Abstract

We address the problem of achieving a random laser with a cloud of cold atoms, in which gain and scattering are provided by the same atoms. In this system, the elastic scattering cross-section is related to the complex atomic polarizability. As a consequence, the random laser threshold is expressed as a function of this polarizability, which can be fully determined by spectroscopic measurements. We apply this idea to experimentally evaluate the threshold of a random laser based on Raman gain between non-degenerate Zeeman states and find a critical optical thickness on the order of 200, which is within reach of state-of-the-art cold-atom experiments.

©2009 Optical Society of America

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  1. V. S. Letokhov, “Generation of light by a scattering medium with negative resonance absorption,” Sov. Phys. JETP 26, 835–840 (1968).
  2. C. Gouedard, D. Husson, D. Sauteret, F. Auzel, and A. Migus, “Generation of spatially incoherent short pulses in laser-pumped neodymium stoichiometric crystals and powders,” J. Opt. Soc. Am. B 10, 2358–2362 (1993).
    [Crossref]
  3. J. Martorell, R. M. Balachandran, and N. M. Lawandy, “Radiative coupling between photonic paint layers,” Opt. Lett. 21, 239–241 (1996).
    [Crossref] [PubMed]
  4. H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet Lasing in Resonators Formed by Scattering in Semiconductor Polycrystalline Films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
    [Crossref]
  5. D. S. Wiersma and S. Cavalier, “Light emission: A temperature-tunable random laser,” Nature 414, 708–709 (2001).
    [Crossref] [PubMed]
  6. G. Strangi, S. Ferjani, V. Barna, A. D. Luca, C. Versace, N. Scaramuzza, and R. Bartolino, “Random lasing and weak localization of light in dye-doped nematic liquid crystals,” Opt. Express 14, 7737–7744 (2006).
    [Crossref] [PubMed]
  7. D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
    [Crossref]
  8. A. L. Burin, M. A. Ratner, H. Cao, and R. P. H. Chang, “Model for a Random Laser,” Phys. Rev. Lett. 87, 215503 (2001).
    [Crossref] [PubMed]
  9. C. Vanneste, P. Sebbah, and H. Cao, “Lasing with Resonant Feedback in Weakly Scattering Random Systems,” Phys. Rev. Lett. 98, 143902 (2007).
    [Crossref] [PubMed]
  10. H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong Interactions in Multimode Random Lasers,” Science 320, 643–646 (2008).
    [Crossref] [PubMed]
  11. D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4, 359–367 (2008).
    [Crossref]
  12. C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4, 794–798 (2008).
    [Crossref]
  13. H. Cao, “Lasing in random media,” Waves Random Media 13, R1–R39 (2003).
    [Crossref]
  14. H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
    [Crossref]
  15. H. Metcalf and P. van der Straten, Laser cooling and Trapping (Springer, New York, 1999).
    [Crossref]
  16. A. Fioretti, A. F. Molisch, J. H. Mutter, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415–422 (1998).
    [Crossref]
  17. 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] [PubMed]
  18. L. Hilico, C. Fabre, and E. Giacobino, “Operation of a “Cold-Atom Laser” in a Magneto-Optical Trap,” Europhys. Lett. 18, 685–688 (1992).
    [Crossref]
  19. W. Guerin, F. Michaud, and R. Kaiser, “Mechanisms for Lasing with Cold Atoms as the Gain Medium,” Phys. Rev. Lett. 101, 093002 (2008).
    [Crossref] [PubMed]
  20. Note that even though new interesting features appear when coherent feedback is involved [14], we will consider only incoherent (intensity) feedback.
  21. L. S. Froufe-Pérez, W. Guerin, R. Carminati, and R. Kaiser, “Threshold of a Random Laser with Cold Atoms,” Phys. Rev. Lett. 102, 173903 (2009).
    [Crossref] [PubMed]
  22. B. R. Mollow, “Stimulated Emission and Absorption near Resonance for Driven Systems,” Phys. Rev. A 5, 2217–2222 (1972).
    [Crossref]
  23. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).
  24. 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).
    [Crossref]
  25. 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] [PubMed]
  26. M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
    [Crossref]
  27. We consider only isotropic scattering so that the transport length equals the scattering mean free path [26].
  28. K. Case and P. Zweifel, Linear transport theory (Addison-Wesley, 1967).
  29. K. Drozdowicz, E. Krynicka, and J. Dąbrowska, “Diffusion cooling of thermal neutrons in basic rock minerals by Monte Carlo simulation of the pulsed neutron experiments,” App. Rad. Isot. 58, 727–733 (2003).
    [Crossref]
  30. A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
    [Crossref]
  31. D. Brivio, “Random laser with cold atoms: extracting information from atomic fluorescence,” Master Thesis, Università di Milano (2008).
  32. 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]
  33. G. Grynberg and C. Robilliard, “Cold atoms in dissipative optical lattices,” Phys. Rep. 355, 335–451 (2001).
    [Crossref]
  34. Y.-C. Chen, Y.-W. Chen, J.-J. Su, J.-Y. Huang, and I. A. Yu, “Pump-probe spectroscopy of cold 87Rb atoms in various polarization configurations,” Phys. Rev. A 63, 043808 (2001).
    [Crossref]
  35. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley, New York, 1992).
  36. B. Gao, “Effects of Zeeman degeneracy on the steady-state properties of an atom interacting with a near-resonant laser field: Resonance fluorescence,” Phys. Rev. A 50, 4139–4156 (1994).
    [Crossref] [PubMed]
  37. B. R. Mollow, “Power Spectrum of Light Scattered by Two-Level Systems,” Phys. Rev. 188, 1969–1975 (1969).
    [Crossref]
  38. W. Ketterle, K. B. Davis, M. A. Joffre, A. Pritchard, and D. E. Martin, “High Densities of Cold Atoms in a Dark Spontaneous-Force trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
    [Crossref] [PubMed]
  39. M. T. dePue, S. L. Winoto, D. J. Han, and D. S. Weiss, “Transient compression of a MOT and high intensity fluorescent imaging of optically thick clouds of atoms,” Opt. Commun. 180, 73–79 (2000).
    [Crossref]
  40. C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a three-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
    [Crossref] [PubMed]
  41. C. Jurczak, K. Sengstock, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Observation of intensity correlations in the fluorescence from laser cooled atoms,” Opt. Commun. 115, 480–484 (1995).
    [Crossref]
  42. S. Bali, D. Hoffmann, J. Simán, and T. Walker, “Measurements of intensity correlations of scattered light from laser-cooled atoms,” Phys. Rev. A 53, 3469–3472 (1996).
    [Crossref] [PubMed]
  43. M. A. Noginov, J. Novak, D. Grigsby, and L. Deych, “Applicability of the diffusion model to random lasers with non-resonant feedback,” J. Opt. A: Pure Appl. Opt. 8, S285–S295 (2006).
    [Crossref]

