Abstract

We report a new nonlinear optical process that occurs in a cloud of cold atoms at low-light-levels when the incident optical fields simultaneously polarize, cool, and spatially-organize the atoms. We observe an extremely large effective fifth-order nonlinear susceptibility of χ(5) = 7.6 × 10−15 (m/V)4, which results in efficient Bragg scattering via six-wave mixing, slow group velocities (∼ c/105), and enhanced atomic coherence times (> 100 μs). In addition, this process is particularly sensitive to the atomic temperatures, and provides a new tool for in-situ monitoring of the atomic momentum distribution in an optical lattice. For sufficiently large light-matter couplings, we observe an optical instability for intensities as low as ∼ 1 mW/cm2 in which new, intense beams of light are generated and result in the formation of controllable transverse optical patterns.

© 2011 OSA

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  1. P. Kolchin, R. F. Oulton, and X. Zhang, “Nonlinear quantum optics in a waveguide: Distinct single photons strongly interacting at the single atom level,” Phys. Rev. Lett. 106, 113601 (2011).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  14. A. M. C. Dawes, D. J. Gauthier, S. Schumacher, N. H. Kwong, R. Binder, and A. Smirl, “Transverse optical patterns for ultra-low-light-level-all-optical switching,” Laser Photon. Rev. 4, 221–243 (2010).
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    [CrossRef] [PubMed]
  22. M. Brzozowska, T. M. Brzozowski, J. Zachorowski, and W. Gawlik, “Nondestructive study of nonequilibrium states of cold trapped atoms,” Phys. Rev. A 72, 061401(R) (2005).
    [CrossRef]
  23. H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. A. Yu, and Y.-F. Chen, “Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A 83, 041804(R) (2011).
    [CrossRef]
  24. S. Jonsell, C. M. Dion, A. Kastberg, S. J. H. Petra, and P. Sjolun, “A non-adiabatic semi-classical method for Sisyphus cooling,” Eur. Phys. J. D. 39, 67–74 (2006).
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    [CrossRef]
  27. M. G. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. Lett. 83, 5202–5205 (1999).
    [CrossRef]

2011 (2)

P. Kolchin, R. F. Oulton, and X. Zhang, “Nonlinear quantum optics in a waveguide: Distinct single photons strongly interacting at the single atom level,” Phys. Rev. Lett. 106, 113601 (2011).
[CrossRef] [PubMed]

H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. A. Yu, and Y.-F. Chen, “Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A 83, 041804(R) (2011).
[CrossRef]

2010 (2)

A. M. C. Dawes, D. J. Gauthier, S. Schumacher, N. H. Kwong, R. Binder, and A. Smirl, “Transverse optical patterns for ultra-low-light-level-all-optical switching,” Laser Photon. Rev. 4, 221–243 (2010).
[CrossRef]

D. Felinto, D. Moretti, R. de Oliveira, and J. Tabosa, “Delayed four- and six-wave mixing in a coherently prepared atomic ensemble,” Opt. Lett. 35, 3937–3939 (2010).
[CrossRef] [PubMed]

2009 (1)

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

2008 (1)

2007 (2)

J. A. Greenberg, M. Oriá, A. M. C. Dawes, and D. J. Gauthier, “Absorption-induced trapping in an anisotropic magneto-optical trap,” Opt. Express 15, 17699–17708 (2007).
[CrossRef] [PubMed]

G. Fibich, N. Gavish, and X. P. Wang, “Singular ring solutions of critical and supercritical nonlinear Schrödinger equations,” Physica D 231, 55–86 (2007).
[CrossRef]

2006 (3)

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[CrossRef]

S. Jonsell, C. M. Dion, A. Kastberg, S. J. H. Petra, and P. Sjolun, “A non-adiabatic semi-classical method for Sisyphus cooling,” Eur. Phys. J. D. 39, 67–74 (2006).
[CrossRef]

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[CrossRef] [PubMed]

2005 (2)

M. Brzozowska, T. M. Brzozowski, J. Zachorowski, and W. Gawlik, “Nondestructive study of nonequilibrium states of cold trapped atoms,” Phys. Rev. A 72, 061401(R) (2005).
[CrossRef]

A. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Phys. Rev. A 308, 672–674 (2005).

