Abstract

We demonstrate a new imaging technique for cold atom clouds based on phase retrieval from a single diffraction measurement. Most single-shot diffractive imaging methods for cold atoms assume a monomorphic object to extract the column density. The method described here allows quantitative imaging of an inhomogeneous cloud, enabling recovery of either the atomic density or the refractive index, provided the other is known. Using ideas borrowed from density functional theory, we calculate the approximate paraxial diffracted intensity derivative from the measured diffracted intensity distribution and use it to solve the Transport of Intensity Equation (TIE) for the phase of the wave at the detector plane. Back-propagation to the object plane yields the object exit surface wave and then provides a quantitative measurement of either the atomic column density or refractive index. Images of homogeneous clouds showed good quantitative agreement with conventional techniques. An inhomogeneous cloud was created using a cascade electromagnetically induced transparency scheme and images of both phase and amplitude parts of refractive index across the cloud were separately retrieved, showing good agreement with theoretical results.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. M. Quiney, G. J. Williams, and K. A. Nugent, "Non-iterative solution of the phase retrieval problem using a single diffraction measurement," Opt. Express 16, 6896-6903 (2008).
    [CrossRef] [PubMed]
  2. A. Gaetan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, "Observation of collective excitation of two individual atoms in the Rydberg blockade regime," Nat. Phys. 5,115-118 (2009).
    [CrossRef]
  3. E. Urban, A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, "Observation of Rydberg blockade between two atoms," Nat. Phys. 5, 110-114 (2009).
    [CrossRef]
  4. H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro "Observation of transient electromagnetically induced transparency in a rubidium Λ system," Phys. Rev. A 58, 1545-1548 (1998).
    [CrossRef]
  5. M. D. Lukin and A. Imamuglu "Nonlinear optics and quantum entanglement of ultra slow single photons," Phys. Rev. Lett. 84(7), 1419-1422 (2000).
    [CrossRef]
  6. N. S. Ginsberg, S. R. Garner, and L. V. Hau "Coherent control of optical information with matter wave dynamics," Nature 400, 623-626 (2007).
    [CrossRef]
  7. B. J. Claessens, M. P. Reijnders, G. Taban, O. J. Luiten, and E. J. D. Vredenbregt, "Cold electron and ion beams generated from trapped atoms," Phys. Plas. 14, 093101 (2007).
    [CrossRef]
  8. O. J. Luiten, B. J. Claessens, S. B. Van der Geer, M. P. Reijnders, G. Taban, and E. J. D. Vredenbregt, "Ultracold electron sources," Int. J. Mod. Phys. A 22, 3882-3897 (2007).
    [CrossRef]
  9. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wiemann, and E. A. Cornell "Observation of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198-201 (1995).
    [CrossRef] [PubMed]
  10. D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
    [CrossRef]
  11. L. D. Turner, K. P. Weber, D. Paganin, and R. E. Scholten, " Off-resonant defocus contrast imaging of cold atoms," Opt. Lett. 29, 232-234 (2004).
    [CrossRef] [PubMed]
  12. L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, "Diffraction-contrast imaging of cold atoms," Phys. Rev. A 72, 031403 (2005).
    [CrossRef]
  13. M. R. Teague, "Deterministic phase retrieval: a Green’s function solution," J. Opt. Soc. Am. 73, 1434-1441 (1983).
    [CrossRef]
  14. K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, "Unique phase recovery for non-periodic objects" Phys. Rev. Lett. 91, 203902 (2003).
    [CrossRef] [PubMed]
  15. T. E. Gureyev and K. A. Nugent, "Rapid quantitative phase imaging using the transport of intensity equation," Opt. Commun. 133, 339-346 (1997).
    [CrossRef]
  16. J. B. Tiller, A. Barty, D. Paganin, and K. A. Nugent, "The holograhic twin image problem: a deterministic phase solution," Opt. Commun. 183, 7-14 (2000).
    [CrossRef]
  17. D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, " Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object," J. Microsc. 206, 33-40 (2002).
    [CrossRef]
  18. D. Paganin and K. A. Nugent, "Noninterferometic phase imaging with partially coherent light," Phys. Rev. Lett. 80(12), 2586-2589 (1998).
    [CrossRef]
  19. M. R. Dennis, K. O’Holleran, and M. J. Padgett, "Singular Optics: Optical vortices and polarization singularities," Prog. Opt. 53, 293-363 (2009)
    [CrossRef]
  20. A. Tikhonov and V. Arsenin, Solutions of Ill-posed Problems (V. H. Winston and Sons, New York, 1977).
  21. D. Paganin, Coherent X-Ray Optics (Oxford University Press, Oxford UK, 2006).
    [CrossRef]
  22. R. N. Bracewell, The Fourier Transform and its Applications 3rd Ed. (McGraw-Hill, USA, 2000).
  23. L. P. Maguire, R. M.W. van Bijnen, E. Mese, and R. E. Scholten, "Theoretical calculation of saturated absorption spectra for multi-level atoms," J. Phys. B: At. Mol. Opt. Phys. 39, 2709-2720 (2006).
    [CrossRef]
  24. R. M. Whitley and C. R. StroudJr., "Double optical resonance," Phys. Rev. A 141498-1513 (1976).
    [CrossRef]
  25. C. Wieman, G. Flowers, and S. Gilbert, "Inexpensive laser cooling and trapping experiment for undergraduate laboratories," Am. J. Phys. 63, 317-329 (1995).
    [CrossRef]
  26. H. J. Metcalf and P. van der Straten, "Laser cooling and trapping," Springer-Verlag, Berlin. (1999).
  27. C. J. Hawthorn, K. P. Weber, and R. E. Scholten, "Littrow configuration tunable external cavity diode laser with fixed direction output beam," Rev. Sci. Inst. 72, 4477 (2001).
    [CrossRef]
  28. L. D. Turner, K. P. Weber, C. J. Hawthorn, and R. E. Scholten, "Frequency noise characterisation of narrow linewidth diode lasers," Opt. Commun. 201, 391-397 (2002).
    [CrossRef]
  29. MOGlabs laser diode controller, www.moglabs.com.
  30. A. C. Wilson, J. C. Sharpe, C. R. McKenzie, P. J. Manson, and D. M Warrington, "Narrow-linewidth masteroscillator power amplifier based on a semiconductor tapered amplifier," Appl. Opt. 37, 4871-4875 (1998).
    [CrossRef]
  31. L. P. Maguire, R. M. W. van Bijnen, E. Mese, and R. Scholten "Theoretical calculation of saturated absorption spectra for multi-level atoms," J. Phys. B. 39, 2709-2720 (2006).
    [CrossRef]
  32. D. A. Steck, "Rubidium 85 D line Data," Los Alamos National Laboratory, available online at http://steck.us/alkalidata (2008).
  33. K. Kowalski, K. Vaseva, S. Gateva, M. Glodz, L. Petrov, and J. Szonert, "Laser system for EIT spectroscopy of cold Rb atoms," Proc. SPIE. 6604, 66040 (2007).
    [CrossRef]
  34. J. Wang, L. B. Kong, X. H. Tu, K. J. Jiang, K. Li, H. W. Xiong, Y. Zhu, and M. S. Zhan, "Electromagnetically induced transparency in multi-level cascade scheme of cold rubidium atoms," Phys. Rev. A 328, 437-443 (2004).
  35. T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould "Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 State," Phys. Script. 52, 271-276 (1995).
    [CrossRef]
  36. J. R. Fienup "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982).
    [CrossRef] [PubMed]

