Abstract

Using a pump–probe scheme with a large cloud of cold rubidium atoms, we observe very large double-pass gain (1800%) due to interference between Raman gain and four-wave mixing. A simple model explains the main features observed.

© 2007 Optical Society of America

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  1. P. W. Anderson, "Absence of diffusion in certain random lattices," Phys. Rev. 109, 1492-1505 (1958).
    [CrossRef]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef]
  3. D. Clément, A. Varón, M. Hugbart, J. Retter, P. Bouyer, L. Sanchez-Palencia, D. Gangardt, G. Shlyapnikov, and A. Aspect, "Suppression of transport of an interacting elongated Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 170409 (2005).
    [CrossRef]
  4. C. Fort, L. Fallani, V. Guarrera, J. Lye, M. Modugno, D. Wiersma, and M. Inguscio, "Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide," Phys. Rev. Lett. 95, 170410 (2005).
    [CrossRef]
  5. J. E. Lye, L. Fallani, M. Modugno, D. Wiersma, C. Fort, and M. Inguscio, "A Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 070401 (2005).
    [CrossRef]
  6. T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. Arlt, K. Sacha, J. Zakrzewski, and M. Lewenstein, "Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices," Phys. Rev. Lett. 95, 170411 (2005).
    [CrossRef]
  7. P.-E. Wolf and G. Maret, "Weak localization and coherent backscattering of photons in disordered media," Phys. Rev. Lett. 55, 2696-2699 (1985).
    [CrossRef]
  8. M. P. van Albada and A. Lagendijk, "Observation of weak localization of light in a random medium," Phys. Rev. Lett. 55, 2692-2695 (1985).
    [CrossRef]
  9. Y. Kuga and A. Ishimaru, "Retroreflectance from a dense distribution of spherical particles," J. Opt. Soc. Am. A 8, 831-836 (1984).
  10. A. A. Chabanov, M. Stoytchev, and A. Z. Genack, "Statistical approach to photon localization," Nature 404, 850-853 (2000).
    [CrossRef]
  11. G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, Ch. Miniatura, and R. Kaiser, "Coherent backscattering of light by cold atoms," Phys. Rev. Lett. 83, 5266-5269 (1999).
    [CrossRef]
  12. C. M. Aegerter, M. Störzer, and G. Maret, "Experimental determination of critical exponents in Anderson localization of light," Europhys. Lett. 75, 562-568 (2006).
    [CrossRef]
  13. A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, "Breakdown of diffusion in dynamics of extended waves in mesoscopic media," Phys. Rev. Lett. 90, 203903 (2003).
    [CrossRef]
  14. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, "Localization of light in a disordered medium," Nature 390, 671-673 (1997).
    [CrossRef]
  15. F. Scheffold, R. Lenke, R. Tweer, and G. Maret, "Localization or classical diffusion of light," Nature 398, 206-207 (1999).
    [CrossRef]
  16. D. S. Wiersma, J. Gomez Rivas, P. Bartolini, A. Lagendijk, and R. Righini, "Wiersma reply," Nature 398, 207 (1999).
    [CrossRef]
  17. V. S. Letokhov, "Generation of light by a scattering medium with negative resonance absorption," Zh. Eksp. Teor. Fiz. 53, 1442-1452 (1967) [V. S. Letokhov, Sov. Phys. JETP 26, 835-840 (1968)].
  18. N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, "Laser action in strongly scattering media," Nature 369, 436-438 (1994).
  19. H. Cao, Y. Xu, S.-H. Chang, and S. T. Ho, "Transition from amplified spontaneous emission to laser action in strongly scattering media," Phys. Rev. E 61, 1985-1989 (2000).
    [CrossRef]
  20. Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, and R. Kaiser, "Coherent light transport in a cold strontium cloud," Phys. Rev. Lett. 88, 203902 (2002).
    [CrossRef]
  21. D. V. Kupriyanov, I. M. Sokolov, P. Kulatunga, C. I. Sukenik, and M. D. Havey, "Coherent backscattering of light in atomic systems: application to weak localization in an ensemble of cold alkali-metal atoms," Phys. Rev. A 67, 013814 (2003).
    [CrossRef]
  22. G. Labeyrie, E. Vaujour, C. A. Müller, D. Delande, C. Miniatura, D. Wilkowski, and R. Kaiser, "Slow diffusion of light in a cold atomic cloud," Phys. Rev. Lett. 91, 223904 (2003).
    [CrossRef]
  23. G. Grynberg and C. Robillard, "Cold atoms in dissipative optical lattices," Phys. Rep. 355, 335-451 (2001).
    [CrossRef]
  24. F. Y. Wu, S. Ezekiel, M. Ducloy, and B. R. Mollow, "Observation of amplification in a strongly driven two-level atomic system at optical frequencies," Phys. Rev. Lett. 38, 1077-1080 (1977).
    [CrossRef]
  25. C. Mennerat-Robilliard, L. Guidoni, K. I. Petsas, P. Verkerk, J.-Y. Courtois, and G. Grynberg, "Bright optical lattices in a longitudinal magnetic field, experimental study of the oscillating and jumping regimes," Eur. Phys. J. D 1, 33-45 (1998).
    [CrossRef]
  26. J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, "Nonlinear spectroscopy of cold atoms in a spontaneous-force optical trap," Phys. Rev. Lett. 66, 3245-3248 (1991).
    [CrossRef]
  27. D. Grison, B. Lounis, C. Salomon, J.-Y. Courtois, and G. Grynberg, "Raman spectroscopy of cesium atoms in a laser trap," Europhys. Lett. 15, 149-154 (1991).
  28. T. M. Brzozowski, M. Brzozowska, J. Zachorowski, M. Zawada, and W. Gawlik, "Probe spectroscopy in an operating magneto-optical trap: the role of Raman transitions between discrete and continuum atomic states," Phys. Rev. A 71, 013401 (2005).
    [CrossRef]
  29. J. Guo, P. R. Berman, B. Dubetsky, and G. Grynberg, "Recoil-induced resonances in nonlinear spectroscopy," Phys. Rev. A 46, 1426-1437 (1992).
    [CrossRef]
  30. J.-Y. Courtois, G. Grynberg, B. Lounis, and P. Verkerk, "Recoil-induced resonances in cesium: an atomic analog to the free-electron laser," Phys. Rev. Lett. 72, 3017-3020 (1994).
    [CrossRef]
  31. L. Hilico, C. Fabre, and E. Giacobino, "Operation of a 'cold-atom laser' in a magneto-optical trap," Europhys. Lett. 18, 685-688 (1992).
  32. A. Lambrecht, J. M. Courty, S. Reynaud, and E. Giacobino, "Cold atoms: a new medium for quantum optics," Appl. Phys. B 60, 129-134 (1995).
  33. C. von Cube, S. Slama, D. Kruse, C. Zimmermann, Ph. W. Courteille, G. R. M. Robb, N. Piovella, and R. Bonifacio, Phys. Rev. Lett. 93, 083601 (2004).
    [CrossRef]
  34. M. Vengalattore and M. Prentiss, "Recoil-induced resonances in the high-gain regime," Phys. Rev. A 72, 021401(R) (2005).
    [CrossRef]
  35. G. L. Gattobigio, F. Michaud, J. Javaloyes, J. W. R. Tabosa, and R. Kaiser, "Bunching induced asymmetry in degenerate four-wave mixing with cold atoms," Phys. Rev. A 74, 043407 (2006).
    [CrossRef]
  36. A. Lezama, G. C. Cardoso, and J. W. R. Tabosa, "Polarization dependence of four-wave mixing in a degenerate two-level system," Phys. Rev. A 63, 013805 (2001).
    [CrossRef]
  37. M. Pinard, D. Grandclement, and G. Grynberg, "Continuous-wave self-oscillation using pair production of photons in four-wave mixing in sodium," Europhys. Lett. 2, 755-760 (1986).
  38. A. Novikov, V. Obukhovski, S. Odoulov, and B. Sturman, "Mirrorless coherent oscillation due to six-beam vectorial mixing in photorefractive crystals," Opt. Lett. 13, 1017-1019 (1988).
  39. G. Grynberg, E. le Bihan, P. Verkerk, and M. Ducloy, "Observation of instabilities due to mirrorless four-wave mixing oscillation in sodium," Opt. Commun. 67, 363-366 (1988).
    [CrossRef]
  40. J. Guo, "Contribution of energy continuum states to probe the absorption signal of atoms in one-dimensional optical molasses," Phys. Rev. A 49, 3934-3942 (1994).
    [CrossRef]
  41. Y.-C. Chen, Y.-W. Chen, J.-J. Su, J.-Y. Huang, and I. A. Yu, "Pump-probe spectroscopy of cold Rb87 atoms in various polarization configurations," Phys. Rev. A 63, 043808 (2001).
    [CrossRef]
  42. J. Y. Courtois, "Spectroscopie Raman et Rayleigh stimulie d'atomes refroidis par laser: dynamique des mélasses optiques unidimensionnelles," Ph.D. dissertation (Ecole Polytechnique, 1993).

