Abstract

We present a first experimental demonstration of classical CW laser light condensation (LC) in the frequency (mode) domain that verifies its prediction (Fischer and Weill, Opt. Express 20, 26704 (2012)). LC is based on weighting the modes in a noisy environment in a loss-gain measure compared to an energy (frequency) scale in Bose-Einstein condensation (BEC). It is characterized by a sharp transition from multi- to single-mode oscillation, occurring when the spectral-filtering (loss-trap) has near the lowest-loss mode (“ground-state”) a power-law dependence with an exponent smaller than 1. An important meaning of the many-mode LC system stems from its relation to lasing and photon-BEC.

© 2016 Optical Society of America

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References

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  1. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
    [Crossref] [PubMed]
  2. J. R. Anglin and W. Ketterle, “Bose-Einstein condensation of atomic gases,” Nature 416(6877), 211–218 (2002).
    [Crossref] [PubMed]
  3. A. J. Leggett, “Bose-Einstein condensation in the alkali gases: Some fundamental concepts,” Rev. Mod. Phys. 73(2), 307–356 (2001).
    [Crossref]
  4. H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002).
    [Crossref] [PubMed]
  5. R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007).
    [Crossref] [PubMed]
  6. S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature 443(7110), 430–433 (2006).
    [Crossref] [PubMed]
  7. J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature 468(7323), 545–548 (2010).
    [Crossref] [PubMed]
  8. R. Weill, B. Fischer, and O. Gat, “Light-mode condensation in actively-mode-locked lasers,” Phys. Rev. Lett. 104(17), 173901 (2010).
    [Crossref] [PubMed]
  9. R. Weill, B. Levit, A. Bekker, O. Gat, and B. Fischer, “Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express 18(16), 16520–16525 (2010).
    [Crossref] [PubMed]
  10. B. Fischer and R. Weill, “When Does Single-Mode Lasing Become a Condensation Phenomenon?” Opt. Express 20(24), 26704–26713 (2012).
    [Crossref] [PubMed]
  11. G. Oren, A. Bekker, and B. Fischer, “Classical condensation of light pulses in a loss trap in a laser cavity,” Optica 1(3), 145–148 (2014).
    [Crossref]
  12. C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett. 95(26), 263901 (2005).
    [Crossref] [PubMed]
  13. C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: Theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett. 101(14), 143901 (2008).
    [Crossref] [PubMed]
  14. A. Fratalocchi, “Mode-locked lasers: light condensation,” Nat. Photonics 4(8), 502–503 (2010).
    [Crossref]
  15. C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8(6), 471–474 (2012).
    [Crossref]
  16. A. Rückriegel and P. Kopietz, “Rayleigh-Jeans Condensation of Pumped Magnons in Thin-Film Ferromagnets,” Phys. Rev. Lett. 115(15), 157203 (2015).
    [Crossref] [PubMed]
  17. B. Fischer and A. Bekker, “Many-body photonics,” Opt. Photonics News 24(9), 40–47 (2013).
    [Crossref]
  18. A. Gordon and B. Fischer, “Phase transition theory of many-mode ordering and pulse formation in lasers,” Phys. Rev. Lett. 89(10), 103901 (2002).
    [Crossref] [PubMed]
  19. A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett. 105(1), 013905 (2010).
    [Crossref] [PubMed]
  20. R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett. 95(1), 013903 (2005).
    [Crossref] [PubMed]
  21. A. Gordon and B. Fischer, “Statistical-mechanics theory of active mode locking with noise,” Opt. Lett. 29(9), 1022–1024 (2004).
    [Crossref] [PubMed]
  22. A. Schwartz and B. Fischer, “Laser mode hyper-combs,” Opt. Express 21(5), 6196–6204 (2013).
    [Crossref] [PubMed]
  23. V. Bagnato and D. Kleppner, “Bose-Einstein condensation in low-dimensional traps,” Phys. Rev. A 44(11), 7439–7441 (1991).
    [Crossref] [PubMed]

2015 (1)

A. Rückriegel and P. Kopietz, “Rayleigh-Jeans Condensation of Pumped Magnons in Thin-Film Ferromagnets,” Phys. Rev. Lett. 115(15), 157203 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (2)