2009 (3)

A. Gaetan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, "Observation of collective excitation of two individual atoms in the Rydberg blockade regime," Nat. Phys. 5,115-118 (2009).
[CrossRef]

E. Urban, A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, "Observation of Rydberg blockade between two atoms," Nat. Phys. 5, 110-114 (2009).
[CrossRef]

M. R. Dennis, K. O’Holleran, and M. J. Padgett, "Singular Optics: Optical vortices and polarization singularities," Prog. Opt. 53, 293-363 (2009)
[CrossRef]

2008 (2)

H. M. Quiney, G. J. Williams, and K. A. Nugent, "Non-iterative solution of the phase retrieval problem using a single diffraction measurement," Opt. Express 16, 6896-6903 (2008).
[CrossRef] [PubMed]

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

2007 (4)

N. S. Ginsberg, S. R. Garner, and L. V. Hau "Coherent control of optical information with matter wave dynamics," Nature 400, 623-626 (2007).
[CrossRef]

B. J. Claessens, M. P. Reijnders, G. Taban, O. J. Luiten, and E. J. D. Vredenbregt, "Cold electron and ion beams generated from trapped atoms," Phys. Plas. 14, 093101 (2007).
[CrossRef]

O. J. Luiten, B. J. Claessens, S. B. Van der Geer, M. P. Reijnders, G. Taban, and E. J. D. Vredenbregt, "Ultracold electron sources," Int. J. Mod. Phys. A 22, 3882-3897 (2007).
[CrossRef]

K. Kowalski, K. Vaseva, S. Gateva, M. Glodz, L. Petrov, and J. Szonert, "Laser system for EIT spectroscopy of cold Rb atoms," Proc. SPIE. 6604, 66040 (2007).
[CrossRef]

2006 (2)

L. P. Maguire, R. M.W. van Bijnen, E. Mese, and R. E. Scholten, "Theoretical calculation of saturated absorption spectra for multi-level atoms," J. Phys. B: At. Mol. Opt. Phys. 39, 2709-2720 (2006).
[CrossRef]

L. P. Maguire, R. M. W. van Bijnen, E. Mese, and R. Scholten "Theoretical calculation of saturated absorption spectra for multi-level atoms," J. Phys. B. 39, 2709-2720 (2006).
[CrossRef]

2005 (1)

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, "Diffraction-contrast imaging of cold atoms," Phys. Rev. A 72, 031403 (2005).
[CrossRef]

2004 (2)

L. D. Turner, K. P. Weber, D. Paganin, and R. E. Scholten, " Off-resonant defocus contrast imaging of cold atoms," Opt. Lett. 29, 232-234 (2004).
[CrossRef] [PubMed]

J. Wang, L. B. Kong, X. H. Tu, K. J. Jiang, K. Li, H. W. Xiong, Y. Zhu, and M. S. Zhan, "Electromagnetically induced transparency in multi-level cascade scheme of cold rubidium atoms," Phys. Rev. A 328, 437-443 (2004).

2003 (1)

K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, "Unique phase recovery for non-periodic objects" Phys. Rev. Lett. 91, 203902 (2003).
[CrossRef] [PubMed]

2002 (2)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, " Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object," J. Microsc. 206, 33-40 (2002).
[CrossRef]

L. D. Turner, K. P. Weber, C. J. Hawthorn, and R. E. Scholten, "Frequency noise characterisation of narrow linewidth diode lasers," Opt. Commun. 201, 391-397 (2002).
[CrossRef]

2001 (1)

C. J. Hawthorn, K. P. Weber, and R. E. Scholten, "Littrow configuration tunable external cavity diode laser with fixed direction output beam," Rev. Sci. Inst. 72, 4477 (2001).
[CrossRef]

2000 (2)

J. B. Tiller, A. Barty, D. Paganin, and K. A. Nugent, "The holograhic twin image problem: a deterministic phase solution," Opt. Commun. 183, 7-14 (2000).
[CrossRef]

M. D. Lukin and A. Imamuglu "Nonlinear optics and quantum entanglement of ultra slow single photons," Phys. Rev. Lett. 84(7), 1419-1422 (2000).
[CrossRef]

1998 (3)

H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro "Observation of transient electromagnetically induced transparency in a rubidium Λ system," Phys. Rev. A 58, 1545-1548 (1998).
[CrossRef]