2004 (1)

J. Jersblad, H. Ellmann, K. Stochkel, A. Kastberg, L. Sanchez-Palencia, and R. Kaiser, “Non-Gaussian velocity distributions in optical lattices,” Phys. Rev. A 69, 013410 (2004).
[CrossRef]

2002 (1)

M. S. Zubairy, A. B. Matsko, and M. O. Scully, “Resonant enhancement of high-order optical nonlinearities based on atomic coherence,” Phys. Rev. A 65, 043804 (2002).
[CrossRef]

2000 (1)

J. Jersblad, H. Ellmann, and A. Kastberg, “Experimental investigation of the limit of Sisyphus cooling,” Phys. Rev. A 62, 051401 (2000).
[CrossRef]

1999 (2)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

M. G. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. Lett. 83, 5202–5205 (1999).
[CrossRef]

1998 (1)

1995 (1)

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef] [PubMed]

1994 (1)

R. Bonifacio and L. De Salvo, “Collective atomic recoil laser (CARL) optical gain without inversion by collective atomic recoil and self-bunching of two-level atoms,” Nucl. Instrum. Methods Phys. 341, 360–362 (1994).
[CrossRef]

1991 (1)

Y. Castin and J. Dalibard, “Quantization of atomic motion in optical molasses,” Europhys. Lett. 14, 761–766 (1991).
[CrossRef]

1977 (1)

Anderson, B.

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Binder, R.

A. M. C. Dawes, D. J. Gauthier, S. Schumacher, N. H. Kwong, R. Binder, and A. Smirl, “Transverse optical patterns for ultra-low-light-level-all-optical switching,” Laser Photon. Rev. 4, 221–243 (2010).
[CrossRef]

Bonifacio, R.

R. Bonifacio and L. De Salvo, “Collective atomic recoil laser (CARL) optical gain without inversion by collective atomic recoil and self-bunching of two-level atoms,” Nucl. Instrum. Methods Phys. 341, 360–362 (1994).
[CrossRef]

Boyd, R. W.

R. W. Boyd, K. Dolgaleva, and H. Shin, “Strong, fifth-order, nonlinear optical response resulting from local-field-induced microscopic cascading in C60,” in Nonlinear Optics: Materials, Fundamentals and Applications (Optical Society of America, 2009), p. NWB2.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008), Chap. 3.

Brzozowska, M.

M. Brzozowska, T. M. Brzozowski, J. Zachorowski, and W. Gawlik, “Nondestructive study of nonequilibrium states of cold trapped atoms,” Phys. Rev. A 72, 061401(R) (2005).
[CrossRef]

Brzozowski, T. M.

M. Brzozowska, T. M. Brzozowski, J. Zachorowski, and W. Gawlik, “Nondestructive study of nonequilibrium states of cold trapped atoms,” Phys. Rev. A 72, 061401(R) (2005).
[CrossRef]

Castin, Y.

Y. Castin and J. Dalibard, “Quantization of atomic motion in optical molasses,” Europhys. Lett. 14, 761–766 (1991).
[CrossRef]

Chen, H.-C.

H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. A. Yu, and Y.-F. Chen, “Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A 83, 041804(R) (2011).
[CrossRef]

Chen, J.-X.

H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. A. Yu, and Y.-F. Chen, “Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A 83, 041804(R) (2011).
[CrossRef]

Chen, Y.-C.

H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. A. Yu, and Y.-F. Chen, “Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A 83, 041804(R) (2011).
[CrossRef]

H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. A. Yu, and Y.-F. Chen, “Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A 83, 041804(R) (2011).
[CrossRef]

Chen, Y.-F.

H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. A. Yu, and Y.-F. Chen, “Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A 83, 041804(R) (2011).
[CrossRef]

Cirloganu, C. M.

Clark, S. M.

A. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Phys. Rev. A 308, 672–674 (2005).

Dalibard, J.

Y. Castin and J. Dalibard, “Quantization of atomic motion in optical molasses,” Europhys. Lett. 14, 761–766 (1991).
[CrossRef]

Dawes, A.

A. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Phys. Rev. A 308, 672–674 (2005).

Dawes, A. M. C.

A. M. C. Dawes, D. J. Gauthier, S. Schumacher, N. H. Kwong, R. Binder, and A. Smirl, “Transverse optical patterns for ultra-low-light-level-all-optical switching,” Laser Photon. Rev. 4, 221–243 (2010).
[CrossRef]

J. A. Greenberg, M. Oriá, A. M. C. Dawes, and D. J. Gauthier, “Absorption-induced trapping in an anisotropic magneto-optical trap,” Opt. Express 15, 17699–17708 (2007).
[CrossRef] [PubMed]

de Oliveira, R.