B. Fischer and A. Bekker, “Many-body photonics,” Opt. Photonics News 24(9), 40–47 (2013).
[Crossref]

A. Schwartz and B. Fischer, “Laser mode hyper-combs,” Opt. Express 21(5), 6196–6204 (2013).
[Crossref] [PubMed]

2012 (2)

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8(6), 471–474 (2012).
[Crossref]

B. Fischer and R. Weill, “When Does Single-Mode Lasing Become a Condensation Phenomenon?” Opt. Express 20(24), 26704–26713 (2012).
[Crossref] [PubMed]

2010 (5)

A. Fratalocchi, “Mode-locked lasers: light condensation,” Nat. Photonics 4(8), 502–503 (2010).
[Crossref]

J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature 468(7323), 545–548 (2010).
[Crossref] [PubMed]

R. Weill, B. Fischer, and O. Gat, “Light-mode condensation in actively-mode-locked lasers,” Phys. Rev. Lett. 104(17), 173901 (2010).
[Crossref] [PubMed]

R. Weill, B. Levit, A. Bekker, O. Gat, and B. Fischer, “Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express 18(16), 16520–16525 (2010).
[Crossref] [PubMed]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett. 105(1), 013905 (2010).
[Crossref] [PubMed]

2008 (1)

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: Theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett. 101(14), 143901 (2008).
[Crossref] [PubMed]

2007 (1)

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007).
[Crossref] [PubMed]

2006 (1)

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature 443(7110), 430–433 (2006).
[Crossref] [PubMed]

2005 (2)

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett. 95(26), 263901 (2005).
[Crossref] [PubMed]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett. 95(1), 013903 (2005).
[Crossref] [PubMed]

2004 (1)

2002 (3)

A. Gordon and B. Fischer, “Phase transition theory of many-mode ordering and pulse formation in lasers,” Phys. Rev. Lett. 89(10), 103901 (2002).
[Crossref] [PubMed]

J. R. Anglin and W. Ketterle, “Bose-Einstein condensation of atomic gases,” Nature 416(6877), 211–218 (2002).
[Crossref] [PubMed]

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002).
[Crossref] [PubMed]

2001 (1)

A. J. Leggett, “Bose-Einstein condensation in the alkali gases: Some fundamental concepts,” Rev. Mod. Phys. 73(2), 307–356 (2001).
[Crossref]

1995 (1)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[Crossref] [PubMed]

1991 (1)

V. Bagnato and D. Kleppner, “Bose-Einstein condensation in low-dimensional traps,” Phys. Rev. A 44(11), 7439–7441 (1991).
[Crossref] [PubMed]

Anderson, M. H.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[Crossref] [PubMed]

Angelani, L.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: Theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett. 101(14), 143901 (2008).
[Crossref] [PubMed]

Anglin, J. R.

J. R. Anglin and W. Ketterle, “Bose-Einstein condensation of atomic gases,” Nature 416(6877), 211–218 (2002).
[Crossref] [PubMed]

Bagnato, V.

V. Bagnato and D. Kleppner, “Bose-Einstein condensation in low-dimensional traps,” Phys. Rev. A 44(11), 7439–7441 (1991).
[Crossref] [PubMed]

Balili, R.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007).
[Crossref] [PubMed]

Barsi, C.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8(6), 471–474 (2012).
[Crossref]

Bekker, A.

G. Oren, A. Bekker, and B. Fischer, “Classical condensation of light pulses in a loss trap in a laser cavity,” Optica 1(3), 145–148 (2014).
[Crossref]

B. Fischer and A. Bekker, “Many-body photonics,” Opt. Photonics News 24(9), 40–47 (2013).
[Crossref]

R. Weill, B. Levit, A. Bekker, O. Gat, and B. Fischer, “Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express 18(16), 16520–16525 (2010).
[Crossref] [PubMed]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett. 105(1), 013905 (2010).
[Crossref] [PubMed]

Bloch, J.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002).
[Crossref] [PubMed]