D. Paganin and K. A. Nugent, "Noninterferometic phase imaging with partially coherent light," Phys. Rev. Lett. 80(12), 2586-2589 (1998).
[CrossRef]

A. C. Wilson, J. C. Sharpe, C. R. McKenzie, P. J. Manson, and D. M Warrington, "Narrow-linewidth masteroscillator power amplifier based on a semiconductor tapered amplifier," Appl. Opt. 37, 4871-4875 (1998).
[CrossRef]

1997 (1)

T. E. Gureyev and K. A. Nugent, "Rapid quantitative phase imaging using the transport of intensity equation," Opt. Commun. 133, 339-346 (1997).
[CrossRef]

1995 (3)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wiemann, and E. A. Cornell "Observation of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198-201 (1995).
[CrossRef] [PubMed]

C. Wieman, G. Flowers, and S. Gilbert, "Inexpensive laser cooling and trapping experiment for undergraduate laboratories," Am. J. Phys. 63, 317-329 (1995).
[CrossRef]

T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould "Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 State," Phys. Script. 52, 271-276 (1995).
[CrossRef]

1983 (1)

1982 (1)

1976 (1)

R. M. Whitley and C. R. StroudJr., "Double optical resonance," Phys. Rev. A 141498-1513 (1976).
[CrossRef]

Anderson, M. H.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wiemann, and E. A. Cornell "Observation of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198-201 (1995).
[CrossRef] [PubMed]

Anderson, R.

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

Barty, A.

J. B. Tiller, A. Barty, D. Paganin, and K. A. Nugent, "The holograhic twin image problem: a deterministic phase solution," Opt. Commun. 183, 7-14 (2000).
[CrossRef]

Bell, S. C.

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

Browaeys, A.

A. Gaetan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, "Observation of collective excitation of two individual atoms in the Rydberg blockade regime," Nat. Phys. 5,115-118 (2009).
[CrossRef]

Chapman, H. N.

K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, "Unique phase recovery for non-periodic objects" Phys. Rev. Lett. 91, 203902 (2003).
[CrossRef] [PubMed]

Chen, H. X.

H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro "Observation of transient electromagnetically induced transparency in a rubidium Λ system," Phys. Rev. A 58, 1545-1548 (1998).
[CrossRef]

Chotia, A.

A. Gaetan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, "Observation of collective excitation of two individual atoms in the Rydberg blockade regime," Nat. Phys. 5,115-118 (2009).
[CrossRef]

Claessens, B. J.

B. J. Claessens, M. P. Reijnders, G. Taban, O. J. Luiten, and E. J. D. Vredenbregt, "Cold electron and ion beams generated from trapped atoms," Phys. Plas. 14, 093101 (2007).
[CrossRef]

O. J. Luiten, B. J. Claessens, S. B. Van der Geer, M. P. Reijnders, G. Taban, and E. J. D. Vredenbregt, "Ultracold electron sources," Int. J. Mod. Phys. A 22, 3882-3897 (2007).
[CrossRef]

Comparat, D.

A. Gaetan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, "Observation of collective excitation of two individual atoms in the Rydberg blockade regime," Nat. Phys. 5,115-118 (2009).
[CrossRef]

Cornell, E. A.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wiemann, and E. A. Cornell "Observation of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198-201 (1995).
[CrossRef] [PubMed]

Dennis, M. R.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, "Singular Optics: Optical vortices and polarization singularities," Prog. Opt. 53, 293-363 (2009)
[CrossRef]

Domen, K. F. E. M.

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, "Diffraction-contrast imaging of cold atoms," Phys. Rev. A 72, 031403 (2005).
[CrossRef]

Duncan, B. C.

T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould "Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 State," Phys. Script. 52, 271-276 (1995).
[CrossRef]

Durrant, A. V.

H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro "Observation of transient electromagnetically induced transparency in a rubidium Λ system," Phys. Rev. A 58, 1545-1548 (1998).
[CrossRef]

Ensher, J. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wiemann, and E. A. Cornell "Observation of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198-201 (1995).
[CrossRef] [PubMed]

Fienup, J. R.

Flowers, G.

C. Wieman, G. Flowers, and S. Gilbert, "Inexpensive laser cooling and trapping experiment for undergraduate laboratories," Am. J. Phys. 63, 317-329 (1995).
[CrossRef]

Gaetan, A.

A. Gaetan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, "Observation of collective excitation of two individual atoms in the Rydberg blockade regime," Nat. Phys. 5,115-118 (2009).
[CrossRef]

Garner, S. R.

N. S. Ginsberg, S. R. Garner, and L. V. Hau "Coherent control of optical information with matter wave dynamics," Nature 400, 623-626 (2007).
[CrossRef]

Gateva, S.

K. Kowalski, K. Vaseva, S. Gateva, M. Glodz, L. Petrov, and J. Szonert, "Laser system for EIT spectroscopy of cold Rb atoms," Proc. SPIE. 6604, 66040 (2007).
[CrossRef]

Gilbert, S.

C. Wieman, G. Flowers, and S. Gilbert, "Inexpensive laser cooling and trapping experiment for undergraduate laboratories," Am. J. Phys. 63, 317-329 (1995).
[CrossRef]

Ginsberg, N. S.

N. S. Ginsberg, S. R. Garner, and L. V. Hau "Coherent control of optical information with matter wave dynamics," Nature 400, 623-626 (2007).
[CrossRef]

Glodz, M.

K. Kowalski, K. Vaseva, S. Gateva, M. Glodz, L. Petrov, and J. Szonert, "Laser system for EIT spectroscopy of cold Rb atoms," Proc. SPIE. 6604, 66040 (2007).
[CrossRef]

Gould, P. L.

T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould "Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 State," Phys. Script. 52, 271-276 (1995).
[CrossRef]

Grangier, P.

A. Gaetan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, "Observation of collective excitation of two individual atoms in the Rydberg blockade regime," Nat. Phys. 5,115-118 (2009).
[CrossRef]

Grove, T. T.