2006 (2)

C. M. Aegerter, M. Störzer, and G. Maret, "Experimental determination of critical exponents in Anderson localization of light," Europhys. Lett. 75, 562-568 (2006).
[CrossRef]

G. L. Gattobigio, F. Michaud, J. Javaloyes, J. W. R. Tabosa, and R. Kaiser, "Bunching induced asymmetry in degenerate four-wave mixing with cold atoms," Phys. Rev. A 74, 043407 (2006).
[CrossRef]

2005 (6)

M. Vengalattore and M. Prentiss, "Recoil-induced resonances in the high-gain regime," Phys. Rev. A 72, 021401(R) (2005).
[CrossRef]

T. M. Brzozowski, M. Brzozowska, J. Zachorowski, M. Zawada, and W. Gawlik, "Probe spectroscopy in an operating magneto-optical trap: the role of Raman transitions between discrete and continuum atomic states," Phys. Rev. A 71, 013401 (2005).
[CrossRef]

D. Clément, A. Varón, M. Hugbart, J. Retter, P. Bouyer, L. Sanchez-Palencia, D. Gangardt, G. Shlyapnikov, and A. Aspect, "Suppression of transport of an interacting elongated Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 170409 (2005).
[CrossRef]

C. Fort, L. Fallani, V. Guarrera, J. Lye, M. Modugno, D. Wiersma, and M. Inguscio, "Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide," Phys. Rev. Lett. 95, 170410 (2005).
[CrossRef]

J. E. Lye, L. Fallani, M. Modugno, D. Wiersma, C. Fort, and M. Inguscio, "A Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 070401 (2005).
[CrossRef]

T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. Arlt, K. Sacha, J. Zakrzewski, and M. Lewenstein, "Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices," Phys. Rev. Lett. 95, 170411 (2005).
[CrossRef]

2004 (1)

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, Ph. W. Courteille, G. R. M. Robb, N. Piovella, and R. Bonifacio, Phys. Rev. Lett. 93, 083601 (2004).
[CrossRef]

2003 (3)

A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, "Breakdown of diffusion in dynamics of extended waves in mesoscopic media," Phys. Rev. Lett. 90, 203903 (2003).
[CrossRef]

D. V. Kupriyanov, I. M. Sokolov, P. Kulatunga, C. I. Sukenik, and M. D. Havey, "Coherent backscattering of light in atomic systems: application to weak localization in an ensemble of cold alkali-metal atoms," Phys. Rev. A 67, 013814 (2003).
[CrossRef]

G. Labeyrie, E. Vaujour, C. A. Müller, D. Delande, C. Miniatura, D. Wilkowski, and R. Kaiser, "Slow diffusion of light in a cold atomic cloud," Phys. Rev. Lett. 91, 223904 (2003).
[CrossRef]

2002 (1)

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, and R. Kaiser, "Coherent light transport in a cold strontium cloud," Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef]

2001 (3)

A. Lezama, G. C. Cardoso, and J. W. R. Tabosa, "Polarization dependence of four-wave mixing in a degenerate two-level system," Phys. Rev. A 63, 013805 (2001).
[CrossRef]

G. Grynberg and C. Robillard, "Cold atoms in dissipative optical lattices," Phys. Rep. 355, 335-451 (2001).
[CrossRef]

Y.-C. Chen, Y.-W. Chen, J.-J. Su, J.-Y. Huang, and I. A. Yu, "Pump-probe spectroscopy of cold Rb87 atoms in various polarization configurations," Phys. Rev. A 63, 043808 (2001).
[CrossRef]

2000 (2)

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, "Statistical approach to photon localization," Nature 404, 850-853 (2000).
[CrossRef]

H. Cao, Y. Xu, S.-H. Chang, and S. T. Ho, "Transition from amplified spontaneous emission to laser action in strongly scattering media," Phys. Rev. E 61, 1985-1989 (2000).
[CrossRef]

1999 (3)

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, Ch. Miniatura, and R. Kaiser, "Coherent backscattering of light by cold atoms," Phys. Rev. Lett. 83, 5266-5269 (1999).
[CrossRef]

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, "Localization or classical diffusion of light," Nature 398, 206-207 (1999).
[CrossRef]

D. S. Wiersma, J. Gomez Rivas, P. Bartolini, A. Lagendijk, and R. Righini, "Wiersma reply," Nature 398, 207 (1999).
[CrossRef]

1998 (1)

C. Mennerat-Robilliard, L. Guidoni, K. I. Petsas, P. Verkerk, J.-Y. Courtois, and G. Grynberg, "Bright optical lattices in a longitudinal magnetic field, experimental study of the oscillating and jumping regimes," Eur. Phys. J. D 1, 33-45 (1998).
[CrossRef]

1997 (1)

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, "Localization of light in a disordered medium," Nature 390, 671-673 (1997).
[CrossRef]

1995 (1)

A. Lambrecht, J. M. Courty, S. Reynaud, and E. Giacobino, "Cold atoms: a new medium for quantum optics," Appl. Phys. B 60, 129-134 (1995).

1994 (3)

J. Guo, "Contribution of energy continuum states to probe the absorption signal of atoms in one-dimensional optical molasses," Phys. Rev. A 49, 3934-3942 (1994).
[CrossRef]

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, "Laser action in strongly scattering media," Nature 369, 436-438 (1994).

J.-Y. Courtois, G. Grynberg, B. Lounis, and P. Verkerk, "Recoil-induced resonances in cesium: an atomic analog to the free-electron laser," Phys. Rev. Lett. 72, 3017-3020 (1994).
[CrossRef]

1992 (2)

L. Hilico, C. Fabre, and E. Giacobino, "Operation of a 'cold-atom laser' in a magneto-optical trap," Europhys. Lett. 18, 685-688 (1992).

J. Guo, P. R. Berman, B. Dubetsky, and G. Grynberg, "Recoil-induced resonances in nonlinear spectroscopy," Phys. Rev. A 46, 1426-1437 (1992).
[CrossRef]

1991 (2)

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, "Nonlinear spectroscopy of cold atoms in a spontaneous-force optical trap," Phys. Rev. Lett. 66, 3245-3248 (1991).
[CrossRef]

D. Grison, B. Lounis, C. Salomon, J.-Y. Courtois, and G. Grynberg, "Raman spectroscopy of cesium atoms in a laser trap," Europhys. Lett. 15, 149-154 (1991).