2009 (1)

L. S. Froufe-Pérez, W. Guerin, R. Carminati, and R. Kaiser, “Threshold of a Random Laser with Cold Atoms,” Phys. Rev. Lett. 102, 173903 (2009).
[Crossref] [PubMed]

2008 (4)

W. Guerin, F. Michaud, and R. Kaiser, “Mechanisms for Lasing with Cold Atoms as the Gain Medium,” Phys. Rev. Lett. 101, 093002 (2008).
[Crossref] [PubMed]

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong Interactions in Multimode Random Lasers,” Science 320, 643–646 (2008).
[Crossref] [PubMed]

D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4, 359–367 (2008).
[Crossref]

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4, 794–798 (2008).
[Crossref]

2007 (1)

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with Resonant Feedback in Weakly Scattering Random Systems,” Phys. Rev. Lett. 98, 143902 (2007).
[Crossref] [PubMed]

2006 (2)

G. Strangi, S. Ferjani, V. Barna, A. D. Luca, C. Versace, N. Scaramuzza, and R. Bartolino, “Random lasing and weak localization of light in dye-doped nematic liquid crystals,” Opt. Express 14, 7737–7744 (2006).
[Crossref] [PubMed]

M. A. Noginov, J. Novak, D. Grigsby, and L. Deych, “Applicability of the diffusion model to random lasers with non-resonant feedback,” J. Opt. A: Pure Appl. Opt. 8, S285–S295 (2006).
[Crossref]

2005 (2)

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (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]

2003 (3)

K. Drozdowicz, E. Krynicka, and J. Dąbrowska, “Diffusion cooling of thermal neutrons in basic rock minerals by Monte Carlo simulation of the pulsed neutron experiments,” App. Rad. Isot. 58, 727–733 (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] [PubMed]

H. Cao, “Lasing in random media,” Waves Random Media 13, R1–R39 (2003).
[Crossref]

2001 (4)

D. S. Wiersma and S. Cavalier, “Light emission: A temperature-tunable random laser,” Nature 414, 708–709 (2001).
[Crossref] [PubMed]

A. L. Burin, M. A. Ratner, H. Cao, and R. P. H. Chang, “Model for a Random Laser,” Phys. Rev. Lett. 87, 215503 (2001).
[Crossref] [PubMed]

G. Grynberg and C. Robilliard, “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 87Rb atoms in various polarization configurations,” Phys. Rev. A 63, 043808 (2001).
[Crossref]

2000 (1)

M. T. dePue, S. L. Winoto, D. J. Han, and D. S. Weiss, “Transient compression of a MOT and high intensity fluorescent imaging of optically thick clouds of atoms,” Opt. Commun. 180, 73–79 (2000).
[Crossref]