T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould "Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 State," Phys. Script. 52, 271-276 (1995).
[CrossRef]

Gureyev, T. E.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, " Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object," J. Microsc. 206, 33-40 (2002).
[CrossRef]

T. E. Gureyev and K. A. Nugent, "Rapid quantitative phase imaging using the transport of intensity equation," Opt. Commun. 133, 339-346 (1997).
[CrossRef]

Hau, L. V.

N. S. Ginsberg, S. R. Garner, and L. V. Hau "Coherent control of optical information with matter wave dynamics," Nature 400, 623-626 (2007).
[CrossRef]

Hawthorn, C. J.

L. D. Turner, K. P. Weber, C. J. Hawthorn, and R. E. Scholten, "Frequency noise characterisation of narrow linewidth diode lasers," Opt. Commun. 201, 391-397 (2002).
[CrossRef]

C. J. Hawthorn, K. P. Weber, and R. E. Scholten, "Littrow configuration tunable external cavity diode laser with fixed direction output beam," Rev. Sci. Inst. 72, 4477 (2001).
[CrossRef]

Henage, T.

E. Urban, A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, "Observation of Rydberg blockade between two atoms," Nat. Phys. 5, 110-114 (2009).
[CrossRef]

Hofmann, C. S.

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

Imamuglu, A.

M. D. Lukin and A. Imamuglu "Nonlinear optics and quantum entanglement of ultra slow single photons," Phys. Rev. Lett. 84(7), 1419-1422 (2000).
[CrossRef]

Isenhower, L.

E. Urban, A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, "Observation of Rydberg blockade between two atoms," Nat. Phys. 5, 110-114 (2009).
[CrossRef]

Jiang, K. J.

J. Wang, L. B. Kong, X. H. Tu, K. J. Jiang, K. Li, H. W. Xiong, Y. Zhu, and M. S. Zhan, "Electromagnetically induced transparency in multi-level cascade scheme of cold rubidium atoms," Phys. Rev. A 328, 437-443 (2004).

Johnson, A.

E. Urban, A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, "Observation of Rydberg blockade between two atoms," Nat. Phys. 5, 110-114 (2009).
[CrossRef]

Kong, L. B.

J. Wang, L. B. Kong, X. H. Tu, K. J. Jiang, K. Li, H. W. Xiong, Y. Zhu, and M. S. Zhan, "Electromagnetically induced transparency in multi-level cascade scheme of cold rubidium atoms," Phys. Rev. A 328, 437-443 (2004).

Kowalski, K.

K. Kowalski, K. Vaseva, S. Gateva, M. Glodz, L. Petrov, and J. Szonert, "Laser system for EIT spectroscopy of cold Rb atoms," Proc. SPIE. 6604, 66040 (2007).
[CrossRef]

Li, K.

J. Wang, L. B. Kong, X. H. Tu, K. J. Jiang, K. Li, H. W. Xiong, Y. Zhu, and M. S. Zhan, "Electromagnetically induced transparency in multi-level cascade scheme of cold rubidium atoms," Phys. Rev. A 328, 437-443 (2004).

Luiten, O. J.

O. J. Luiten, B. J. Claessens, S. B. Van der Geer, M. P. Reijnders, G. Taban, and E. J. D. Vredenbregt, "Ultracold electron sources," Int. J. Mod. Phys. A 22, 3882-3897 (2007).
[CrossRef]

B. J. Claessens, M. P. Reijnders, G. Taban, O. J. Luiten, and E. J. D. Vredenbregt, "Cold electron and ion beams generated from trapped atoms," Phys. Plas. 14, 093101 (2007).
[CrossRef]

Lukin, M. D.

M. D. Lukin and A. Imamuglu "Nonlinear optics and quantum entanglement of ultra slow single photons," Phys. Rev. Lett. 84(7), 1419-1422 (2000).
[CrossRef]

Maguire, L. P.

L. P. Maguire, R. M. W. van Bijnen, E. Mese, and R. Scholten "Theoretical calculation of saturated absorption spectra for multi-level atoms," J. Phys. B. 39, 2709-2720 (2006).
[CrossRef]

L. P. Maguire, R. M.W. van Bijnen, E. Mese, and R. E. Scholten, "Theoretical calculation of saturated absorption spectra for multi-level atoms," J. Phys. B: At. Mol. Opt. Phys. 39, 2709-2720 (2006).
[CrossRef]

Maleki, S.

T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould "Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 State," Phys. Script. 52, 271-276 (1995).
[CrossRef]

Mancuso, A. P.

K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, "Unique phase recovery for non-periodic objects" Phys. Rev. Lett. 91, 203902 (2003).
[CrossRef] [PubMed]

Manson, P. J.

Marangos, J. P.

H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro "Observation of transient electromagnetically induced transparency in a rubidium Λ system," Phys. Rev. A 58, 1545-1548 (1998).
[CrossRef]

Matthews, M. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wiemann, and E. A. Cornell "Observation of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198-201 (1995).
[CrossRef] [PubMed]

Mayo, S. C.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, " Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object," J. Microsc. 206, 33-40 (2002).
[CrossRef]

McKenzie, C. R.

Mese, E.

L. P. Maguire, R. M. W. van Bijnen, E. Mese, and R. Scholten "Theoretical calculation of saturated absorption spectra for multi-level atoms," J. Phys. B. 39, 2709-2720 (2006).
[CrossRef]

L. P. Maguire, R. M.W. van Bijnen, E. Mese, and R. E. Scholten, "Theoretical calculation of saturated absorption spectra for multi-level atoms," J. Phys. B: At. Mol. Opt. Phys. 39, 2709-2720 (2006).
[CrossRef]

Miller, P. R.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, " Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object," J. Microsc. 206, 33-40 (2002).
[CrossRef]

Miroshnychenko, Y.

A. Gaetan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, "Observation of collective excitation of two individual atoms in the Rydberg blockade regime," Nat. Phys. 5,115-118 (2009).
[CrossRef]

Nugent, K. A.