1988 (2)

G. Grynberg, E. le Bihan, P. Verkerk, and M. Ducloy, "Observation of instabilities due to mirrorless four-wave mixing oscillation in sodium," Opt. Commun. 67, 363-366 (1988).
[CrossRef]

A. Novikov, V. Obukhovski, S. Odoulov, and B. Sturman, "Mirrorless coherent oscillation due to six-beam vectorial mixing in photorefractive crystals," Opt. Lett. 13, 1017-1019 (1988).

1987 (1)

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef]

1986 (1)

M. Pinard, D. Grandclement, and G. Grynberg, "Continuous-wave self-oscillation using pair production of photons in four-wave mixing in sodium," Europhys. Lett. 2, 755-760 (1986).

1985 (2)

P.-E. Wolf and G. Maret, "Weak localization and coherent backscattering of photons in disordered media," Phys. Rev. Lett. 55, 2696-2699 (1985).
[CrossRef]

M. P. van Albada and A. Lagendijk, "Observation of weak localization of light in a random medium," Phys. Rev. Lett. 55, 2692-2695 (1985).
[CrossRef]

1984 (1)

Y. Kuga and A. Ishimaru, "Retroreflectance from a dense distribution of spherical particles," J. Opt. Soc. Am. A 8, 831-836 (1984).

1977 (1)

F. Y. Wu, S. Ezekiel, M. Ducloy, and B. R. Mollow, "Observation of amplification in a strongly driven two-level atomic system at optical frequencies," Phys. Rev. Lett. 38, 1077-1080 (1977).
[CrossRef]

1967 (1)

V. S. Letokhov, "Generation of light by a scattering medium with negative resonance absorption," Zh. Eksp. Teor. Fiz. 53, 1442-1452 (1967) [V. S. Letokhov, Sov. Phys. JETP 26, 835-840 (1968)].

1958 (1)

P. W. Anderson, "Absence of diffusion in certain random lattices," Phys. Rev. 109, 1492-1505 (1958).
[CrossRef]

Aegerter, C. M.

C. M. Aegerter, M. Störzer, and G. Maret, "Experimental determination of critical exponents in Anderson localization of light," Europhys. Lett. 75, 562-568 (2006).
[CrossRef]

Anderson, P. W.

P. W. Anderson, "Absence of diffusion in certain random lattices," Phys. Rev. 109, 1492-1505 (1958).
[CrossRef]

Arlt, J.

T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. Arlt, K. Sacha, J. Zakrzewski, and M. Lewenstein, "Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices," Phys. Rev. Lett. 95, 170411 (2005).
[CrossRef]

Aspect, A.

D. Clément, A. Varón, M. Hugbart, J. Retter, P. Bouyer, L. Sanchez-Palencia, D. Gangardt, G. Shlyapnikov, and A. Aspect, "Suppression of transport of an interacting elongated Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 170409 (2005).
[CrossRef]

Balachandran, R. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, "Laser action in strongly scattering media," Nature 369, 436-438 (1994).

Bartolini, P.

D. S. Wiersma, J. Gomez Rivas, P. Bartolini, A. Lagendijk, and R. Righini, "Wiersma reply," Nature 398, 207 (1999).
[CrossRef]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, "Localization of light in a disordered medium," Nature 390, 671-673 (1997).
[CrossRef]

Berman, P. R.

J. Guo, P. R. Berman, B. Dubetsky, and G. Grynberg, "Recoil-induced resonances in nonlinear spectroscopy," Phys. Rev. A 46, 1426-1437 (1992).
[CrossRef]

Bernard, J. C.

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, and R. Kaiser, "Coherent light transport in a cold strontium cloud," Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef]

Bernard, J.-C.

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, Ch. Miniatura, and R. Kaiser, "Coherent backscattering of light by cold atoms," Phys. Rev. Lett. 83, 5266-5269 (1999).
[CrossRef]

Bidel, Y.

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, and R. Kaiser, "Coherent light transport in a cold strontium cloud," Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef]

Bonifacio, R.

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, Ph. W. Courteille, G. R. M. Robb, N. Piovella, and R. Bonifacio, Phys. Rev. Lett. 93, 083601 (2004).
[CrossRef]

Bouyer, P.

D. Clément, A. Varón, M. Hugbart, J. Retter, P. Bouyer, L. Sanchez-Palencia, D. Gangardt, G. Shlyapnikov, and A. Aspect, "Suppression of transport of an interacting elongated Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 170409 (2005).
[CrossRef]

Brzozowska, M.

T. M. Brzozowski, M. Brzozowska, J. Zachorowski, M. Zawada, and W. Gawlik, "Probe spectroscopy in an operating magneto-optical trap: the role of Raman transitions between discrete and continuum atomic states," Phys. Rev. A 71, 013401 (2005).
[CrossRef]

Brzozowski, T. M.

T. M. Brzozowski, M. Brzozowska, J. Zachorowski, M. Zawada, and W. Gawlik, "Probe spectroscopy in an operating magneto-optical trap: the role of Raman transitions between discrete and continuum atomic states," Phys. Rev. A 71, 013401 (2005).
[CrossRef]

Cao, H.

H. Cao, Y. Xu, S.-H. Chang, and S. T. Ho, "Transition from amplified spontaneous emission to laser action in strongly scattering media," Phys. Rev. E 61, 1985-1989 (2000).
[CrossRef]

Cardoso, G. C.

A. Lezama, G. C. Cardoso, and J. W. R. Tabosa, "Polarization dependence of four-wave mixing in a degenerate two-level system," Phys. Rev. A 63, 013805 (2001).
[CrossRef]

Chabanov, A. A.

A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, "Breakdown of diffusion in dynamics of extended waves in mesoscopic media," Phys. Rev. Lett. 90, 203903 (2003).
[CrossRef]

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, "Statistical approach to photon localization," Nature 404, 850-853 (2000).
[CrossRef]

Chang, S.-H.

H. Cao, Y. Xu, S.-H. Chang, and S. T. Ho, "Transition from amplified spontaneous emission to laser action in strongly scattering media," Phys. Rev. E 61, 1985-1989 (2000).
[CrossRef]

Chen, G.

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, "Nonlinear spectroscopy of cold atoms in a spontaneous-force optical trap," Phys. Rev. Lett. 66, 3245-3248 (1991).
[CrossRef]

Chen, Y.-C.

Y.-C. Chen, Y.-W. Chen, J.-J. Su, J.-Y. Huang, and I. A. Yu, "Pump-probe spectroscopy of cold Rb87 atoms in various polarization configurations," Phys. Rev. A 63, 043808 (2001).
[CrossRef]

Chen, Y.-W.

Y.-C. Chen, Y.-W. Chen, J.-J. Su, J.-Y. Huang, and I. A. Yu, "Pump-probe spectroscopy of cold Rb87 atoms in various polarization configurations," Phys. Rev. A 63, 043808 (2001).
[CrossRef]

Clément, D.

D. Clément, A. Varón, M. Hugbart, J. Retter, P. Bouyer, L. Sanchez-Palencia, D. Gangardt, G. Shlyapnikov, and A. Aspect, "Suppression of transport of an interacting elongated Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 170409 (2005).
[CrossRef]

Courteille, Ph. W.

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, Ph. W. Courteille, G. R. M. Robb, N. Piovella, and R. Bonifacio, Phys. Rev. Lett. 93, 083601 (2004).
[CrossRef]

Courtois, J. Y.