1999 (1)

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

1998 (2)

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet Lasing in Resonators Formed by Scattering in Semiconductor Polycrystalline Films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[Crossref]

A. Fioretti, A. F. Molisch, J. H. Mutter, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415–422 (1998).
[Crossref]

1996 (4)

J. Martorell, R. M. Balachandran, and N. M. Lawandy, “Radiative coupling between photonic paint layers,” Opt. Lett. 21, 239–241 (1996).
[Crossref] [PubMed]

D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
[Crossref]

A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[Crossref]

S. Bali, D. Hoffmann, J. Simán, and T. Walker, “Measurements of intensity correlations of scattered light from laser-cooled atoms,” Phys. Rev. A 53, 3469–3472 (1996).
[Crossref] [PubMed]

1995 (1)

C. Jurczak, K. Sengstock, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Observation of intensity correlations in the fluorescence from laser cooled atoms,” Opt. Commun. 115, 480–484 (1995).
[Crossref]

1994 (1)

B. Gao, “Effects of Zeeman degeneracy on the steady-state properties of an atom interacting with a near-resonant laser field: Resonance fluorescence,” Phys. Rev. A 50, 4139–4156 (1994).
[Crossref] [PubMed]

1993 (2)

W. Ketterle, K. B. Davis, M. A. Joffre, A. Pritchard, and D. E. Martin, “High Densities of Cold Atoms in a Dark Spontaneous-Force trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[Crossref] [PubMed]

C. Gouedard, D. Husson, D. Sauteret, F. Auzel, and A. Migus, “Generation of spatially incoherent short pulses in laser-pumped neodymium stoichiometric crystals and powders,” J. Opt. Soc. Am. B 10, 2358–2362 (1993).
[Crossref]

1992 (1)

L. Hilico, C. Fabre, and E. Giacobino, “Operation of a “Cold-Atom Laser” in a Magneto-Optical Trap,” Europhys. Lett. 18, 685–688 (1992).
[Crossref]

1991 (2)

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).
[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] [PubMed]

1990 (1)

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a three-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[Crossref] [PubMed]

1972 (1)

B. R. Mollow, “Stimulated Emission and Absorption near Resonance for Driven Systems,” Phys. Rev. A 5, 2217–2222 (1972).
[Crossref]

1969 (1)

B. R. Mollow, “Power Spectrum of Light Scattered by Two-Level Systems,” Phys. Rev. 188, 1969–1975 (1969).
[Crossref]

1968 (1)

V. S. Letokhov, “Generation of light by a scattering medium with negative resonance absorption,” Sov. Phys. JETP 26, 835–840 (1968).

Allegrini, M.

A. Fioretti, A. F. Molisch, J. H. Mutter, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415–422 (1998).
[Crossref]

Aspect, A.

C. Jurczak, K. Sengstock, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Observation of intensity correlations in the fluorescence from laser cooled atoms,” Opt. Commun. 115, 480–484 (1995).
[Crossref]

Auzel, F.

Balachandran, R. M.

Bali, S.

S. Bali, D. Hoffmann, J. Simán, and T. Walker, “Measurements of intensity correlations of scattered light from laser-cooled atoms,” Phys. Rev. A 53, 3469–3472 (1996).
[Crossref] [PubMed]

Barna, V.

Bartolino, R.

Brivio, D.

D. Brivio, “Random laser with cold atoms: extracting information from atomic fluorescence,” Master Thesis, Università di Milano (2008).

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]

Burin, A. L.

A. L. Burin, M. A. Ratner, H. Cao, and R. P. H. Chang, “Model for a Random Laser,” Phys. Rev. Lett. 87, 215503 (2001).
[Crossref] [PubMed]

Cao, H.

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with Resonant Feedback in Weakly Scattering Random Systems,” Phys. Rev. Lett. 98, 143902 (2007).
[Crossref] [PubMed]

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
[Crossref]

H. Cao, “Lasing in random media,” Waves Random Media 13, R1–R39 (2003).
[Crossref]

A. L. Burin, M. A. Ratner, H. Cao, and R. P. H. Chang, “Model for a Random Laser,” Phys. Rev. Lett. 87, 215503 (2001).
[Crossref] [PubMed]

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet Lasing in Resonators Formed by Scattering in Semiconductor Polycrystalline Films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[Crossref]

Carminati, R.

L. S. Froufe-Pérez, W. Guerin, R. Carminati, and R. Kaiser, “Threshold of a Random Laser with Cold Atoms,” Phys. Rev. Lett. 102, 173903 (2009).
[Crossref] [PubMed]

Case, K.

K. Case and P. Zweifel, Linear transport theory (Addison-Wesley, 1967).

Cavalier, S.