H. M. Quiney, G. J. Williams, and K. A. Nugent, "Non-iterative solution of the phase retrieval problem using a single diffraction measurement," Opt. Express 16, 6896-6903 (2008).
[CrossRef] [PubMed]

K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, "Unique phase recovery for non-periodic objects" Phys. Rev. Lett. 91, 203902 (2003).
[CrossRef] [PubMed]

J. B. Tiller, A. Barty, D. Paganin, and K. A. Nugent, "The holograhic twin image problem: a deterministic phase solution," Opt. Commun. 183, 7-14 (2000).
[CrossRef]

D. Paganin and K. A. Nugent, "Noninterferometic phase imaging with partially coherent light," Phys. Rev. Lett. 80(12), 2586-2589 (1998).
[CrossRef]

T. E. Gureyev and K. A. Nugent, "Rapid quantitative phase imaging using the transport of intensity equation," Opt. Commun. 133, 339-346 (1997).
[CrossRef]

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, "Singular Optics: Optical vortices and polarization singularities," Prog. Opt. 53, 293-363 (2009)
[CrossRef]

Padgett, M. J.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, "Singular Optics: Optical vortices and polarization singularities," Prog. Opt. 53, 293-363 (2009)
[CrossRef]

Paganin, D.

L. D. Turner, K. P. Weber, D. Paganin, and R. E. Scholten, " Off-resonant defocus contrast imaging of cold atoms," Opt. Lett. 29, 232-234 (2004).
[CrossRef] [PubMed]

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, " Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object," J. Microsc. 206, 33-40 (2002).
[CrossRef]

J. B. Tiller, A. Barty, D. Paganin, and K. A. Nugent, "The holograhic twin image problem: a deterministic phase solution," Opt. Commun. 183, 7-14 (2000).
[CrossRef]

D. Paganin and K. A. Nugent, "Noninterferometic phase imaging with partially coherent light," Phys. Rev. Lett. 80(12), 2586-2589 (1998).
[CrossRef]

Peele, A. G.

K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, "Unique phase recovery for non-periodic objects" Phys. Rev. Lett. 91, 203902 (2003).
[CrossRef] [PubMed]

Petrov, L.

K. Kowalski, K. Vaseva, S. Gateva, M. Glodz, L. Petrov, and J. Szonert, "Laser system for EIT spectroscopy of cold Rb atoms," Proc. SPIE. 6604, 66040 (2007).
[CrossRef]

Pillet, P.

A. Gaetan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, "Observation of collective excitation of two individual atoms in the Rydberg blockade regime," Nat. Phys. 5,115-118 (2009).
[CrossRef]

Quiney, H. M.

Reijnders, M. P.

B. J. Claessens, M. P. Reijnders, G. Taban, O. J. Luiten, and E. J. D. Vredenbregt, "Cold electron and ion beams generated from trapped atoms," Phys. Plas. 14, 093101 (2007).
[CrossRef]

O. J. Luiten, B. J. Claessens, S. B. Van der Geer, M. P. Reijnders, G. Taban, and E. J. D. Vredenbregt, "Ultracold electron sources," Int. J. Mod. Phys. A 22, 3882-3897 (2007).
[CrossRef]

Saffman, M.

E. Urban, A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, "Observation of Rydberg blockade between two atoms," Nat. Phys. 5, 110-114 (2009).
[CrossRef]

Sanchez-Villicana, V.

T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould "Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 State," Phys. Script. 52, 271-276 (1995).
[CrossRef]

Scholten, R.

L. P. Maguire, R. M. W. van Bijnen, E. Mese, and R. Scholten "Theoretical calculation of saturated absorption spectra for multi-level atoms," J. Phys. B. 39, 2709-2720 (2006).
[CrossRef]

Scholten, R. E.

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

L. P. Maguire, R. M.W. van Bijnen, E. Mese, and R. E. Scholten, "Theoretical calculation of saturated absorption spectra for multi-level atoms," J. Phys. B: At. Mol. Opt. Phys. 39, 2709-2720 (2006).
[CrossRef]

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, "Diffraction-contrast imaging of cold atoms," Phys. Rev. A 72, 031403 (2005).
[CrossRef]

L. D. Turner, K. P. Weber, D. Paganin, and R. E. Scholten, " Off-resonant defocus contrast imaging of cold atoms," Opt. Lett. 29, 232-234 (2004).
[CrossRef] [PubMed]

L. D. Turner, K. P. Weber, C. J. Hawthorn, and R. E. Scholten, "Frequency noise characterisation of narrow linewidth diode lasers," Opt. Commun. 201, 391-397 (2002).
[CrossRef]

C. J. Hawthorn, K. P. Weber, and R. E. Scholten, "Littrow configuration tunable external cavity diode laser with fixed direction output beam," Rev. Sci. Inst. 72, 4477 (2001).
[CrossRef]

Sharpe, J. C.

Sheludko, D. V.

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

Stroud, C. R.

R. M. Whitley and C. R. StroudJr., "Double optical resonance," Phys. Rev. A 141498-1513 (1976).
[CrossRef]

Szonert, J.

K. Kowalski, K. Vaseva, S. Gateva, M. Glodz, L. Petrov, and J. Szonert, "Laser system for EIT spectroscopy of cold Rb atoms," Proc. SPIE. 6604, 66040 (2007).
[CrossRef]

Taban, G.

O. J. Luiten, B. J. Claessens, S. B. Van der Geer, M. P. Reijnders, G. Taban, and E. J. D. Vredenbregt, "Ultracold electron sources," Int. J. Mod. Phys. A 22, 3882-3897 (2007).
[CrossRef]

B. J. Claessens, M. P. Reijnders, G. Taban, O. J. Luiten, and E. J. D. Vredenbregt, "Cold electron and ion beams generated from trapped atoms," Phys. Plas. 14, 093101 (2007).
[CrossRef]

Teague, M. R.

Tiller, J. B.