J. Y. Courtois, "Spectroscopie Raman et Rayleigh stimulie d'atomes refroidis par laser: dynamique des mélasses optiques unidimensionnelles," Ph.D. dissertation (Ecole Polytechnique, 1993).

Courtois, J.-Y.

C. Mennerat-Robilliard, L. Guidoni, K. I. Petsas, P. Verkerk, J.-Y. Courtois, and G. Grynberg, "Bright optical lattices in a longitudinal magnetic field, experimental study of the oscillating and jumping regimes," Eur. Phys. J. D 1, 33-45 (1998).
[CrossRef]

J.-Y. Courtois, G. Grynberg, B. Lounis, and P. Verkerk, "Recoil-induced resonances in cesium: an atomic analog to the free-electron laser," Phys. Rev. Lett. 72, 3017-3020 (1994).
[CrossRef]

D. Grison, B. Lounis, C. Salomon, J.-Y. Courtois, and G. Grynberg, "Raman spectroscopy of cesium atoms in a laser trap," Europhys. Lett. 15, 149-154 (1991).

Courty, J. M.

A. Lambrecht, J. M. Courty, S. Reynaud, and E. Giacobino, "Cold atoms: a new medium for quantum optics," Appl. Phys. B 60, 129-134 (1995).

de Tomasi, F.

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, Ch. Miniatura, and R. Kaiser, "Coherent backscattering of light by cold atoms," Phys. Rev. Lett. 83, 5266-5269 (1999).
[CrossRef]

Delande, D.

G. Labeyrie, E. Vaujour, C. A. Müller, D. Delande, C. Miniatura, D. Wilkowski, and R. Kaiser, "Slow diffusion of light in a cold atomic cloud," Phys. Rev. Lett. 91, 223904 (2003).
[CrossRef]

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, and R. Kaiser, "Coherent light transport in a cold strontium cloud," Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef]

Drenkelforth, S.

T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. Arlt, K. Sacha, J. Zakrzewski, and M. Lewenstein, "Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices," Phys. Rev. Lett. 95, 170411 (2005).
[CrossRef]

Dubetsky, B.

J. Guo, P. R. Berman, B. Dubetsky, and G. Grynberg, "Recoil-induced resonances in nonlinear spectroscopy," Phys. Rev. A 46, 1426-1437 (1992).
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Ducloy, M.

G. Grynberg, E. le Bihan, P. Verkerk, and M. Ducloy, "Observation of instabilities due to mirrorless four-wave mixing oscillation in sodium," Opt. Commun. 67, 363-366 (1988).
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F. Y. Wu, S. Ezekiel, M. Ducloy, and B. R. Mollow, "Observation of amplification in a strongly driven two-level atomic system at optical frequencies," Phys. Rev. Lett. 38, 1077-1080 (1977).
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T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. Arlt, K. Sacha, J. Zakrzewski, and M. Lewenstein, "Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices," Phys. Rev. Lett. 95, 170411 (2005).
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F. Y. Wu, S. Ezekiel, M. Ducloy, and B. R. Mollow, "Observation of amplification in a strongly driven two-level atomic system at optical frequencies," Phys. Rev. Lett. 38, 1077-1080 (1977).
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L. Hilico, C. Fabre, and E. Giacobino, "Operation of a 'cold-atom laser' in a magneto-optical trap," Europhys. Lett. 18, 685-688 (1992).

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J. E. Lye, L. Fallani, M. Modugno, D. Wiersma, C. Fort, and M. Inguscio, "A Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 070401 (2005).
[CrossRef]

C. Fort, L. Fallani, V. Guarrera, J. Lye, M. Modugno, D. Wiersma, and M. Inguscio, "Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide," Phys. Rev. Lett. 95, 170410 (2005).
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C. Fort, L. Fallani, V. Guarrera, J. Lye, M. Modugno, D. Wiersma, and M. Inguscio, "Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide," Phys. Rev. Lett. 95, 170410 (2005).
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J. E. Lye, L. Fallani, M. Modugno, D. Wiersma, C. Fort, and M. Inguscio, "A Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 070401 (2005).
[CrossRef]

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D. Clément, A. Varón, M. Hugbart, J. Retter, P. Bouyer, L. Sanchez-Palencia, D. Gangardt, G. Shlyapnikov, and A. Aspect, "Suppression of transport of an interacting elongated Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 170409 (2005).
[CrossRef]

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G. L. Gattobigio, F. Michaud, J. Javaloyes, J. W. R. Tabosa, and R. Kaiser, "Bunching induced asymmetry in degenerate four-wave mixing with cold atoms," Phys. Rev. A 74, 043407 (2006).
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T. M. Brzozowski, M. Brzozowska, J. Zachorowski, M. Zawada, and W. Gawlik, "Probe spectroscopy in an operating magneto-optical trap: the role of Raman transitions between discrete and continuum atomic states," Phys. Rev. A 71, 013401 (2005).
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A. A. Chabanov, M. Stoytchev, and A. Z. Genack, "Statistical approach to photon localization," Nature 404, 850-853 (2000).
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A. Lambrecht, J. M. Courty, S. Reynaud, and E. Giacobino, "Cold atoms: a new medium for quantum optics," Appl. Phys. B 60, 129-134 (1995).

L. Hilico, C. Fabre, and E. Giacobino, "Operation of a 'cold-atom laser' in a magneto-optical trap," Europhys. Lett. 18, 685-688 (1992).

Gomes, A. S. L.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, "Laser action in strongly scattering media," Nature 369, 436-438 (1994).

Gomez Rivas, J.

D. S. Wiersma, J. Gomez Rivas, P. Bartolini, A. Lagendijk, and R. Righini, "Wiersma reply," Nature 398, 207 (1999).
[CrossRef]

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M. Pinard, D. Grandclement, and G. Grynberg, "Continuous-wave self-oscillation using pair production of photons in four-wave mixing in sodium," Europhys. Lett. 2, 755-760 (1986).

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D. Grison, B. Lounis, C. Salomon, J.-Y. Courtois, and G. Grynberg, "Raman spectroscopy of cesium atoms in a laser trap," Europhys. Lett. 15, 149-154 (1991).

Grynberg, G.

G. Grynberg and C. Robillard, "Cold atoms in dissipative optical lattices," Phys. Rep. 355, 335-451 (2001).
[CrossRef]

C. Mennerat-Robilliard, L. Guidoni, K. I. Petsas, P. Verkerk, J.-Y. Courtois, and G. Grynberg, "Bright optical lattices in a longitudinal magnetic field, experimental study of the oscillating and jumping regimes," Eur. Phys. J. D 1, 33-45 (1998).
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J.-Y. Courtois, G. Grynberg, B. Lounis, and P. Verkerk, "Recoil-induced resonances in cesium: an atomic analog to the free-electron laser," Phys. Rev. Lett. 72, 3017-3020 (1994).
[CrossRef]

J. Guo, P. R. Berman, B. Dubetsky, and G. Grynberg, "Recoil-induced resonances in nonlinear spectroscopy," Phys. Rev. A 46, 1426-1437 (1992).
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D. Grison, B. Lounis, C. Salomon, J.-Y. Courtois, and G. Grynberg, "Raman spectroscopy of cesium atoms in a laser trap," Europhys. Lett. 15, 149-154 (1991).

G. Grynberg, E. le Bihan, P. Verkerk, and M. Ducloy, "Observation of instabilities due to mirrorless four-wave mixing oscillation in sodium," Opt. Commun. 67, 363-366 (1988).
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M. Pinard, D. Grandclement, and G. Grynberg, "Continuous-wave self-oscillation using pair production of photons in four-wave mixing in sodium," Europhys. Lett. 2, 755-760 (1986).