D. S. Wiersma and S. Cavalier, “Light emission: A temperature-tunable random laser,” Nature 414, 708–709 (2001).
[Crossref] [PubMed]

Chang, R. P. H.

A. L. Burin, M. A. Ratner, H. Cao, and R. P. H. Chang, “Model for a Random Laser,” Phys. Rev. Lett. 87, 215503 (2001).
[Crossref] [PubMed]

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet Lasing in Resonators Formed by Scattering in Semiconductor Polycrystalline Films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[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] [PubMed]

Chen, Y.-C.

Y.-C. Chen, Y.-W. Chen, J.-J. Su, J.-Y. Huang, and I. A. Yu, “Pump-probe spectroscopy of cold 87Rb 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 87Rb atoms in various polarization configurations,” Phys. Rev. A 63, 043808 (2001).
[Crossref]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley, New York, 1992).

Conti, C.

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4, 794–798 (2008).
[Crossref]

Courtois, J.-Y.

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).
[Crossref]

Dabrowska, J.

K. Drozdowicz, E. Krynicka, and J. Dąbrowska, “Diffusion cooling of thermal neutrons in basic rock minerals by Monte Carlo simulation of the pulsed neutron experiments,” App. Rad. Isot. 58, 727–733 (2003).
[Crossref]

Dai, J. Y.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet Lasing in Resonators Formed by Scattering in Semiconductor Polycrystalline Films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[Crossref]

Davis, K. B.

W. Ketterle, K. B. Davis, M. A. Joffre, A. Pritchard, and D. E. Martin, “High Densities of Cold Atoms in a Dark Spontaneous-Force trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[Crossref] [PubMed]

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] [PubMed]

dePue, M. T.

M. T. dePue, S. L. Winoto, D. J. Han, and D. S. Weiss, “Transient compression of a MOT and high intensity fluorescent imaging of optically thick clouds of atoms,” Opt. Commun. 180, 73–79 (2000).
[Crossref]

Deych, L.

M. A. Noginov, J. Novak, D. Grigsby, and L. Deych, “Applicability of the diffusion model to random lasers with non-resonant feedback,” J. Opt. A: Pure Appl. Opt. 8, S285–S295 (2006).
[Crossref]

Drozdowicz, K.

K. Drozdowicz, E. Krynicka, and J. Dąbrowska, “Diffusion cooling of thermal neutrons in basic rock minerals by Monte Carlo simulation of the pulsed neutron experiments,” App. Rad. Isot. 58, 727–733 (2003).
[Crossref]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley, New York, 1992).

Fabre, C.

L. Hilico, C. Fabre, and E. Giacobino, “Operation of a “Cold-Atom Laser” in a Magneto-Optical Trap,” Europhys. Lett. 18, 685–688 (1992).
[Crossref]

Ferjani, S.

Fioretti, A.

A. Fioretti, A. F. Molisch, J. H. Mutter, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415–422 (1998).
[Crossref]

Fratalocchi, A.

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4, 794–798 (2008).
[Crossref]

Froufe-Pérez, L. S.

L. S. Froufe-Pérez, W. Guerin, R. Carminati, and R. Kaiser, “Threshold of a Random Laser with Cold Atoms,” Phys. Rev. Lett. 102, 173903 (2009).
[Crossref] [PubMed]

Gao, B.

B. Gao, “Effects of Zeeman degeneracy on the steady-state properties of an atom interacting with a near-resonant laser field: Resonance fluorescence,” Phys. Rev. A 50, 4139–4156 (1994).
[Crossref] [PubMed]

Gawlik, W.

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]

Ge, L.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong Interactions in Multimode Random Lasers,” Science 320, 643–646 (2008).
[Crossref] [PubMed]

Giacobino, E.

L. Hilico, C. Fabre, and E. Giacobino, “Operation of a “Cold-Atom Laser” in a Magneto-Optical Trap,” Europhys. Lett. 18, 685–688 (1992).
[Crossref]

Gouedard, C.

Gould, P. L.

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a three-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[Crossref] [PubMed]

Grigsby, D.

M. A. Noginov, J. Novak, D. Grigsby, and L. Deych, “Applicability of the diffusion model to random lasers with non-resonant feedback,” J. Opt. A: Pure Appl. Opt. 8, S285–S295 (2006).
[Crossref]

Grison, D.

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).
[Crossref]

Grynberg, G.

G. Grynberg and C. Robilliard, “Cold atoms in dissipative optical lattices,” Phys. Rep. 355, 335–451 (2001).
[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).
[Crossref]

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley, New York, 1992).

Guerin, W.