J. B. Tiller, A. Barty, D. Paganin, and K. A. Nugent, "The holograhic twin image problem: a deterministic phase solution," Opt. Commun. 183, 7-14 (2000).
[CrossRef]

Tu, X. H.

J. Wang, L. B. Kong, X. H. Tu, K. J. Jiang, K. Li, H. W. Xiong, Y. Zhu, and M. S. Zhan, "Electromagnetically induced transparency in multi-level cascade scheme of cold rubidium atoms," Phys. Rev. A 328, 437-443 (2004).

Turner, L. D.

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, "Diffraction-contrast imaging of cold atoms," Phys. Rev. A 72, 031403 (2005).
[CrossRef]

L. D. Turner, K. P. Weber, D. Paganin, and R. E. Scholten, " Off-resonant defocus contrast imaging of cold atoms," Opt. Lett. 29, 232-234 (2004).
[CrossRef] [PubMed]

L. D. Turner, K. P. Weber, C. J. Hawthorn, and R. E. Scholten, "Frequency noise characterisation of narrow linewidth diode lasers," Opt. Commun. 201, 391-397 (2002).
[CrossRef]

Urban, E.

E. Urban, A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, "Observation of Rydberg blockade between two atoms," Nat. Phys. 5, 110-114 (2009).
[CrossRef]

Vaccaro, J. A.

H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro "Observation of transient electromagnetically induced transparency in a rubidium Λ system," Phys. Rev. A 58, 1545-1548 (1998).
[CrossRef]

van Bijnen, R. M. W.

L. P. Maguire, R. M. W. van Bijnen, E. Mese, and R. Scholten "Theoretical calculation of saturated absorption spectra for multi-level atoms," J. Phys. B. 39, 2709-2720 (2006).
[CrossRef]

van Bijnen, R. M.W.

L. P. Maguire, R. M.W. van Bijnen, E. Mese, and R. E. Scholten, "Theoretical calculation of saturated absorption spectra for multi-level atoms," J. Phys. B: At. Mol. Opt. Phys. 39, 2709-2720 (2006).
[CrossRef]

Van der Geer, S. B.

O. J. Luiten, B. J. Claessens, S. B. Van der Geer, M. P. Reijnders, G. Taban, and E. J. D. Vredenbregt, "Ultracold electron sources," Int. J. Mod. Phys. A 22, 3882-3897 (2007).
[CrossRef]

Vaseva, K.

K. Kowalski, K. Vaseva, S. Gateva, M. Glodz, L. Petrov, and J. Szonert, "Laser system for EIT spectroscopy of cold Rb atoms," Proc. SPIE. 6604, 66040 (2007).
[CrossRef]

Viteau, M.

A. Gaetan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, "Observation of collective excitation of two individual atoms in the Rydberg blockade regime," Nat. Phys. 5,115-118 (2009).
[CrossRef]

Vredenbregt, E. J. D.

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

O. J. Luiten, B. J. Claessens, S. B. Van der Geer, M. P. Reijnders, G. Taban, and E. J. D. Vredenbregt, "Ultracold electron sources," Int. J. Mod. Phys. A 22, 3882-3897 (2007).
[CrossRef]

B. J. Claessens, M. P. Reijnders, G. Taban, O. J. Luiten, and E. J. D. Vredenbregt, "Cold electron and ion beams generated from trapped atoms," Phys. Plas. 14, 093101 (2007).
[CrossRef]

Walker, T. G.

E. Urban, A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, "Observation of Rydberg blockade between two atoms," Nat. Phys. 5, 110-114 (2009).
[CrossRef]

Wang, J.

J. Wang, L. B. Kong, X. H. Tu, K. J. Jiang, K. Li, H. W. Xiong, Y. Zhu, and M. S. Zhan, "Electromagnetically induced transparency in multi-level cascade scheme of cold rubidium atoms," Phys. Rev. A 328, 437-443 (2004).

Warrington, D. M

Weber, K. P.

L. D. Turner, K. P. Weber, D. Paganin, and R. E. Scholten, " Off-resonant defocus contrast imaging of cold atoms," Opt. Lett. 29, 232-234 (2004).
[CrossRef] [PubMed]

L. D. Turner, K. P. Weber, C. J. Hawthorn, and R. E. Scholten, "Frequency noise characterisation of narrow linewidth diode lasers," Opt. Commun. 201, 391-397 (2002).
[CrossRef]

C. J. Hawthorn, K. P. Weber, and R. E. Scholten, "Littrow configuration tunable external cavity diode laser with fixed direction output beam," Rev. Sci. Inst. 72, 4477 (2001).
[CrossRef]

Whitley, R. M.

R. M. Whitley and C. R. StroudJr., "Double optical resonance," Phys. Rev. A 141498-1513 (1976).
[CrossRef]

Wieman, C.

C. Wieman, G. Flowers, and S. Gilbert, "Inexpensive laser cooling and trapping experiment for undergraduate laboratories," Am. J. Phys. 63, 317-329 (1995).
[CrossRef]

Wiemann, C. E.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wiemann, and E. A. Cornell "Observation of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198-201 (1995).
[CrossRef] [PubMed]

Wilk, T.

A. Gaetan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, "Observation of collective excitation of two individual atoms in the Rydberg blockade regime," Nat. Phys. 5,115-118 (2009).
[CrossRef]

Wilkins, S. W.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, " Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object," J. Microsc. 206, 33-40 (2002).
[CrossRef]

Williams, G. J.

Wilson, A. C.

Xiong, H. W.

J. Wang, L. B. Kong, X. H. Tu, K. J. Jiang, K. Li, H. W. Xiong, Y. Zhu, and M. S. Zhan, "Electromagnetically induced transparency in multi-level cascade scheme of cold rubidium atoms," Phys. Rev. A 328, 437-443 (2004).

Yavuz, D. D.

E. Urban, A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, "Observation of Rydberg blockade between two atoms," Nat. Phys. 5, 110-114 (2009).
[CrossRef]

Zhan, M. S.