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C. Fort, L. Fallani, V. Guarrera, J. Lye, M. Modugno, D. Wiersma, and M. Inguscio, "Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide," Phys. Rev. Lett. 95, 170410 (2005).
[CrossRef]

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C. Mennerat-Robilliard, L. Guidoni, K. I. Petsas, P. Verkerk, J.-Y. Courtois, and G. Grynberg, "Bright optical lattices in a longitudinal magnetic field, experimental study of the oscillating and jumping regimes," Eur. Phys. J. D 1, 33-45 (1998).
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J. Guo, P. R. Berman, B. Dubetsky, and G. Grynberg, "Recoil-induced resonances in nonlinear spectroscopy," Phys. Rev. A 46, 1426-1437 (1992).
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D. V. Kupriyanov, I. M. Sokolov, P. Kulatunga, C. I. Sukenik, and M. D. Havey, "Coherent backscattering of light in atomic systems: application to weak localization in an ensemble of cold alkali-metal atoms," Phys. Rev. A 67, 013814 (2003).
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L. Hilico, C. Fabre, and E. Giacobino, "Operation of a 'cold-atom laser' in a magneto-optical trap," Europhys. Lett. 18, 685-688 (1992).

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J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, "Nonlinear spectroscopy of cold atoms in a spontaneous-force optical trap," Phys. Rev. Lett. 66, 3245-3248 (1991).
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Y.-C. Chen, Y.-W. Chen, J.-J. Su, J.-Y. Huang, and I. A. Yu, "Pump-probe spectroscopy of cold Rb87 atoms in various polarization configurations," Phys. Rev. A 63, 043808 (2001).
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D. Clément, A. Varón, M. Hugbart, J. Retter, P. Bouyer, L. Sanchez-Palencia, D. Gangardt, G. Shlyapnikov, and A. Aspect, "Suppression of transport of an interacting elongated Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 170409 (2005).
[CrossRef]

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J. E. Lye, L. Fallani, M. Modugno, D. Wiersma, C. Fort, and M. Inguscio, "A Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 070401 (2005).
[CrossRef]

C. Fort, L. Fallani, V. Guarrera, J. Lye, M. Modugno, D. Wiersma, and M. Inguscio, "Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide," Phys. Rev. Lett. 95, 170410 (2005).
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G. L. Gattobigio, F. Michaud, J. Javaloyes, J. W. R. Tabosa, and R. Kaiser, "Bunching induced asymmetry in degenerate four-wave mixing with cold atoms," Phys. Rev. A 74, 043407 (2006).
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S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
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G. L. Gattobigio, F. Michaud, J. Javaloyes, J. W. R. Tabosa, and R. Kaiser, "Bunching induced asymmetry in degenerate four-wave mixing with cold atoms," Phys. Rev. A 74, 043407 (2006).
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G. Labeyrie, E. Vaujour, C. A. Müller, D. Delande, C. Miniatura, D. Wilkowski, and R. Kaiser, "Slow diffusion of light in a cold atomic cloud," Phys. Rev. Lett. 91, 223904 (2003).
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Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, and R. Kaiser, "Coherent light transport in a cold strontium cloud," Phys. Rev. Lett. 88, 203902 (2002).
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G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, Ch. Miniatura, and R. Kaiser, "Coherent backscattering of light by cold atoms," Phys. Rev. Lett. 83, 5266-5269 (1999).
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J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, "Nonlinear spectroscopy of cold atoms in a spontaneous-force optical trap," Phys. Rev. Lett. 66, 3245-3248 (1991).
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Klappauf, B.

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, and R. Kaiser, "Coherent light transport in a cold strontium cloud," Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef]

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C. von Cube, S. Slama, D. Kruse, C. Zimmermann, Ph. W. Courteille, G. R. M. Robb, N. Piovella, and R. Bonifacio, Phys. Rev. Lett. 93, 083601 (2004).
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Kruse, J.

T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. Arlt, K. Sacha, J. Zakrzewski, and M. Lewenstein, "Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices," Phys. Rev. Lett. 95, 170411 (2005).
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Y. Kuga and A. Ishimaru, "Retroreflectance from a dense distribution of spherical particles," J. Opt. Soc. Am. A 8, 831-836 (1984).

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D. V. Kupriyanov, I. M. Sokolov, P. Kulatunga, C. I. Sukenik, and M. D. Havey, "Coherent backscattering of light in atomic systems: application to weak localization in an ensemble of cold alkali-metal atoms," Phys. Rev. A 67, 013814 (2003).
[CrossRef]

Kupriyanov, D. V.

D. V. Kupriyanov, I. M. Sokolov, P. Kulatunga, C. I. Sukenik, and M. D. Havey, "Coherent backscattering of light in atomic systems: application to weak localization in an ensemble of cold alkali-metal atoms," Phys. Rev. A 67, 013814 (2003).
[CrossRef]

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G. Labeyrie, E. Vaujour, C. A. Müller, D. Delande, C. Miniatura, D. Wilkowski, and R. Kaiser, "Slow diffusion of light in a cold atomic cloud," Phys. Rev. Lett. 91, 223904 (2003).
[CrossRef]

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, and R. Kaiser, "Coherent light transport in a cold strontium cloud," Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef]

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, Ch. Miniatura, and R. Kaiser, "Coherent backscattering of light by cold atoms," Phys. Rev. Lett. 83, 5266-5269 (1999).
[CrossRef]

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D. S. Wiersma, J. Gomez Rivas, P. Bartolini, A. Lagendijk, and R. Righini, "Wiersma reply," Nature 398, 207 (1999).
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D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, "Localization of light in a disordered medium," Nature 390, 671-673 (1997).
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A. Lambrecht, J. M. Courty, S. Reynaud, and E. Giacobino, "Cold atoms: a new medium for quantum optics," Appl. Phys. B 60, 129-134 (1995).

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N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, "Laser action in strongly scattering media," Nature 369, 436-438 (1994).

le Bihan, E.

G. Grynberg, E. le Bihan, P. Verkerk, and M. Ducloy, "Observation of instabilities due to mirrorless four-wave mixing oscillation in sodium," Opt. Commun. 67, 363-366 (1988).
[CrossRef]

Lee, R. B.

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, "Nonlinear spectroscopy of cold atoms in a spontaneous-force optical trap," Phys. Rev. Lett. 66, 3245-3248 (1991).
[CrossRef]

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F. Scheffold, R. Lenke, R. Tweer, and G. Maret, "Localization or classical diffusion of light," Nature 398, 206-207 (1999).
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V. S. Letokhov, "Generation of light by a scattering medium with negative resonance absorption," Zh. Eksp. Teor. Fiz. 53, 1442-1452 (1967) [V. S. Letokhov, Sov. Phys. JETP 26, 835-840 (1968)].

Lewenstein, M.

T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. Arlt, K. Sacha, J. Zakrzewski, and M. Lewenstein, "Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices," Phys. Rev. Lett. 95, 170411 (2005).
[CrossRef]

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A. Lezama, G. C. Cardoso, and J. W. R. Tabosa, "Polarization dependence of four-wave mixing in a degenerate two-level system," Phys. Rev. A 63, 013805 (2001).
[CrossRef]

Lounis, B.

J.-Y. Courtois, G. Grynberg, B. Lounis, and P. Verkerk, "Recoil-induced resonances in cesium: an atomic analog to the free-electron laser," Phys. Rev. Lett. 72, 3017-3020 (1994).
[CrossRef]

D. Grison, B. Lounis, C. Salomon, J.-Y. Courtois, and G. Grynberg, "Raman spectroscopy of cesium atoms in a laser trap," Europhys. Lett. 15, 149-154 (1991).

Lye, J.