L. S. Froufe-Pérez, W. Guerin, R. Carminati, and R. Kaiser, “Threshold of a Random Laser with Cold Atoms,” Phys. Rev. Lett. 102, 173903 (2009).
[Crossref] [PubMed]

W. Guerin, F. Michaud, and R. Kaiser, “Mechanisms for Lasing with Cold Atoms as the Gain Medium,” Phys. Rev. Lett. 101, 093002 (2008).
[Crossref] [PubMed]

Han, D. J.

M. T. dePue, S. L. Winoto, D. J. Han, and D. S. Weiss, “Transient compression of a MOT and high intensity fluorescent imaging of optically thick clouds of atoms,” Opt. Commun. 180, 73–79 (2000).
[Crossref]

Hilico, L.

L. Hilico, C. Fabre, and E. Giacobino, “Operation of a “Cold-Atom Laser” in a Magneto-Optical Trap,” Europhys. Lett. 18, 685–688 (1992).
[Crossref]

Ho, S. T.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet Lasing in Resonators Formed by Scattering in Semiconductor Polycrystalline Films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[Crossref]

Hoffmann, D.

S. Bali, D. Hoffmann, J. Simán, and T. Walker, “Measurements of intensity correlations of scattered light from laser-cooled atoms,” Phys. Rev. A 53, 3469–3472 (1996).
[Crossref] [PubMed]

Hu, Z.

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] [PubMed]

Huang, J.-Y.

Y.-C. Chen, Y.-W. Chen, J.-J. Su, J.-Y. Huang, and I. A. Yu, “Pump-probe spectroscopy of cold 87Rb atoms in various polarization configurations,” Phys. Rev. A 63, 043808 (2001).
[Crossref]

Husson, D.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

Joffre, M. A.

W. Ketterle, K. B. Davis, M. A. Joffre, A. Pritchard, and D. E. Martin, “High Densities of Cold Atoms in a Dark Spontaneous-Force trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[Crossref] [PubMed]

Jurczak, C.

C. Jurczak, K. Sengstock, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Observation of intensity correlations in the fluorescence from laser cooled atoms,” Opt. Commun. 115, 480–484 (1995).
[Crossref]

Kaiser, R.

L. S. Froufe-Pérez, W. Guerin, R. Carminati, and R. Kaiser, “Threshold of a Random Laser with Cold Atoms,” Phys. Rev. Lett. 102, 173903 (2009).
[Crossref] [PubMed]

W. Guerin, F. Michaud, and R. Kaiser, “Mechanisms for Lasing with Cold Atoms as the Gain Medium,” Phys. Rev. Lett. 101, 093002 (2008).
[Crossref] [PubMed]

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] [PubMed]

C. Jurczak, K. Sengstock, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Observation of intensity correlations in the fluorescence from laser cooled atoms,” Opt. Commun. 115, 480–484 (1995).
[Crossref]

Ketterle, W.

W. Ketterle, K. B. Davis, M. A. Joffre, A. Pritchard, and D. E. Martin, “High Densities of Cold Atoms in a Dark Spontaneous-Force trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[Crossref] [PubMed]

Kimble, H. J.

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] [PubMed]

Krynicka, E.

K. Drozdowicz, E. Krynicka, and J. Dąbrowska, “Diffusion cooling of thermal neutrons in basic rock minerals by Monte Carlo simulation of the pulsed neutron experiments,” App. Rad. Isot. 58, 727–733 (2003).
[Crossref]

Labeyrie, G.

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] [PubMed]

Lagendijk, A.

D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
[Crossref]

A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[Crossref]

Lawandy, N. M.

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] [PubMed]

Letokhov, V. S.

V. S. Letokhov, “Generation of light by a scattering medium with negative resonance absorption,” Sov. Phys. JETP 26, 835–840 (1968).

Lett, P. D.

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a three-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[Crossref] [PubMed]

Lounis, B.

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).
[Crossref]

Luca, A. D.

Martin, D. E.

W. Ketterle, K. B. Davis, M. A. Joffre, A. Pritchard, and D. E. Martin, “High Densities of Cold Atoms in a Dark Spontaneous-Force trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[Crossref] [PubMed]

Martorell, J.

Metcalf, H.

H. Metcalf and P. van der Straten, Laser cooling and Trapping (Springer, New York, 1999).
[Crossref]

Michaud, F.

W. Guerin, F. Michaud, and R. Kaiser, “Mechanisms for Lasing with Cold Atoms as the Gain Medium,” Phys. Rev. Lett. 101, 093002 (2008).
[Crossref] [PubMed]

Migus, A.

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] [PubMed]

Molisch, A. F.

A. Fioretti, A. F. Molisch, J. H. Mutter, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415–422 (1998).
[Crossref]

Mollow, B. R.

B. R. Mollow, “Stimulated Emission and Absorption near Resonance for Driven Systems,” Phys. Rev. A 5, 2217–2222 (1972).
[Crossref]

B. R. Mollow, “Power Spectrum of Light Scattered by Two-Level Systems,” Phys. Rev. 188, 1969–1975 (1969).
[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] [PubMed]

Mutter, J. H.