J. Wang, L. B. Kong, X. H. Tu, K. J. Jiang, K. Li, H. W. Xiong, Y. Zhu, and M. S. Zhan, "Electromagnetically induced transparency in multi-level cascade scheme of cold rubidium atoms," Phys. Rev. A 328, 437-443 (2004).

Zhu, Y.

J. Wang, L. B. Kong, X. H. Tu, K. J. Jiang, K. Li, H. W. Xiong, Y. Zhu, and M. S. Zhan, "Electromagnetically induced transparency in multi-level cascade scheme of cold rubidium atoms," Phys. Rev. A 328, 437-443 (2004).

Am. J. Phys. (1)

C. Wieman, G. Flowers, and S. Gilbert, "Inexpensive laser cooling and trapping experiment for undergraduate laboratories," Am. J. Phys. 63, 317-329 (1995).
[CrossRef]

Appl. Opt. (2)

Int. J. Mod. Phys. A (1)

O. J. Luiten, B. J. Claessens, S. B. Van der Geer, M. P. Reijnders, G. Taban, and E. J. D. Vredenbregt, "Ultracold electron sources," Int. J. Mod. Phys. A 22, 3882-3897 (2007).
[CrossRef]

J. Microsc. (1)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, " Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object," J. Microsc. 206, 33-40 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. B. (1)

L. P. Maguire, R. M. W. van Bijnen, E. Mese, and R. Scholten "Theoretical calculation of saturated absorption spectra for multi-level atoms," J. Phys. B. 39, 2709-2720 (2006).
[CrossRef]

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

L. P. Maguire, R. M.W. van Bijnen, E. Mese, and R. E. Scholten, "Theoretical calculation of saturated absorption spectra for multi-level atoms," J. Phys. B: At. Mol. Opt. Phys. 39, 2709-2720 (2006).
[CrossRef]

Nat. Phys. (2)

A. Gaetan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, "Observation of collective excitation of two individual atoms in the Rydberg blockade regime," Nat. Phys. 5,115-118 (2009).
[CrossRef]

E. Urban, A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, "Observation of Rydberg blockade between two atoms," Nat. Phys. 5, 110-114 (2009).
[CrossRef]

Nature (1)

N. S. Ginsberg, S. R. Garner, and L. V. Hau "Coherent control of optical information with matter wave dynamics," Nature 400, 623-626 (2007).
[CrossRef]

Opt. Commun. (3)

T. E. Gureyev and K. A. Nugent, "Rapid quantitative phase imaging using the transport of intensity equation," Opt. Commun. 133, 339-346 (1997).
[CrossRef]

J. B. Tiller, A. Barty, D. Paganin, and K. A. Nugent, "The holograhic twin image problem: a deterministic phase solution," Opt. Commun. 183, 7-14 (2000).
[CrossRef]

L. D. Turner, K. P. Weber, C. J. Hawthorn, and R. E. Scholten, "Frequency noise characterisation of narrow linewidth diode lasers," Opt. Commun. 201, 391-397 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Plas. (1)

B. J. Claessens, M. P. Reijnders, G. Taban, O. J. Luiten, and E. J. D. Vredenbregt, "Cold electron and ion beams generated from trapped atoms," Phys. Plas. 14, 093101 (2007).
[CrossRef]

Phys. Rev. A (5)

H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro "Observation of transient electromagnetically induced transparency in a rubidium Λ system," Phys. Rev. A 58, 1545-1548 (1998).
[CrossRef]

L. D. Turner, K. F. E. M. Domen, and R. E. Scholten, "Diffraction-contrast imaging of cold atoms," Phys. Rev. A 72, 031403 (2005).
[CrossRef]

D. V. Sheludko, S. C. Bell, R. Anderson, C. S. Hofmann, E. J. D. Vredenbregt, and R. E. Scholten, "State-selective imaging of cold atoms," Phys. Rev. A 77, 033401 (2008).
[CrossRef]

J. Wang, L. B. Kong, X. H. Tu, K. J. Jiang, K. Li, H. W. Xiong, Y. Zhu, and M. S. Zhan, "Electromagnetically induced transparency in multi-level cascade scheme of cold rubidium atoms," Phys. Rev. A 328, 437-443 (2004).

R. M. Whitley and C. R. StroudJr., "Double optical resonance," Phys. Rev. A 141498-1513 (1976).
[CrossRef]

Phys. Rev. Lett. (3)

D. Paganin and K. A. Nugent, "Noninterferometic phase imaging with partially coherent light," Phys. Rev. Lett. 80(12), 2586-2589 (1998).
[CrossRef]

K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, "Unique phase recovery for non-periodic objects" Phys. Rev. Lett. 91, 203902 (2003).
[CrossRef] [PubMed]

M. D. Lukin and A. Imamuglu "Nonlinear optics and quantum entanglement of ultra slow single photons," Phys. Rev. Lett. 84(7), 1419-1422 (2000).
[CrossRef]

Phys. Script. (1)

T. T. Grove, V. Sanchez-Villicana, B. C. Duncan, S. Maleki, and P. L. Gould "Two-photon two-color diode laser spectroscopy of the Rb 5D5/2 State," Phys. Script. 52, 271-276 (1995).
[CrossRef]

Proc. SPIE. (1)

K. Kowalski, K. Vaseva, S. Gateva, M. Glodz, L. Petrov, and J. Szonert, "Laser system for EIT spectroscopy of cold Rb atoms," Proc. SPIE. 6604, 66040 (2007).
[CrossRef]

Prog. Opt. (1)

M. R. Dennis, K. O’Holleran, and M. J. Padgett, "Singular Optics: Optical vortices and polarization singularities," Prog. Opt. 53, 293-363 (2009)
[CrossRef]

Rev. Sci. Inst. (1)

C. J. Hawthorn, K. P. Weber, and R. E. Scholten, "Littrow configuration tunable external cavity diode laser with fixed direction output beam," Rev. Sci. Inst. 72, 4477 (2001).
[CrossRef]

Science (1)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wiemann, and E. A. Cornell "Observation of Bose-Einstein condensation in a dilute atomic vapor," Science 269, 198-201 (1995).
[CrossRef] [PubMed]

Other (6)

MOGlabs laser diode controller, www.moglabs.com.