C. Fort, L. Fallani, V. Guarrera, J. Lye, M. Modugno, D. Wiersma, and M. Inguscio, "Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide," Phys. Rev. Lett. 95, 170410 (2005).
[CrossRef]

Lye, J. E.

J. E. Lye, L. Fallani, M. Modugno, D. Wiersma, C. Fort, and M. Inguscio, "A Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 070401 (2005).
[CrossRef]

Maret, G.

C. M. Aegerter, M. Störzer, and G. Maret, "Experimental determination of critical exponents in Anderson localization of light," Europhys. Lett. 75, 562-568 (2006).
[CrossRef]

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, "Localization or classical diffusion of light," Nature 398, 206-207 (1999).
[CrossRef]

P.-E. Wolf and G. Maret, "Weak localization and coherent backscattering of photons in disordered media," Phys. Rev. Lett. 55, 2696-2699 (1985).
[CrossRef]

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C. Mennerat-Robilliard, L. Guidoni, K. I. Petsas, P. Verkerk, J.-Y. Courtois, and G. Grynberg, "Bright optical lattices in a longitudinal magnetic field, experimental study of the oscillating and jumping regimes," Eur. Phys. J. D 1, 33-45 (1998).
[CrossRef]

Michaud, F.

G. L. Gattobigio, F. Michaud, J. Javaloyes, J. W. R. Tabosa, and R. Kaiser, "Bunching induced asymmetry in degenerate four-wave mixing with cold atoms," Phys. Rev. A 74, 043407 (2006).
[CrossRef]

Miniatura, C.

G. Labeyrie, E. Vaujour, C. A. Müller, D. Delande, C. Miniatura, D. Wilkowski, and R. Kaiser, "Slow diffusion of light in a cold atomic cloud," Phys. Rev. Lett. 91, 223904 (2003).
[CrossRef]

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, and R. Kaiser, "Coherent light transport in a cold strontium cloud," Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef]

Miniatura, Ch.

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, Ch. Miniatura, and R. Kaiser, "Coherent backscattering of light by cold atoms," Phys. Rev. Lett. 83, 5266-5269 (1999).
[CrossRef]

Modugno, M.

C. Fort, L. Fallani, V. Guarrera, J. Lye, M. Modugno, D. Wiersma, and M. Inguscio, "Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide," Phys. Rev. Lett. 95, 170410 (2005).
[CrossRef]

J. E. Lye, L. Fallani, M. Modugno, D. Wiersma, C. Fort, and M. Inguscio, "A Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 070401 (2005).
[CrossRef]

Mollow, B. R.

F. Y. Wu, S. Ezekiel, M. Ducloy, and B. R. Mollow, "Observation of amplification in a strongly driven two-level atomic system at optical frequencies," Phys. Rev. Lett. 38, 1077-1080 (1977).
[CrossRef]

Müller, C. A.

G. Labeyrie, E. Vaujour, C. A. Müller, D. Delande, C. Miniatura, D. Wilkowski, and R. Kaiser, "Slow diffusion of light in a cold atomic cloud," Phys. Rev. Lett. 91, 223904 (2003).
[CrossRef]

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, Ch. Miniatura, and R. Kaiser, "Coherent backscattering of light by cold atoms," Phys. Rev. Lett. 83, 5266-5269 (1999).
[CrossRef]

Novikov, A.

Obukhovski, V.

Odoulov, S.

Petsas, K. I.

C. Mennerat-Robilliard, L. Guidoni, K. I. Petsas, P. Verkerk, J.-Y. Courtois, and G. Grynberg, "Bright optical lattices in a longitudinal magnetic field, experimental study of the oscillating and jumping regimes," Eur. Phys. J. D 1, 33-45 (1998).
[CrossRef]

Pinard, M.

M. Pinard, D. Grandclement, and G. Grynberg, "Continuous-wave self-oscillation using pair production of photons in four-wave mixing in sodium," Europhys. Lett. 2, 755-760 (1986).

Piovella, N.

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, Ph. W. Courteille, G. R. M. Robb, N. Piovella, and R. Bonifacio, Phys. Rev. Lett. 93, 083601 (2004).
[CrossRef]

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M. Vengalattore and M. Prentiss, "Recoil-induced resonances in the high-gain regime," Phys. Rev. A 72, 021401(R) (2005).
[CrossRef]

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D. Clément, A. Varón, M. Hugbart, J. Retter, P. Bouyer, L. Sanchez-Palencia, D. Gangardt, G. Shlyapnikov, and A. Aspect, "Suppression of transport of an interacting elongated Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 170409 (2005).
[CrossRef]

Reynaud, S.

A. Lambrecht, J. M. Courty, S. Reynaud, and E. Giacobino, "Cold atoms: a new medium for quantum optics," Appl. Phys. B 60, 129-134 (1995).

Righini, R.

D. S. Wiersma, J. Gomez Rivas, P. Bartolini, A. Lagendijk, and R. Righini, "Wiersma reply," Nature 398, 207 (1999).
[CrossRef]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, "Localization of light in a disordered medium," Nature 390, 671-673 (1997).
[CrossRef]

Robb, G. R. M.

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, Ph. W. Courteille, G. R. M. Robb, N. Piovella, and R. Bonifacio, Phys. Rev. Lett. 93, 083601 (2004).
[CrossRef]

Robillard, C.

G. Grynberg and C. Robillard, "Cold atoms in dissipative optical lattices," Phys. Rep. 355, 335-451 (2001).
[CrossRef]

Sacha, K.

T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. Arlt, K. Sacha, J. Zakrzewski, and M. Lewenstein, "Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices," Phys. Rev. Lett. 95, 170411 (2005).
[CrossRef]

Salomon, C.

D. Grison, B. Lounis, C. Salomon, J.-Y. Courtois, and G. Grynberg, "Raman spectroscopy of cesium atoms in a laser trap," Europhys. Lett. 15, 149-154 (1991).

Sanchez-Palencia, L.

D. Clément, A. Varón, M. Hugbart, J. Retter, P. Bouyer, L. Sanchez-Palencia, D. Gangardt, G. Shlyapnikov, and A. Aspect, "Suppression of transport of an interacting elongated Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 170409 (2005).
[CrossRef]

Sauvain, E.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, "Laser action in strongly scattering media," Nature 369, 436-438 (1994).

Scheffold, F.

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, "Localization or classical diffusion of light," Nature 398, 206-207 (1999).
[CrossRef]

Schulte, T.

T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. Arlt, K. Sacha, J. Zakrzewski, and M. Lewenstein, "Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices," Phys. Rev. Lett. 95, 170411 (2005).
[CrossRef]

Shlyapnikov, G.

D. Clément, A. Varón, M. Hugbart, J. Retter, P. Bouyer, L. Sanchez-Palencia, D. Gangardt, G. Shlyapnikov, and A. Aspect, "Suppression of transport of an interacting elongated Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 170409 (2005).
[CrossRef]

Slama, S.

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, Ph. W. Courteille, G. R. M. Robb, N. Piovella, and R. Bonifacio, Phys. Rev. Lett. 93, 083601 (2004).
[CrossRef]

Sokolov, I. M.

D. V. Kupriyanov, I. M. Sokolov, P. Kulatunga, C. I. Sukenik, and M. D. Havey, "Coherent backscattering of light in atomic systems: application to weak localization in an ensemble of cold alkali-metal atoms," Phys. Rev. A 67, 013814 (2003).
[CrossRef]

Störzer, M.

C. M. Aegerter, M. Störzer, and G. Maret, "Experimental determination of critical exponents in Anderson localization of light," Europhys. Lett. 75, 562-568 (2006).
[CrossRef]

Stoytchev, M.