A. Fioretti, A. F. Molisch, J. H. Mutter, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415–422 (1998).
[Crossref]

Nieuwenhuizen, T. M.

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

Noginov, M. A.

M. A. Noginov, J. Novak, D. Grigsby, and L. Deych, “Applicability of the diffusion model to random lasers with non-resonant feedback,” J. Opt. A: Pure Appl. Opt. 8, S285–S295 (2006).
[Crossref]

Novak, J.

M. A. Noginov, J. Novak, D. Grigsby, and L. Deych, “Applicability of the diffusion model to random lasers with non-resonant feedback,” J. Opt. A: Pure Appl. Opt. 8, S285–S295 (2006).
[Crossref]

Ong, H. C.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet Lasing in Resonators Formed by Scattering in Semiconductor Polycrystalline Films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[Crossref]

Phillips, W. D.

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a three-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[Crossref] [PubMed]

Pritchard, A.

W. Ketterle, K. B. Davis, M. A. Joffre, A. Pritchard, and D. E. Martin, “High Densities of Cold Atoms in a Dark Spontaneous-Force trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[Crossref] [PubMed]

Ratner, M. A.

A. L. Burin, M. A. Ratner, H. Cao, and R. P. H. Chang, “Model for a Random Laser,” Phys. Rev. Lett. 87, 215503 (2001).
[Crossref] [PubMed]

Robilliard, C.

G. Grynberg and C. Robilliard, “Cold atoms in dissipative optical lattices,” Phys. Rep. 355, 335–451 (2001).
[Crossref]

Rolston, S. L.

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a three-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[Crossref] [PubMed]

Rotter, S.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong Interactions in Multimode Random Lasers,” Science 320, 643–646 (2008).
[Crossref] [PubMed]

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).
[Crossref]

Sauteret, D.

Scaramuzza, N.

Sebbah, P.

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with Resonant Feedback in Weakly Scattering Random Systems,” Phys. Rev. Lett. 98, 143902 (2007).
[Crossref] [PubMed]

Sengstock, K.

C. Jurczak, K. Sengstock, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Observation of intensity correlations in the fluorescence from laser cooled atoms,” Opt. Commun. 115, 480–484 (1995).
[Crossref]

Simán, J.

S. Bali, D. Hoffmann, J. Simán, and T. Walker, “Measurements of intensity correlations of scattered light from laser-cooled atoms,” Phys. Rev. A 53, 3469–3472 (1996).
[Crossref] [PubMed]

Stone, A. D.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong Interactions in Multimode Random Lasers,” Science 320, 643–646 (2008).
[Crossref] [PubMed]

Strangi, G.

Su, J.-J.

Y.-C. Chen, Y.-W. Chen, J.-J. Su, J.-Y. Huang, and I. A. Yu, “Pump-probe spectroscopy of cold 87Rb atoms in various polarization configurations,” Phys. Rev. A 63, 043808 (2001).
[Crossref]

Tabosa, J. W. R.

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] [PubMed]

Tanner, C. E.

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a three-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[Crossref] [PubMed]

Türeci, H. E.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong Interactions in Multimode Random Lasers,” Science 320, 643–646 (2008).
[Crossref] [PubMed]

van der Straten, P.

H. Metcalf and P. van der Straten, Laser cooling and Trapping (Springer, New York, 1999).
[Crossref]

van Rossum, M. C. W.

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

van Tiggelen, B. A.

A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[Crossref]

Vanneste, C.

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with Resonant Feedback in Weakly Scattering Random Systems,” Phys. Rev. Lett. 98, 143902 (2007).
[Crossref] [PubMed]

Vansteenkiste, N.

C. Jurczak, K. Sengstock, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Observation of intensity correlations in the fluorescence from laser cooled atoms,” Opt. Commun. 115, 480–484 (1995).
[Crossref]

Vaujour, E.

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] [PubMed]

Verkerk, P.

A. Fioretti, A. F. Molisch, J. H. Mutter, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415–422 (1998).
[Crossref]

Versace, C.

Walker, T.

S. Bali, D. Hoffmann, J. Simán, and T. Walker, “Measurements of intensity correlations of scattered light from laser-cooled atoms,” Phys. Rev. A 53, 3469–3472 (1996).
[Crossref] [PubMed]

Watts, R. N.

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a three-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[Crossref] [PubMed]

Weiss, D. S.

M. T. dePue, S. L. Winoto, D. J. Han, and D. S. Weiss, “Transient compression of a MOT and high intensity fluorescent imaging of optically thick clouds of atoms,” Opt. Commun. 180, 73–79 (2000).
[Crossref]

Westbrook, C. I.