Connaughton, C.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett. 95(26), 263901 (2005).
[Crossref] [PubMed]

Conti, C.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: Theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett. 101(14), 143901 (2008).
[Crossref] [PubMed]

Cornell, E. A.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[Crossref] [PubMed]

Demidov, V. E.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature 443(7110), 430–433 (2006).
[Crossref] [PubMed]

Demokritov, S. O.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature 443(7110), 430–433 (2006).
[Crossref] [PubMed]

Deng, H.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002).
[Crossref] [PubMed]

Dzyapko, O.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature 443(7110), 430–433 (2006).
[Crossref] [PubMed]

Ensher, J. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[Crossref] [PubMed]

Fischer, B.

G. Oren, A. Bekker, and B. Fischer, “Classical condensation of light pulses in a loss trap in a laser cavity,” Optica 1(3), 145–148 (2014).
[Crossref]

B. Fischer and A. Bekker, “Many-body photonics,” Opt. Photonics News 24(9), 40–47 (2013).
[Crossref]

A. Schwartz and B. Fischer, “Laser mode hyper-combs,” Opt. Express 21(5), 6196–6204 (2013).
[Crossref] [PubMed]

B. Fischer and R. Weill, “When Does Single-Mode Lasing Become a Condensation Phenomenon?” Opt. Express 20(24), 26704–26713 (2012).
[Crossref] [PubMed]

R. Weill, B. Levit, A. Bekker, O. Gat, and B. Fischer, “Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express 18(16), 16520–16525 (2010).
[Crossref] [PubMed]

R. Weill, B. Fischer, and O. Gat, “Light-mode condensation in actively-mode-locked lasers,” Phys. Rev. Lett. 104(17), 173901 (2010).
[Crossref] [PubMed]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett. 105(1), 013905 (2010).
[Crossref] [PubMed]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett. 95(1), 013903 (2005).
[Crossref] [PubMed]

A. Gordon and B. Fischer, “Statistical-mechanics theory of active mode locking with noise,” Opt. Lett. 29(9), 1022–1024 (2004).
[Crossref] [PubMed]

A. Gordon and B. Fischer, “Phase transition theory of many-mode ordering and pulse formation in lasers,” Phys. Rev. Lett. 89(10), 103901 (2002).
[Crossref] [PubMed]

Fleischer, J. W.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8(6), 471–474 (2012).
[Crossref]

Fratalocchi, A.

A. Fratalocchi, “Mode-locked lasers: light condensation,” Nat. Photonics 4(8), 502–503 (2010).
[Crossref]

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: Theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett. 101(14), 143901 (2008).
[Crossref] [PubMed]

Gat, O.

R. Weill, B. Fischer, and O. Gat, “Light-mode condensation in actively-mode-locked lasers,” Phys. Rev. Lett. 104(17), 173901 (2010).
[Crossref] [PubMed]

R. Weill, B. Levit, A. Bekker, O. Gat, and B. Fischer, “Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express 18(16), 16520–16525 (2010).
[Crossref] [PubMed]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett. 95(1), 013903 (2005).
[Crossref] [PubMed]

Gordon, A.

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett. 95(1), 013903 (2005).
[Crossref] [PubMed]

A. Gordon and B. Fischer, “Statistical-mechanics theory of active mode locking with noise,” Opt. Lett. 29(9), 1022–1024 (2004).
[Crossref] [PubMed]

A. Gordon and B. Fischer, “Phase transition theory of many-mode ordering and pulse formation in lasers,” Phys. Rev. Lett. 89(10), 103901 (2002).
[Crossref] [PubMed]

Hartwell, V.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007).
[Crossref] [PubMed]

Hillebrands, B.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature 443(7110), 430–433 (2006).
[Crossref] [PubMed]

Jia, S.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8(6), 471–474 (2012).
[Crossref]

Josserand, C.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett. 95(26), 263901 (2005).
[Crossref] [PubMed]

Ketterle, W.

J. R. Anglin and W. Ketterle, “Bose-Einstein condensation of atomic gases,” Nature 416(6877), 211–218 (2002).
[Crossref] [PubMed]

Klaers, J.