De Salvo, L.

R. Bonifacio and L. De Salvo, “Collective atomic recoil laser (CARL) optical gain without inversion by collective atomic recoil and self-bunching of two-level atoms,” Nucl. Instrum. Methods Phys. 341, 360–362 (1994).
[CrossRef]

Dion, C. M.

S. Jonsell, C. M. Dion, A. Kastberg, S. J. H. Petra, and P. Sjolun, “A non-adiabatic semi-classical method for Sisyphus cooling,” Eur. Phys. J. D. 39, 67–74 (2006).
[CrossRef]

Dolgaleva, K.

R. W. Boyd, K. Dolgaleva, and H. Shin, “Strong, fifth-order, nonlinear optical response resulting from local-field-induced microscopic cascading in C60,” in Nonlinear Optics: Materials, Fundamentals and Applications (Optical Society of America, 2009), p. NWB2.

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Ellmann, H.

J. Jersblad, H. Ellmann, K. Stochkel, A. Kastberg, L. Sanchez-Palencia, and R. Kaiser, “Non-Gaussian velocity distributions in optical lattices,” Phys. Rev. A 69, 013410 (2004).
[CrossRef]

J. Jersblad, H. Ellmann, and A. Kastberg, “Experimental investigation of the limit of Sisyphus cooling,” Phys. Rev. A 62, 051401 (2000).
[CrossRef]

Felinto, D.

Fibich, G.

G. Fibich, N. Gavish, and X. P. Wang, “Singular ring solutions of critical and supercritical nonlinear Schrödinger equations,” Physica D 231, 55–86 (2007).
[CrossRef]

Gauthier, D. J.

A. M. C. Dawes, D. J. Gauthier, S. Schumacher, N. H. Kwong, R. Binder, and A. Smirl, “Transverse optical patterns for ultra-low-light-level-all-optical switching,” Laser Photon. Rev. 4, 221–243 (2010).
[CrossRef]

J. A. Greenberg, M. Oriá, A. M. C. Dawes, and D. J. Gauthier, “Absorption-induced trapping in an anisotropic magneto-optical trap,” Opt. Express 15, 17699–17708 (2007).
[CrossRef] [PubMed]

A. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Phys. Rev. A 308, 672–674 (2005).

Gavish, N.

G. Fibich, N. Gavish, and X. P. Wang, “Singular ring solutions of critical and supercritical nonlinear Schrödinger equations,” Physica D 231, 55–86 (2007).
[CrossRef]

Gawlik, W.

M. Brzozowska, T. M. Brzozowski, J. Zachorowski, and W. Gawlik, “Nondestructive study of nonequilibrium states of cold trapped atoms,” Phys. Rev. A 72, 061401(R) (2005).
[CrossRef]

Greenberg, J. A.

Hagan, D. J.

Hang, C.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[CrossRef]

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Hood, C. J.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef] [PubMed]

Huang, G.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[CrossRef]

Illing, L.

A. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Phys. Rev. A 308, 672–674 (2005).

Imoto, N.

Jersblad, J.

J. Jersblad, H. Ellmann, K. Stochkel, A. Kastberg, L. Sanchez-Palencia, and R. Kaiser, “Non-Gaussian velocity distributions in optical lattices,” Phys. Rev. A 69, 013410 (2004).
[CrossRef]

J. Jersblad, H. Ellmann, and A. Kastberg, “Experimental investigation of the limit of Sisyphus cooling,” Phys. Rev. A 62, 051401 (2000).
[CrossRef]

Jonsell, S.

S. Jonsell, C. M. Dion, A. Kastberg, S. J. H. Petra, and P. Sjolun, “A non-adiabatic semi-classical method for Sisyphus cooling,” Eur. Phys. J. D. 39, 67–74 (2006).
[CrossRef]

Kaiser, R.

J. Jersblad, H. Ellmann, K. Stochkel, A. Kastberg, L. Sanchez-Palencia, and R. Kaiser, “Non-Gaussian velocity distributions in optical lattices,” Phys. Rev. A 69, 013410 (2004).
[CrossRef]

Kastberg, A.