C. Jurczak, K. Sengstock, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Observation of intensity correlations in the fluorescence from laser cooled atoms,” Opt. Commun. 115, 480–484 (1995).
[Crossref]

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a three-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[Crossref] [PubMed]

Wiersma, D. S.

D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4, 359–367 (2008).
[Crossref]

D. S. Wiersma and S. Cavalier, “Light emission: A temperature-tunable random laser,” Nature 414, 708–709 (2001).
[Crossref] [PubMed]

D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
[Crossref]

Wilkowski, 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] [PubMed]

Winoto, S. L.

M. T. dePue, S. L. Winoto, D. J. Han, and D. S. Weiss, “Transient compression of a MOT and high intensity fluorescent imaging of optically thick clouds of atoms,” Opt. Commun. 180, 73–79 (2000).
[Crossref]

Wu, J. Y.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet Lasing in Resonators Formed by Scattering in Semiconductor Polycrystalline Films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[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 87Rb atoms in various polarization configurations,” Phys. Rev. A 63, 043808 (2001).
[Crossref]

Zachorowski, J.

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]

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]

Zhao, Y. G.

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet Lasing in Resonators Formed by Scattering in Semiconductor Polycrystalline Films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
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Zweifel, P.

K. Case and P. Zweifel, Linear transport theory (Addison-Wesley, 1967).

App. Rad. Isot. (1)

K. Drozdowicz, E. Krynicka, and J. Dąbrowska, “Diffusion cooling of thermal neutrons in basic rock minerals by Monte Carlo simulation of the pulsed neutron experiments,” App. Rad. Isot. 58, 727–733 (2003).
[Crossref]

Appl. Phys. Lett. (1)

H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet Lasing in Resonators Formed by Scattering in Semiconductor Polycrystalline Films,” Appl. Phys. Lett. 73, 3656–3658 (1998).
[Crossref]

Europhys. Lett. (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).
[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).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

M. A. Noginov, J. Novak, D. Grigsby, and L. Deych, “Applicability of the diffusion model to random lasers with non-resonant feedback,” J. Opt. A: Pure Appl. Opt. 8, S285–S295 (2006).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. A (1)

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
[Crossref]

Nat. Phys. (2)

D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4, 359–367 (2008).
[Crossref]

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4, 794–798 (2008).
[Crossref]

Nature (1)

D. S. Wiersma and S. Cavalier, “Light emission: A temperature-tunable random laser,” Nature 414, 708–709 (2001).
[Crossref] [PubMed]

Opt. Commun. (3)

A. Fioretti, A. F. Molisch, J. H. Mutter, P. Verkerk, and M. Allegrini, “Observation of radiation trapping in a dense Cs magneto-optical trap,” Opt. Commun. 149, 415–422 (1998).
[Crossref]

M. T. dePue, S. L. Winoto, D. J. Han, and D. S. Weiss, “Transient compression of a MOT and high intensity fluorescent imaging of optically thick clouds of atoms,” Opt. Commun. 180, 73–79 (2000).
[Crossref]

C. Jurczak, K. Sengstock, R. Kaiser, N. Vansteenkiste, C. I. Westbrook, and A. Aspect, “Observation of intensity correlations in the fluorescence from laser cooled atoms,” Opt. Commun. 115, 480–484 (1995).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rep. (2)

G. Grynberg and C. Robilliard, “Cold atoms in dissipative optical lattices,” Phys. Rep. 355, 335–451 (2001).
[Crossref]

A. Lagendijk and B. A. van Tiggelen, “Resonant multiple scattering of light,” Phys. Rep. 270, 143–215 (1996).
[Crossref]

Phys. Rev. (1)

B. R. Mollow, “Power Spectrum of Light Scattered by Two-Level Systems,” Phys. Rev. 188, 1969–1975 (1969).
[Crossref]

Phys. Rev. A (5)

Y.-C. Chen, Y.-W. Chen, J.-J. Su, J.-Y. Huang, and I. A. Yu, “Pump-probe spectroscopy of cold 87Rb atoms in various polarization configurations,” Phys. Rev. A 63, 043808 (2001).
[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]

B. Gao, “Effects of Zeeman degeneracy on the steady-state properties of an atom interacting with a near-resonant laser field: Resonance fluorescence,” Phys. Rev. A 50, 4139–4156 (1994).
[Crossref] [PubMed]

B. R. Mollow, “Stimulated Emission and Absorption near Resonance for Driven Systems,” Phys. Rev. A 5, 2217–2222 (1972).
[Crossref]

S. Bali, D. Hoffmann, J. Simán, and T. Walker, “Measurements of intensity correlations of scattered light from laser-cooled atoms,” Phys. Rev. A 53, 3469–3472 (1996).
[Crossref] [PubMed]

Phys. Rev. E (1)