J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature 468(7323), 545–548 (2010).
[Crossref] [PubMed]

Kleppner, D.

V. Bagnato and D. Kleppner, “Bose-Einstein condensation in low-dimensional traps,” Phys. Rev. A 44(11), 7439–7441 (1991).
[Crossref] [PubMed]

Kopietz, P.

A. Rückriegel and P. Kopietz, “Rayleigh-Jeans Condensation of Pumped Magnons in Thin-Film Ferromagnets,” Phys. Rev. Lett. 115(15), 157203 (2015).
[Crossref] [PubMed]

Leggett, A. J.

A. J. Leggett, “Bose-Einstein condensation in the alkali gases: Some fundamental concepts,” Rev. Mod. Phys. 73(2), 307–356 (2001).
[Crossref]

Leonetti, M.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: Theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett. 101(14), 143901 (2008).
[Crossref] [PubMed]

Levit, B.

R. Weill, B. Levit, A. Bekker, O. Gat, and B. Fischer, “Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express 18(16), 16520–16525 (2010).
[Crossref] [PubMed]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett. 105(1), 013905 (2010).
[Crossref] [PubMed]

Matthews, M. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[Crossref] [PubMed]

Melkov, G. A.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature 443(7110), 430–433 (2006).
[Crossref] [PubMed]

Oren, G.

Pfeiffer, L.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007).
[Crossref] [PubMed]

Picozzi, A.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8(6), 471–474 (2012).
[Crossref]

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett. 95(26), 263901 (2005).
[Crossref] [PubMed]

Pomeau, Y.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett. 95(26), 263901 (2005).
[Crossref] [PubMed]

Rica, S.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8(6), 471–474 (2012).
[Crossref]

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett. 95(26), 263901 (2005).
[Crossref] [PubMed]

Rosen, A.

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett. 105(1), 013905 (2010).
[Crossref] [PubMed]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett. 95(1), 013903 (2005).
[Crossref] [PubMed]

Rückriegel, A.

A. Rückriegel and P. Kopietz, “Rayleigh-Jeans Condensation of Pumped Magnons in Thin-Film Ferromagnets,” Phys. Rev. Lett. 115(15), 157203 (2015).
[Crossref] [PubMed]

Ruocco, G.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: Theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett. 101(14), 143901 (2008).
[Crossref] [PubMed]

Santori, C.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002).
[Crossref] [PubMed]

Schmitt, J.

J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature 468(7323), 545–548 (2010).
[Crossref] [PubMed]

Schwartz, A.

Serga, A. A.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature 443(7110), 430–433 (2006).
[Crossref] [PubMed]

Slavin, A. N.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature 443(7110), 430–433 (2006).
[Crossref] [PubMed]

Smulakovsky, V.

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett. 105(1), 013905 (2010).
[Crossref] [PubMed]

Snoke, D.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007).
[Crossref] [PubMed]

Sun, C.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8(6), 471–474 (2012).
[Crossref]

Vewinger, F.

J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature 468(7323), 545–548 (2010).
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Weihs, G.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002).
[Crossref] [PubMed]

Weill, R.

B. Fischer and R. Weill, “When Does Single-Mode Lasing Become a Condensation Phenomenon?” Opt. Express 20(24), 26704–26713 (2012).
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A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett. 105(1), 013905 (2010).
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R. Weill, B. Fischer, and O. Gat, “Light-mode condensation in actively-mode-locked lasers,” Phys. Rev. Lett. 104(17), 173901 (2010).
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R. Weill, B. Levit, A. Bekker, O. Gat, and B. Fischer, “Laser light condensate: experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express 18(16), 16520–16525 (2010).
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R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett. 95(1), 013903 (2005).
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Weitz, M.

J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature 468(7323), 545–548 (2010).
[Crossref] [PubMed]

West, K.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007).
[Crossref] [PubMed]

Wieman, C. E.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[Crossref] [PubMed]

Yamamoto, Y.

