

S. Gupta, A. E. Leanhardt, A. D. Cronin, and D. E. Pritchard, "Coherent Manipulation of Atoms with Standing Light Waves," C. R. Acad. Sci., Paris 2, 479-495 (2001).

IEEE Trans. Sonics Ultrasonics (1)

W. R. Klein and B. D. Cook, "Unified Approach to Ultrasonic Light Diffraction," IEEE Trans. Sonics Ultrasonics 14, 123-134 (1967).

J. Phys. B: At. Mol. Opt. Phys. (2)

J. Hecker Denschlag, J. E. Simsarian, H. Haffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S. L. Rolston, and W. D. Phillips, "A Bose-Einstein condensate in an optical lattice," J. Phys. B: At. Mol. Opt. Phys. 35, 3095-3110 (2002).
[CrossRef]

D. Pertot, D. Greif, S. Albert, B. Gadway, and D. Schneble, "Versatile transporter apparatus for experiments with optically trapped Bose-Einstein condensates," J. Phys. B: At. Mol. Opt. Phys. (to be published), http://arxiv.org/abs/0907.1323 (2009).
[CrossRef]

Phys. Rep. (1)

C. Adams, M. Sigel, and J. Mlynek, "Atom Optics," Phys. Rep. 240, 143-210 (1994).
[CrossRef]

Phys. Rev. A (2)

M. Cristiani, O. Morsch, J. H. Muller, D. Ciampini, and E. Arimondo, "Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects," Phys. Rev. A 65, 063612 (2002).
[CrossRef]

R. J. Cook and A. F. Bernhardt, "Deflection of atoms by a resonant standing electromagnetic wave," Phys. Rev. A 18, 2533-2537 (1978).
[CrossRef]

Phys. Rev. Lett. (8)

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]

Yu. B. Ovchinnikov, J. H. Muller, M. R. Doery, E. J. D. Vredenbregt, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Diffraction of a Released Bose-Einstein Condensate by a Pulsed Standing Light Wave," Phys. Rev. Lett. 83, 284-287 (1999).
[CrossRef]

D. L. Freimund and H. Batelaan, "Bragg Scattering of Free Electrons Using the Kapitza-Dirac Effect," Phys. Rev. Lett. 89, 283602 (2002).
[CrossRef]

P. L. Gould, G. A. Ruff, and D. E. Pritchard, "Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect," Phys. Rev. Lett. 56, 827-830 (1986).
[CrossRef] [PubMed]

S. B. Cahn, A. Kumarakrishnan, U. Shim, T. Sleator, P. R. Berman, and B. Dubetsky, "Time-Domain de Broglie Wave Interferometry," Phys. Rev. Lett. 79, 784-787 (1997).
[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]

S. Gupta, K. Dieckmann, Z. Hadzibabic, and D. E. Pritchard, "Contrast Interferometry using Bose-Einstein Condensates to Measure h=m and a," Phys. Rev. Lett. 89, 140401 (2002).
[CrossRef] [PubMed]

G. K. Campbell, A. E. Leanhardt, J. Mun, M. Boyd, E. W. Streed, W. Ketterle, and D. E. Pritchard, "Photon Recoil Momentum in Dispersive Media," Phys. Rev. Lett. 94, 170403 (2005).
[CrossRef] [PubMed]

Proc. Cambridge Phil. Soc. (1)

P. L. Kapitza and P. A. M. Dirac, "The reflection of electrons from standing light waves." Proc. Cambridge Phil. Soc. 29, 297-300 (1933).
[CrossRef]

Rev. Mod. Phys. (3)

O. Morsch and M. Oberthaler, "Dynamics of Bose-Einstein condensates in optical lattices," Rev. Mod. Phys. 78, 179-215 (2006).
[CrossRef]

I. Bloch, J. Dalibard, and W. Zwerger, "Many-body physics with ultracold gases," Rev. Mod. Phys. 80, 885-964 (2008).
[CrossRef]