S. Jonsell, C. M. Dion, A. Kastberg, S. J. H. Petra, and P. Sjolun, “A non-adiabatic semi-classical method for Sisyphus cooling,” Eur. Phys. J. D. 39, 67–74 (2006).
[CrossRef]

J. Jersblad, H. Ellmann, K. Stochkel, A. Kastberg, L. Sanchez-Palencia, and R. Kaiser, “Non-Gaussian velocity distributions in optical lattices,” Phys. Rev. A 69, 013410 (2004).
[CrossRef]

J. Jersblad, H. Ellmann, and A. Kastberg, “Experimental investigation of the limit of Sisyphus cooling,” Phys. Rev. A 62, 051401 (2000).
[CrossRef]

Khadka, U.

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

Kimble, H. J.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef] [PubMed]

Koashi, M.

Kolchin, P.

P. Kolchin, R. F. Oulton, and X. Zhang, “Nonlinear quantum optics in a waveguide: Distinct single photons strongly interacting at the single atom level,” Phys. Rev. Lett. 106, 113601 (2011).
[CrossRef] [PubMed]

Kwong, N. H.

A. M. C. Dawes, D. J. Gauthier, S. Schumacher, N. H. Kwong, R. Binder, and A. Smirl, “Transverse optical patterns for ultra-low-light-level-all-optical switching,” Laser Photon. Rev. 4, 221–243 (2010).
[CrossRef]

Lange, W.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef] [PubMed]

Li, Y.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[CrossRef]

Lo, H.-Y.

H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. A. Yu, and Y.-F. Chen, “Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A 83, 041804(R) (2011).
[CrossRef]

Ma, L.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[CrossRef]

Mabuchi, H.

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef] [PubMed]

Matsko, A. B.

M. S. Zubairy, A. B. Matsko, and M. O. Scully, “Resonant enhancement of high-order optical nonlinearities based on atomic coherence,” Phys. Rev. A 65, 043804 (2002).
[CrossRef]

Meystre, P.

M. G. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. Lett. 83, 5202–5205 (1999).
[CrossRef]

Michinel, H.

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[CrossRef] [PubMed]

Mitsunaga, M.

Moore, M. G.

M. G. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. Lett. 83, 5202–5205 (1999).
[CrossRef]

Moretti, D.

Muradyan, G. A.

G. A. Muradyan, Y. Wang, W. Williams, and M. Saffman, “Absolute instability and pattern formation in cold atomic vapors,” in Nonlinear Guided Waves and Their Applications (Optical Society of America, 2005), p. ThB29.

Olszak, P. D.

Oriá, M.

Oulton, R. F.

P. Kolchin, R. F. Oulton, and X. Zhang, “Nonlinear quantum optics in a waveguide: Distinct single photons strongly interacting at the single atom level,” Phys. Rev. Lett. 106, 113601 (2011).
[CrossRef] [PubMed]

Padilha, L. A.

Paz-Alonso, M. J.

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[CrossRef] [PubMed]

Pepper, D. M.

Pérez-García, V. M.

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[CrossRef] [PubMed]

Petra, S. J. H.

S. Jonsell, C. M. Dion, A. Kastberg, S. J. H. Petra, and P. Sjolun, “A non-adiabatic semi-classical method for Sisyphus cooling,” Eur. Phys. J. D. 39, 67–74 (2006).
[CrossRef]

Saffman, M.

M. Saffman and Y. Wang, “Collective focusing and modulational instability of light and cold atoms,” in Dissipative Solitons: From Optics to Biology and Medicine, Vol. 751 of Lecture Notes in Physics (Springer, 2008).
[CrossRef]

G. A. Muradyan, Y. Wang, W. Williams, and M. Saffman, “Absolute instability and pattern formation in cold atomic vapors,” in Nonlinear Guided Waves and Their Applications (Optical Society of America, 2005), p. ThB29.

Sanchez-Palencia, L.

J. Jersblad, H. Ellmann, K. Stochkel, A. Kastberg, L. Sanchez-Palencia, and R. Kaiser, “Non-Gaussian velocity distributions in optical lattices,” Phys. Rev. A 69, 013410 (2004).
[CrossRef]

Schumacher, S.

A. M. C. Dawes, D. J. Gauthier, S. Schumacher, N. H. Kwong, R. Binder, and A. Smirl, “Transverse optical patterns for ultra-low-light-level-all-optical switching,” Laser Photon. Rev. 4, 221–243 (2010).
[CrossRef]

Scully, M. O.