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, "Statistical approach to photon localization," Nature 404, 850-853 (2000).
[CrossRef]

Sturman, B.

Su, J.-J.

Y.-C. Chen, Y.-W. Chen, J.-J. Su, J.-Y. Huang, and I. A. Yu, "Pump-probe spectroscopy of cold Rb87 atoms in various polarization configurations," Phys. Rev. A 63, 043808 (2001).
[CrossRef]

Sukenik, C. I.

D. V. Kupriyanov, I. M. Sokolov, P. Kulatunga, C. I. Sukenik, and M. D. Havey, "Coherent backscattering of light in atomic systems: application to weak localization in an ensemble of cold alkali-metal atoms," Phys. Rev. A 67, 013814 (2003).
[CrossRef]

Tabosa, J. W. R.

G. L. Gattobigio, F. Michaud, J. Javaloyes, J. W. R. Tabosa, and R. Kaiser, "Bunching induced asymmetry in degenerate four-wave mixing with cold atoms," Phys. Rev. A 74, 043407 (2006).
[CrossRef]

A. Lezama, G. C. Cardoso, and J. W. R. Tabosa, "Polarization dependence of four-wave mixing in a degenerate two-level system," Phys. Rev. A 63, 013805 (2001).
[CrossRef]

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M. P. van Albada and A. Lagendijk, "Observation of weak localization of light in a random medium," Phys. Rev. Lett. 55, 2692-2695 (1985).
[CrossRef]

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D. Clément, A. Varón, M. Hugbart, J. Retter, P. Bouyer, L. Sanchez-Palencia, D. Gangardt, G. Shlyapnikov, and A. Aspect, "Suppression of transport of an interacting elongated Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 170409 (2005).
[CrossRef]

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G. Labeyrie, E. Vaujour, C. A. Müller, D. Delande, C. Miniatura, D. Wilkowski, and R. Kaiser, "Slow diffusion of light in a cold atomic cloud," Phys. Rev. Lett. 91, 223904 (2003).
[CrossRef]

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M. Vengalattore and M. Prentiss, "Recoil-induced resonances in the high-gain regime," Phys. Rev. A 72, 021401(R) (2005).
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[CrossRef]

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C. von Cube, S. Slama, D. Kruse, C. Zimmermann, Ph. W. Courteille, G. R. M. Robb, N. Piovella, and R. Bonifacio, Phys. Rev. Lett. 93, 083601 (2004).
[CrossRef]

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C. Fort, L. Fallani, V. Guarrera, J. Lye, M. Modugno, D. Wiersma, and M. Inguscio, "Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide," Phys. Rev. Lett. 95, 170410 (2005).
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[CrossRef]

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G. Labeyrie, E. Vaujour, C. A. Müller, D. Delande, C. Miniatura, D. Wilkowski, and R. Kaiser, "Slow diffusion of light in a cold atomic cloud," Phys. Rev. Lett. 91, 223904 (2003).
[CrossRef]

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, and R. Kaiser, "Coherent light transport in a cold strontium cloud," Phys. Rev. Lett. 88, 203902 (2002).
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[CrossRef]

Yu, I. A.

Y.-C. Chen, Y.-W. Chen, J.-J. Su, J.-Y. Huang, and I. A. Yu, "Pump-probe spectroscopy of cold Rb87 atoms in various polarization configurations," Phys. Rev. A 63, 043808 (2001).
[CrossRef]

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T. M. Brzozowski, M. Brzozowska, J. Zachorowski, M. Zawada, and W. Gawlik, "Probe spectroscopy in an operating magneto-optical trap: the role of Raman transitions between discrete and continuum atomic states," Phys. Rev. A 71, 013401 (2005).
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T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. Arlt, K. Sacha, J. Zakrzewski, and M. Lewenstein, "Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices," Phys. Rev. Lett. 95, 170411 (2005).
[CrossRef]

Zawada, M.

T. M. Brzozowski, M. Brzozowska, J. Zachorowski, M. Zawada, and W. Gawlik, "Probe spectroscopy in an operating magneto-optical trap: the role of Raman transitions between discrete and continuum atomic states," Phys. Rev. A 71, 013401 (2005).
[CrossRef]

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A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, "Breakdown of diffusion in dynamics of extended waves in mesoscopic media," Phys. Rev. Lett. 90, 203903 (2003).
[CrossRef]

Zimmermann, C.

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, Ph. W. Courteille, G. R. M. Robb, N. Piovella, and R. Bonifacio, Phys. Rev. Lett. 93, 083601 (2004).
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[CrossRef]

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Nature (5)

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[CrossRef]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, "Localization of light in a disordered medium," Nature 390, 671-673 (1997).
[CrossRef]

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, "Localization or classical diffusion of light," Nature 398, 206-207 (1999).
[CrossRef]

D. S. Wiersma, J. Gomez Rivas, P. Bartolini, A. Lagendijk, and R. Righini, "Wiersma reply," Nature 398, 207 (1999).
[CrossRef]

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Opt. Commun. (1)

G. Grynberg, E. le Bihan, P. Verkerk, and M. Ducloy, "Observation of instabilities due to mirrorless four-wave mixing oscillation in sodium," Opt. Commun. 67, 363-366 (1988).
[CrossRef]

Opt. Lett. (1)

Phys. Rep. (1)

G. Grynberg and C. Robillard, "Cold atoms in dissipative optical lattices," Phys. Rep. 355, 335-451 (2001).
[CrossRef]

Phys. Rev. (1)

P. W. Anderson, "Absence of diffusion in certain random lattices," Phys. Rev. 109, 1492-1505 (1958).
[CrossRef]

Phys. Rev. A (8)

D. V. Kupriyanov, I. M. Sokolov, P. Kulatunga, C. I. Sukenik, and M. D. Havey, "Coherent backscattering of light in atomic systems: application to weak localization in an ensemble of cold alkali-metal atoms," Phys. Rev. A 67, 013814 (2003).
[CrossRef]

T. M. Brzozowski, M. Brzozowska, J. Zachorowski, M. Zawada, and W. Gawlik, "Probe spectroscopy in an operating magneto-optical trap: the role of Raman transitions between discrete and continuum atomic states," Phys. Rev. A 71, 013401 (2005).
[CrossRef]

J. Guo, P. R. Berman, B. Dubetsky, and G. Grynberg, "Recoil-induced resonances in nonlinear spectroscopy," Phys. Rev. A 46, 1426-1437 (1992).
[CrossRef]

M. Vengalattore and M. Prentiss, "Recoil-induced resonances in the high-gain regime," Phys. Rev. A 72, 021401(R) (2005).
[CrossRef]

G. L. Gattobigio, F. Michaud, J. Javaloyes, J. W. R. Tabosa, and R. Kaiser, "Bunching induced asymmetry in degenerate four-wave mixing with cold atoms," Phys. Rev. A 74, 043407 (2006).
[CrossRef]

A. Lezama, G. C. Cardoso, and J. W. R. Tabosa, "Polarization dependence of four-wave mixing in a degenerate two-level system," Phys. Rev. A 63, 013805 (2001).
[CrossRef]

J. Guo, "Contribution of energy continuum states to probe the absorption signal of atoms in one-dimensional optical molasses," Phys. Rev. A 49, 3934-3942 (1994).
[CrossRef]

Y.-C. Chen, Y.-W. Chen, J.-J. Su, J.-Y. Huang, and I. A. Yu, "Pump-probe spectroscopy of cold Rb87 atoms in various polarization configurations," Phys. Rev. A 63, 043808 (2001).
[CrossRef]

Phys. Rev. E (1)