H. Batelaan, "Colloquium: Illuminating the Kapitza-Dirac effect with electron matter optics," Rev. Mod. Phys. 79, 929-941 (2007).
[CrossRef]

Science (2)

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, and W. Ketterle, "Superradiant Rayleigh Scattering from a Bose-Einstein Condensate," Science 285, 571-574 (1999).
[CrossRef] [PubMed]

D. Schneble, Y. Torii, M. Boyd, E. W. Streed, D. E. Pritchard, and W. Ketterle, "The Onset of Matter-Wave Amplification in a Superradiant Bose-Einstein Condensate," Science 300, 475-478 (2003).
[CrossRef] [PubMed]

Other (4)

P. Meystre, Atom Optics (Springer-Verlag, New York, 2001).

P. Berman, Atom Interferometry (Academic Press, San Diego, 1997).

M. Inguscio, S. Stringari, and C. Wieman, (eds.) Bose-Einstein Condensation in Atomic Gases, Proceedings of the International School of Physics "Enrico Fermi" Course CXL (IOS Press Amsterdam, 1999).

J. H. Huckans, I. B. Spielman, B. Laburthe Tolra, W. D. Phillips, and J. V. Porto, "Quantum and Classical Dynamics of a BEC in a Large-Period Optical Lattice," http://arxiv.org/abs/0901.1386 (2009).

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Figures (3)

Fig. 1.
Fig. 1.

Time-of-flight (TOF) absorption images of a condensate diffracted from a 1064 nm standing-wave optical pulses of constant area β=V 0 τ/ħ=4.5, and durations ranging from τ=4 µs =τ r (2)≈0.2) to 360 µs (α≈18). For the data with durations t≳90 ms (for which [β/α]1/2≲1.0), the apparent modulation depth of the standing wave undergoes an oscillatory decay consistent with the form (β/2)sinc(α/2) (see text).

Fig. 2.
Fig. 2.

Suppression and revival of atomic diffraction from a constant-area standing wave light pulse with increasing pulse length. (a,b) Relative populations of the central condensate 0ħk and orders ±2ħk vs. normalized pulse duration α=τ/τ (2) r ~τ/20 ms. Filled blue dots and open red squares refer to pulses of area β=4.5 (cf. Fig. 1) and 1.5, respectively, and the solid lines plot the function J 2 n [(β/2)sinc(α/2)]. The dashed black lines correspond to numerical fits for β=4.5. (c) Decay of the ±4ħk orders in the β=4.5 data set, with the numerical simulation (dashed line) as well as the function J 2 2 [(β/2)sinc(α/2)]. (d) Behavior of β eff/β, where the atomic diffraction patterns are fit with the distribution J 2 n (β eff/2). The black solid line is the analytical form sinc(a=2), and the dashed black line corresponds to a numerical solution of Eq. (4) using β=4.5.

Fig. 3.
Fig. 3.

(a) Comparison of experimental spectra and numerical fits. For each data set, numerical simulations (using Eq. (4)) of the momentum state distribution are shown as solid, dashed, and dotted curves for the 0ħk, ±2ħk, and ±4ħk diffraction components, respectively. The red crosses are data for the 0ħk order, and the blue open squares (green filled dots) are data averaged for the ±2ħk (±4ħk) orders. (b) Comparison of numerical lattice depth calibrations (using Eq. (4)) from relatively short (8 ms) and long (50 ms) optical lattice pulses for various intensities of the standing light wave. The results for numerically-fit lattice depths agree to within 4% (the solid line has a slope of 1).

Equations (10)

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

Ĥ=(22m)z2+V0cos2kz
α=(Er(2)) τ
β=(V0) τ ,
idcndt=αn2τcn+β4τ(cn1+2cn+cn+1)
nˉ=β/α
Pn=Jn2(β2),
P±1=β22β2+4α2 sin2 (β2/2+α22)
P±1=12 (χΩ)2 sin2 (Ω2τ)
Pn=Jn2(β2sincα2),
V0,eff=V0sinc(τ2τr(2)) .

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