M. S. Zubairy, A. B. Matsko, and M. O. Scully, “Resonant enhancement of high-order optical nonlinearities based on atomic coherence,” Phys. Rev. A 65, 043804 (2002).
[CrossRef]

Shin, H.

R. W. Boyd, K. Dolgaleva, and H. Shin, “Strong, fifth-order, nonlinear optical response resulting from local-field-induced microscopic cascading in C60,” in Nonlinear Optics: Materials, Fundamentals and Applications (Optical Society of America, 2009), p. NWB2.

Sjolun, P.

S. Jonsell, C. M. Dion, A. Kastberg, S. J. H. Petra, and P. Sjolun, “A non-adiabatic semi-classical method for Sisyphus cooling,” Eur. Phys. J. D. 39, 67–74 (2006).
[CrossRef]

Smirl, A.

A. M. C. Dawes, D. J. Gauthier, S. Schumacher, N. H. Kwong, R. Binder, and A. Smirl, “Transverse optical patterns for ultra-low-light-level-all-optical switching,” Laser Photon. Rev. 4, 221–243 (2010).
[CrossRef]

Stochkel, K.

J. Jersblad, H. Ellmann, K. Stochkel, A. Kastberg, L. Sanchez-Palencia, and R. Kaiser, “Non-Gaussian velocity distributions in optical lattices,” Phys. Rev. A 69, 013410 (2004).
[CrossRef]

Stryland, E. W. V.

Su, P.-C.

H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. A. Yu, and Y.-F. Chen, “Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A 83, 041804(R) (2011).
[CrossRef]

Tabosa, J.

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Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef] [PubMed]

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G. Fibich, N. Gavish, and X. P. Wang, “Singular ring solutions of critical and supercritical nonlinear Schrödinger equations,” Physica D 231, 55–86 (2007).
[CrossRef]

Wang, Y.

M. Saffman and Y. Wang, “Collective focusing and modulational instability of light and cold atoms,” in Dissipative Solitons: From Optics to Biology and Medicine, Vol. 751 of Lecture Notes in Physics (Springer, 2008).
[CrossRef]

G. A. Muradyan, Y. Wang, W. Williams, and M. Saffman, “Absolute instability and pattern formation in cold atomic vapors,” in Nonlinear Guided Waves and Their Applications (Optical Society of America, 2005), p. ThB29.

Webster, S.

Williams, W.

G. A. Muradyan, Y. Wang, W. Williams, and M. Saffman, “Absolute instability and pattern formation in cold atomic vapors,” in Nonlinear Guided Waves and Their Applications (Optical Society of America, 2005), p. ThB29.

Xiao, M.

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

Yamashita, M.

Yariv, A.

Yu, I. A.

H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. A. Yu, and Y.-F. Chen, “Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A 83, 041804(R) (2011).
[CrossRef]

Zachorowski, J.

M. Brzozowska, T. M. Brzozowski, J. Zachorowski, and W. Gawlik, “Nondestructive study of nonequilibrium states of cold trapped atoms,” Phys. Rev. A 72, 061401(R) (2005).
[CrossRef]

Zhang, X.

P. Kolchin, R. F. Oulton, and X. Zhang, “Nonlinear quantum optics in a waveguide: Distinct single photons strongly interacting at the single atom level,” Phys. Rev. Lett. 106, 113601 (2011).
[CrossRef] [PubMed]

Zhang, Y.

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

Zubairy, M. S.

M. S. Zubairy, A. B. Matsko, and M. O. Scully, “Resonant enhancement of high-order optical nonlinearities based on atomic coherence,” Phys. Rev. A 65, 043804 (2002).
[CrossRef]

Eur. Phys. J. D. (1)

S. Jonsell, C. M. Dion, A. Kastberg, S. J. H. Petra, and P. Sjolun, “A non-adiabatic semi-classical method for Sisyphus cooling,” Eur. Phys. J. D. 39, 67–74 (2006).
[CrossRef]

Europhys. Lett. (1)

Y. Castin and J. Dalibard, “Quantization of atomic motion in optical molasses,” Europhys. Lett. 14, 761–766 (1991).
[CrossRef]

Laser Photon. Rev. (1)

A. M. C. Dawes, D. J. Gauthier, S. Schumacher, N. H. Kwong, R. Binder, and A. Smirl, “Transverse optical patterns for ultra-low-light-level-all-optical switching,” Laser Photon. Rev. 4, 221–243 (2010).
[CrossRef]