D. A. Steck, "Rubidium 85 D line Data," Los Alamos National Laboratory, available online at http://steck.us/alkalidata (2008).

A. Tikhonov and V. Arsenin, Solutions of Ill-posed Problems (V. H. Winston and Sons, New York, 1977).

D. Paganin, Coherent X-Ray Optics (Oxford University Press, Oxford UK, 2006).
[CrossRef]

R. N. Bracewell, The Fourier Transform and its Applications 3rd Ed. (McGraw-Hill, USA, 2000).

H. J. Metcalf and P. van der Straten, "Laser cooling and trapping," Springer-Verlag, Berlin. (1999).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Conceptual arrangement for Single-plane Curved-beam Phase Imaging. A phase curved Gaussian beam is incident on the atom cloud at plane z 1, diffracts and propagates a distance Z to a CCD detector at plane z 2.

Fig. 2.
Fig. 2.

Simulation of diffraction from an atom cloud when illuminated by a near-resonant (detuned +1.5 natural line widths from resonance) curved Gaussian beam, and reconstruction of the column density. (a) input column density (1013 atoms/cm2), (b) simulated normalized diffraction intensity, (c) approximate intensity derivative (see Eq. (8)), (d) reconstructed atomic column density (1013 atoms/cm2). (e) Horizontal line profiles of column density through the point of maximum density in (a), for the input, raw output and worst-case corrected output column densities, as outlined in section 3. Green lines indicate retrieved imaginary part of refractive index (solid) and simulation input (dashed) for inhomogeneous simulations (Sec. 3.3). The refractive index outside the cloud has been removed for clarity.

Fig. 3.
Fig. 3.

2-D and 3-D schematics of the imaging and pump beam paths, and MOT vacuum chamber (not to scale). Waveplates have been omitted for clarity, as have coils in 3D. The pump beam was blocked for homogeneous imaging (section 4.1) and unblocked to create the inhomogeneous atom cloud (section 5.2). BS: Beam splitter; PD: Photodiode.

Fig. 4.
Fig. 4.

Experimental results for Single-plane Curved-beam Phase Imaging. (a) Raw experimental diffraction pattern; (b) after noise subtraction; (c) reconstructed column density cropped to region inside intensity threshold, retrieved from diffraction pattern in (b), and (d) plot of column density through dashed line in (c). The blue line in (d) indicates the column density retrieved from a conventional in-focus, on-resonance absorption image taken on the same day. The diffraction pattern was recorded at a defocus distance of Z = 20 mm, a probe beam detuning of ∆ = 1.5Γ and imaging probe pulse duration of 13 μs. A correction factor of η = 1.3 was used to obtain the density map (see Sec. 3). The circular discontinuity in the column density arises from the threshold function (Eq. (9)).

Fig. 5.
Fig. 5.

Imaging of an inhomogeneous atom cloud and extraction of the complex refractive index. Orange arrows indicate the propagation direction of the EIT pump laser beam. (a) Inhomogeneous diffraction data. The intensity of the unperturbed Gaussian has been subtracted for clarity. (b) Diffraction data from a homogeneous (pump beam off) cloud, unperturbed beam subtracted. (c) Column density reconstructed from (b). (d) Retrieved absorption coefficient, β, calculated using Eq. (5). (e) Retrieved phase coefficient, α. (f) Experimental line profile (black) through dashed line in (d), with theoretical absorption curve shown in red. (g) Phase line profile, with theoretical curve, as in (f). Images were taken at Z = 20 mm defocus distance, ∆ = 2Γ from the F = 3 → F′ = 3 transition. Theoretical lines were calculated using the exact version of Eq. (12), with parameters (Ω1, Ω2, ∆1, ∆2 and slit width) fitted to the data, within their respective experimental error margins. The data was convolved with a Gaussian of FWHM 186 μm prior to reconstruction.

Equations (14)

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

ρ ( r ) = 0 N ( r , z ) d z
ψ ( r , z 1 ) = ψ 0 ( r , z 1 ) T ( r ) .
T ( r ) = exp [ ik { α ( r ) + ( r ) } ρ ( r ) ]
ρ ( r ) = 1 k { ln ( T ( r ) ) 2 α 2 ( r ) + β 2 ( r ) } 1 2 .
α ( r ) + ( r ) = 1 ikρ ( r ) ln ( ψ ( r , z 1 ) ψ 0 ( r , z 1 ) ) .
· I ( r , z ) Φ ( r , z ) = k I ( r , z ) z .
H [ I 0 ] I 0 z = ζ Z w 2 g 0 ( w ) exp ( 2 π i w · r λ Z ) d w
I 0 z H [ I ] .
I ( r 2 , z 2 ) = { I ( r 2 , z 2 ) I ( r 2 , z 2 ) ε I ( r 2 , z 2 ) + ε I ( r 2 , z 2 ) < ε
Ψ ( r 2 , z 2 ) = i λ Z rad exp ( 2 π i Z rad λ ) exp ( i π r 2 2 λ Z rad ) { Ψ ( r 1 , z 1 ) exp ( i π r 1 2 λ Z rad ) } .
ρ corrected = η ρ raw .
ρ 12 Ω 1 2 i π ( Γ 2 + 2 i ( Δ 1 + Δ 2 ) ) 4 π 2 ( Γ 1 + 2 i Δ 1 ) ( Γ 2 + 2 i ( Δ 1 + Δ 2 ) ) + Ω 2 2 .
I 0 ( r 2 , z 2 ) = I 0 ( r 2 , z 2 ) N ( r 2 )
I ' ( r 2 , z 2 ) = I ( r 2 , z 2 ) N ( r 2 ) .

Metrics