D. S. Wiersma and A. Lagendijk, “Light diffusion with gain and random lasers,” Phys. Rev. E 54, 4256–4265 (1996).
[Crossref]

Phys. Rev. Lett. (8)

A. L. Burin, M. A. Ratner, H. Cao, and R. P. H. Chang, “Model for a Random Laser,” Phys. Rev. Lett. 87, 215503 (2001).
[Crossref] [PubMed]

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with Resonant Feedback in Weakly Scattering Random Systems,” Phys. Rev. Lett. 98, 143902 (2007).
[Crossref] [PubMed]

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] [PubMed]

W. Guerin, F. Michaud, and R. Kaiser, “Mechanisms for Lasing with Cold Atoms as the Gain Medium,” Phys. Rev. Lett. 101, 093002 (2008).
[Crossref] [PubMed]

L. S. Froufe-Pérez, W. Guerin, R. Carminati, and R. Kaiser, “Threshold of a Random Laser with Cold Atoms,” Phys. Rev. Lett. 102, 173903 (2009).
[Crossref] [PubMed]

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] [PubMed]

W. Ketterle, K. B. Davis, M. A. Joffre, A. Pritchard, and D. E. Martin, “High Densities of Cold Atoms in a Dark Spontaneous-Force trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[Crossref] [PubMed]

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a three-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[Crossref] [PubMed]

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M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).
[Crossref]

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[Crossref] [PubMed]

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[Crossref]

Other (7)

Note that even though new interesting features appear when coherent feedback is involved [14], we will consider only incoherent (intensity) feedback.

H. Metcalf and P. van der Straten, Laser cooling and Trapping (Springer, New York, 1999).
[Crossref]

We consider only isotropic scattering so that the transport length equals the scattering mean free path [26].

K. Case and P. Zweifel, Linear transport theory (Addison-Wesley, 1967).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

D. Brivio, “Random laser with cold atoms: extracting information from atomic fluorescence,” Master Thesis, Università di Milano (2008).

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions: Basic Processes and Applications (Wiley, New York, 1992).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Principle of the experiment. We send a weak probe beam on the magneto-optical trap (MOT) and the transmission is recorded on a photodetector (PD). The probe frequency ω is ramped during the acquisition in order to record a spectrum. Another, stronger beam of frequency ω P is used as a pump. (b) Principle of the Raman mechanism (depicted here for a F=1→F′=2 transition). (c) Experimental transmission spectra, plotted as a function of the pump-probe detuning δ. Without pumping, spectrum (1) shows only the atomic absorption. A pump beam of detuning Δ=-3.8Γ and intensity 13 mW/cm2, corresponding to a Rabi frequency Ω=2.5Γ, is added to obtain spectrum (2), which then exhibits a Raman resonance in the vicinity of δ=0. The atomic absorption is shifted due to the pump-induced light shift and the absorption is reduced due to saturation.

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Fig. 2.
Fig. 2.

(a) Typical experimental spectrum (red dots) and its fit (black line) around the Raman resonance. The parameters obtained from the fit are A 1=0.21 (gain amplitude), A 2=0.11 (absorption amplitude), γ=0.25Γ=1.5 MHz and δ R=0.09Γ=540 kHz. (b) Gain and scattering cross sections, computed from Eqs. (6,7) with the Raman parameters deduced from the fit. (c) Corresponding critical optical thickness. The minimum is b 0∝220. This set of data corresponds to the pump parameters Δ=-3.4Γ and Ω=3.4Γ.

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Fig. 3.
Fig. 3.

Critical optical thickness b 0cr as a function of the pumping parameters Δ (atompump detuning) and Ω (Rabi frequency of the atom-pump coupling). The minimum is around b 0cr~210-230, for Δ~2Γ and Ω~2-3Γ.

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Equations (11)

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Leff >β π ℓscℓg/3,
ρσ0Leff=ηb0>2π3∣α˜∣2(∣α∣˜2−Im(α˜)),
Im(α˜R)=A1(δ−δR)2+γ2/4−A2(δ+δR)2+γ2/4.
T(δ)=exp [−b0×(Im[α˜R(δ)]+mδ+p)] ,
Re(α˜R)=A1×−2(δ−δR)/γ(δ−δR)2+γ2/4−A2×−2(δ+δR)/γ(δ−δR)2+γ2/4.
σg/σ0=38∣αR˜∣2−12Im(α˜R),
σsc/σ0=38∣αR˜∣2,
ηb0cr=2πσ03σscσg,
b0cr(Δ,Ω)=minδ[b0cr(δ,Δ,Ω)].
σe1=σ01+4Δ2/Γ2×1(1+s)2×𝓒.
σinel=σ01+4Δ2/Γ2×[1(1+s)2×(1−𝓒)+s(1+s)2].

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