Nature (1)

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[CrossRef]

Nucl. Instrum. Methods Phys. (1)

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[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (7)

J. Jersblad, H. Ellmann, K. Stochkel, A. Kastberg, L. Sanchez-Palencia, and R. Kaiser, “Non-Gaussian velocity distributions in optical lattices,” Phys. Rev. A 69, 013410 (2004).
[CrossRef]

M. Brzozowska, T. M. Brzozowski, J. Zachorowski, and W. Gawlik, “Nondestructive study of nonequilibrium states of cold trapped atoms,” Phys. Rev. A 72, 061401(R) (2005).
[CrossRef]

H.-Y. Lo, Y.-C. Chen, P.-C. Su, H.-C. Chen, J.-X. Chen, Y.-C. Chen, I. A. Yu, and Y.-F. Chen, “Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels,” Phys. Rev. A 83, 041804(R) (2011).
[CrossRef]

J. Jersblad, H. Ellmann, and A. Kastberg, “Experimental investigation of the limit of Sisyphus cooling,” Phys. Rev. A 62, 051401 (2000).
[CrossRef]

A. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, “All-optical switching in rubidium vapor,” Phys. Rev. A 308, 672–674 (2005).

M. S. Zubairy, A. B. Matsko, and M. O. Scully, “Resonant enhancement of high-order optical nonlinearities based on atomic coherence,” Phys. Rev. A 65, 043804 (2002).
[CrossRef]

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[CrossRef]

Phys. Rev. Lett. (5)

Y. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

P. Kolchin, R. F. Oulton, and X. Zhang, “Nonlinear quantum optics in a waveguide: Distinct single photons strongly interacting at the single atom level,” Phys. Rev. Lett. 106, 113601 (2011).
[CrossRef] [PubMed]

Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, and H. J. Kimble, “Measurement of conditional phase shifts for quantum logic,” Phys. Rev. Lett. 75, 4710–4713 (1995).
[CrossRef] [PubMed]

H. Michinel, M. J. Paz-Alonso, and V. M. Pérez-García, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[CrossRef] [PubMed]

M. G. Moore and P. Meystre, “Theory of superradiant scattering of laser light from Bose-Einstein condensates,” Phys. Rev. Lett. 83, 5202–5205 (1999).
[CrossRef]

Physica D (1)

G. Fibich, N. Gavish, and X. P. Wang, “Singular ring solutions of critical and supercritical nonlinear Schrödinger equations,” Physica D 231, 55–86 (2007).
[CrossRef]

Other (4)

M. Saffman and Y. Wang, “Collective focusing and modulational instability of light and cold atoms,” in Dissipative Solitons: From Optics to Biology and Medicine, Vol. 751 of Lecture Notes in Physics (Springer, 2008).
[CrossRef]

G. A. Muradyan, Y. Wang, W. Williams, and M. Saffman, “Absolute instability and pattern formation in cold atomic vapors,” in Nonlinear Guided Waves and Their Applications (Optical Society of America, 2005), p. ThB29.

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008), Chap. 3.

R. W. Boyd, K. Dolgaleva, and H. Shin, “Strong, fifth-order, nonlinear optical response resulting from local-field-induced microscopic cascading in C60,” in Nonlinear Optics: Materials, Fundamentals and Applications (Optical Society of America, 2009), p. NWB2.

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Figures (10)

Fig. 1
Fig. 1

a) Schematic of the experimental setup. b) Atomic level scheme used in the theoretical model along with the square of the Clebsh-Gordan coefficients (defined as a fraction of the reduced dipole moment μ) for the J = 1/2 → J = 3/2 transition. c) Optical lattices that form due to the interference of the pump beams (dotted line, p) and a probe and nearly-counterpropagating pump beam (solid line, Ĝ). d) Timing scheme used in the experiment.

Fig. 2
Fig. 2

a) Momentum distribution obtained via numerical simulation (blue, solid line) and a double-Gaussian fit (dashed, red line). pr = h̄k is the recoil momentum. b) Fraction of atoms in the hot and cold component as a function of pump intensity.

Fig. 3
Fig. 3

Normalized intensity spectrum of the a) transmitted signal and b) generated idler beams.