H. Cao, Y. Xu, S.-H. Chang, and S. T. Ho, "Transition from amplified spontaneous emission to laser action in strongly scattering media," Phys. Rev. E 61, 1985-1989 (2000).
[CrossRef]

Phys. Rev. Lett. (15)

Y. Bidel, B. Klappauf, J. C. Bernard, D. Delande, G. Labeyrie, C. Miniatura, D. Wilkowski, and R. Kaiser, "Coherent light transport in a cold strontium cloud," Phys. Rev. Lett. 88, 203902 (2002).
[CrossRef]

G. Labeyrie, E. Vaujour, C. A. Müller, D. Delande, C. Miniatura, D. Wilkowski, and R. Kaiser, "Slow diffusion of light in a cold atomic cloud," Phys. Rev. Lett. 91, 223904 (2003).
[CrossRef]

F. Y. Wu, S. Ezekiel, M. Ducloy, and B. R. Mollow, "Observation of amplification in a strongly driven two-level atomic system at optical frequencies," Phys. Rev. Lett. 38, 1077-1080 (1977).
[CrossRef]

J. W. R. Tabosa, G. Chen, Z. Hu, R. B. Lee, and H. J. Kimble, "Nonlinear spectroscopy of cold atoms in a spontaneous-force optical trap," Phys. Rev. Lett. 66, 3245-3248 (1991).
[CrossRef]

C. von Cube, S. Slama, D. Kruse, C. Zimmermann, Ph. W. Courteille, G. R. M. Robb, N. Piovella, and R. Bonifacio, Phys. Rev. Lett. 93, 083601 (2004).
[CrossRef]

J.-Y. Courtois, G. Grynberg, B. Lounis, and P. Verkerk, "Recoil-induced resonances in cesium: an atomic analog to the free-electron laser," Phys. Rev. Lett. 72, 3017-3020 (1994).
[CrossRef]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef]

D. Clément, A. Varón, M. Hugbart, J. Retter, P. Bouyer, L. Sanchez-Palencia, D. Gangardt, G. Shlyapnikov, and A. Aspect, "Suppression of transport of an interacting elongated Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 170409 (2005).
[CrossRef]

C. Fort, L. Fallani, V. Guarrera, J. Lye, M. Modugno, D. Wiersma, and M. Inguscio, "Effect of optical disorder and single defects on the expansion of a Bose-Einstein condensate in a one-dimensional waveguide," Phys. Rev. Lett. 95, 170410 (2005).
[CrossRef]

J. E. Lye, L. Fallani, M. Modugno, D. Wiersma, C. Fort, and M. Inguscio, "A Bose-Einstein condensate in a random potential," Phys. Rev. Lett. 95, 070401 (2005).
[CrossRef]

T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. Arlt, K. Sacha, J. Zakrzewski, and M. Lewenstein, "Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices," Phys. Rev. Lett. 95, 170411 (2005).
[CrossRef]

P.-E. Wolf and G. Maret, "Weak localization and coherent backscattering of photons in disordered media," Phys. Rev. Lett. 55, 2696-2699 (1985).
[CrossRef]

M. P. van Albada and A. Lagendijk, "Observation of weak localization of light in a random medium," Phys. Rev. Lett. 55, 2692-2695 (1985).
[CrossRef]

G. Labeyrie, F. de Tomasi, J.-C. Bernard, C. A. Müller, Ch. Miniatura, and R. Kaiser, "Coherent backscattering of light by cold atoms," Phys. Rev. Lett. 83, 5266-5269 (1999).
[CrossRef]

A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, "Breakdown of diffusion in dynamics of extended waves in mesoscopic media," Phys. Rev. Lett. 90, 203903 (2003).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

V. S. Letokhov, "Generation of light by a scattering medium with negative resonance absorption," Zh. Eksp. Teor. Fiz. 53, 1442-1452 (1967) [V. S. Letokhov, Sov. Phys. JETP 26, 835-840 (1968)].

Other (1)

J. Y. Courtois, "Spectroscopie Raman et Rayleigh stimulie d'atomes refroidis par laser: dynamique des mélasses optiques unidimensionnelles," Ph.D. dissertation (Ecole Polytechnique, 1993).

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Figures (9)

Fig. 1
Fig. 1

(a) Schematic of the experiment: two strong counterpropagating pump beams (F and B with parallel linear polarization) and one weak probe beam (P with linear polarization orthogonal to that of F and B) are applied; an additional mirror (M) has been used for double-pass gain (see text) and either transmission ( T ) or reflection ( R ) through a beam splitter (BS) has been recorded; (b) timing of the experiment: the MOT beams and magnetic fields are switched off during the short pump–probe pulse.

Fig. 2
Fig. 2

NDFWM spectrum obtained in the F B P configuration. The pump frequency ( Δ = 4.8 Γ ) and intensity ( s F , B = 23 , s P = 0.01 ) are kept fixed as the detuning δ = ω P of the probe beam P is scanned across the NDFWM resonance. Note that the scale of the detuning scan shown here is covering a smaller range than in the subsequent figures.

Fig. 3
Fig. 3

Gain spectrum for F B P polarization. (a) for the quasi-co-propagating pump ( F ) and probe ( P ) beams ( s F = 30 and Δ = 3 Γ ). A distinctive gain of 100 % is seen at the Raman condition, for δ = ω Raman . (b) For the quasi-counter-propagating pump ( B ) and probe ( P ) beams ( s B = 30 and Δ = 3 Γ ) no gain is observed.

Fig. 4
Fig. 4

Raman gain mechanism. (a) Gain spectrum for negative pump detuning and corresponding gain spectrum ( Δ = 5.2 Γ , s F = 30 , s P = 0.07 ). (b) Gain spectrum for positive pump detuning and corresponding gain spectrum ( Δ = + 5.2 Γ , s F = 30 , s p = 0.07 ). Insets indicate the different light shifts and populations corresponding to the gain part of each curve.

Fig. 5
Fig. 5

Gain saturation. Maximum of the gain spectra for different probe intensities at fixed-pump parameters ( s F = 6.8 and Δ = 3 Γ ).

Fig. 6
Fig. 6

Maximum of gain spectra as a function of the (resonant) optical thickness of the cloud, varied by changing the atom number ( s F = 30 , Δ = 3 Γ , and s P = 0.07 ).

Fig. 7
Fig. 7

Maximum of gain spectra as a function of pump detuning Δ at maximum atom number ( N at = 10 10 ) for s F = 30 and s P = 0.07 .

Fig. 8
Fig. 8

Double-pass gain spectrum as a function of pump detuning δ ( Δ = 4.5 Γ , s F , B = 23 , s P = 0.01 at maximum atom number N at = 10 10 ).

Fig. 9
Fig. 9

Simulated double-pass gain spectrum using the experimental FWM result and Raman gain curve as input. (a) Only one interference term between the FWM and the Raman gain is included [see Eq. (4)]. (b) Multiple reflections between the atomic cloud and the back mirror are included [see Eq. (5)]. The signal depends crucially on the distance between the atomic cloud and the mirror ( L 0.2 m ) .

Equations (5)

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g e N at ( π a π b ) f ( δ ) ,
f ( δ ) = A 1 ( δ ω Raman ) 2 + γ 2 4 A 2 ( δ + ω Raman ) 2 + γ 2 4 ,
ω C = 2 ω F , B ω P .
I 1 = r c e i ( ω p 2 δ ) t + t F t B e i ω p t e i ϕ 2 ,
I 2 = r c e i ( ω p 2 δ ) t + t F t B n r c 2 n e 2 n i ϕ e i ω p t + t F t B n r c 2 n + 1 e ( 2 n + 1 ) i ϕ e i ( ω p 2 δ ) t 2 .

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