Fig. 4
Fig. 4

Dependence of NLO phase shift on experimental parameters. a) Experimental data (points) and theoretical predictions from Eq. (18) (solid curves) for Δ/Γ = −3, −5, −7.3, −12.7 (from left to right, respectively). b) For Ip < Id, the experimental data (points, Δ = −3Γ) are well-fit by a quadratic function (solid curve). c) Measured (points) dependence on atomic density and linear fit (solid line) and d) scaling with the incident signal intensity for Δ = −5Γ and Ip = 1.5 mW/cm2.

Fig. 5
Fig. 5

Dependence of the slow-light delay and group velocity on the NLO coupling strength for Δ = −5Γ.

Fig. 6
Fig. 6

(Color online) Growth of βL as a function of time when the signal beam turns on at t = 0. The lower red (upper blue) curve corresponds to the case where we turn the pump beams on at t = 0 (t = −400 μs) for Δ = −5Γ.

Fig. 7
Fig. 7

Decay of the nonlinear coupling coefficient as a function of time after the signal beam is turned off at t = 0 for Δ = −5Γ and Ip = a) 0.45, b) 0.7 and c) 1.25 mW/cm2. The solid and dashed lines correspond to experimental data and a double-Gaussian fit, respectively (note the change in scale of the horizontal axis).

Fig. 8
Fig. 8

Dependence of βc,h on Ip. Points correspond to experimental data extracted from multi-Gaussian fits to the transient decay measurements, and the solid curves are obtained by a fit using Eqs. 22 and 23.

Fig. 9
Fig. 9

Time-dependent intensity of the instability-generated light in the + (signal, red) and − (idler, blue) directions for Ip = 5 mW/cm2 and Δ = −5Γ, where the instability threshold is Ip = 2.3 mW/cm2. The temporal correlation of the signal and idler modes is r = 0.99.

Fig. 10
Fig. 10

a) Beam geometry for pattern-forming instability, where θ′ ∼ 5 mrad. b) Transverse optical patterns, including i) a nearly full ring and ii) a six- iii) four- and iv) two-spot pattern, for Ip = 15 mW/cm2, Δ = −8Γ and an instability threshold of Ip = 6 mW/cm2. The central spot in the images corresponds to residual pump light.

Equations (23)

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( r , t ) = E ( r , t ) e i ω t + c . c . ,
( r , t ) = χ ( r , t ) = P ( r , t ) e i ω t + c . c . ,
( E s , i t ± c E s , i z ) = i ω 2 ɛ 0 P e i k s r ,
p ± = n p n ± ( r ) e i k n r ,
p n ± ( r ) = μ eff ± h ¯ Δ E n ( r )
μ eff ± = j = e 1 / 2 , e ± 3 / 2 μ j , g ± 1 / 2 μ g ± 1 / 2 , j ,
ρ ( p ) = g ( p y , T y ) g ( p , T ) [ f c g ( p | | , T c ) + f h g ( p | | , T h ) ] ,
U ± ( r ) = U 0 ± cos ( G r ) = ( p p 1 ± E i * + ( p p 2 ± ) * E s ) e i G r + c . c ..
η U ± ( r ) = 1 2 I 1 ( ψ ± ) I 0 ( ψ ± ) cos ( G r ) + ,
η U ± ( r ) 1 + b ± ( T ) e i G r + ( b ± ( T ) ) * e i G r
b ± ( T ) = ( μ eff ± E p 1 ) E i * + ( μ eff ± E p 2 * ) E s k B T h ¯ Δ
b ± ( T ) b ± ( T c , T h ) = f c b ± ( T c ) + f h b ± ( T h ) ,
η ± ( r ) = η η p ± η U ± / g ,
( E s t + c E s z ) = i ω η 2 ɛ 0 j = ± μ eff ± h ¯ Δ [ E s + b ± ( T c , T h ) E p ] ,
( E i t c E i z ) = i ω η 2 ɛ 0 j = ± μ eff ± h ¯ Δ [ E i + b ± ( T c , T h ) * E p ] .
d E s d z = i κ E s + i β E i * ,
d E i * d z = i κ E i * + i β E s
β = β c + β h = 2 ω η μ 4 I p 9 ( ɛ 0 c h ¯ Δ ) 2 ( f c k B T c + f h k B T h )
κ = 2 ω η μ 2 3 ɛ 0 c h ¯ Δ + β ,
I s ( L ) I s ( 0 ) = sec 2 ( β L ) ,
I i ( 0 ) I s ( 0 ) = tan 2 ( β L ) ,
β c I p 2 / T c I d
β h I p ( 1 I p / I d ) / T h .

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