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002).
[Crossref] [PubMed]

Nat. Photonics (1)

A. Fratalocchi, “Mode-locked lasers: light condensation,” Nat. Photonics 4(8), 502–503 (2010).
[Crossref]

Nat. Phys. (1)

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, and J. W. Fleischer, “Observation of the kinetic condensation of classical waves,” Nat. Phys. 8(6), 471–474 (2012).
[Crossref]

Nature (3)

J. R. Anglin and W. Ketterle, “Bose-Einstein condensation of atomic gases,” Nature 416(6877), 211–218 (2002).
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S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, “Bose-Einstein condensation of quasi-equilibrium magnons at room temperature under pumping,” Nature 443(7110), 430–433 (2006).
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J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature 468(7323), 545–548 (2010).
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Opt. Express (3)

Opt. Lett. (1)

Opt. Photonics News (1)

B. Fischer and A. Bekker, “Many-body photonics,” Opt. Photonics News 24(9), 40–47 (2013).
[Crossref]

Optica (1)

Phys. Rev. A (1)

V. Bagnato and D. Kleppner, “Bose-Einstein condensation in low-dimensional traps,” Phys. Rev. A 44(11), 7439–7441 (1991).
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Phys. Rev. Lett. (7)

A. Rückriegel and P. Kopietz, “Rayleigh-Jeans Condensation of Pumped Magnons in Thin-Film Ferromagnets,” Phys. Rev. Lett. 115(15), 157203 (2015).
[Crossref] [PubMed]

A. Gordon and B. Fischer, “Phase transition theory of many-mode ordering and pulse formation in lasers,” Phys. Rev. Lett. 89(10), 103901 (2002).
[Crossref] [PubMed]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, and B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett. 105(1), 013905 (2010).
[Crossref] [PubMed]

R. Weill, A. Rosen, A. Gordon, O. Gat, and B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett. 95(1), 013903 (2005).
[Crossref] [PubMed]

R. Weill, B. Fischer, and O. Gat, “Light-mode condensation in actively-mode-locked lasers,” Phys. Rev. Lett. 104(17), 173901 (2010).
[Crossref] [PubMed]

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, and S. Rica, “Condensation of classical nonlinear waves,” Phys. Rev. Lett. 95(26), 263901 (2005).
[Crossref] [PubMed]

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, and G. Ruocco, “Condensation in disordered lasers: Theory, 3D+1 simulations, and experiments,” Phys. Rev. Lett. 101(14), 143901 (2008).
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Rev. Mod. Phys. (1)

A. J. Leggett, “Bose-Einstein condensation in the alkali gases: Some fundamental concepts,” Rev. Mod. Phys. 73(2), 307–356 (2001).
[Crossref]

Science (3)

H. Deng, G. Weihs, C. Santori, J. Bloch, and Y. Yamamoto, “Condensation of semiconductor microcavity exciton polaritons,” Science 298(5591), 199–202 (2002).
[Crossref] [PubMed]

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007).
[Crossref] [PubMed]

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose-Einstein condensation in a dilute atomic vapor,” Science 269(5221), 198–201 (1995).
[Crossref] [PubMed]

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Figures (3)

Fig. 1
Fig. 1 Scheme of the CW many-mode EDF laser system with two special parts: External noise injection (“temperature”) into the cavity by a controlled ASE source, and a wave-shaper that forms the spectral loss-trap.
Fig. 2
Fig. 2 (a) Experimental and (b) theoretical spectra for η = 1 / 2 , 2 and various power (pumping) levels. For η = 1 / 2 (blue curves) the spectrum becomes very narrow even at low pumping levels and shows condensation. For η = 2 (red curves) the apectra are broader and only strong pumping provides “lasing” lines at several wavelengths near the centeral mode.
Fig. 3
Fig. 3 Experimental (dots) and theoretical (solid lines) condensation fractions as a function of (a) the total power P, with a constant noise T 0.015 m W , and (b) the noise T (“temperature”) normalized by the constant power P e 0.625 m W in the experiment, for two spectral filtering exponents η = 1 / 2 , 2 (blue and red curve respectively). We can see the condensation transition effect for η = 1 / 2 and a very small and gradual population fraction for η = 2 . The power or temperature needed for condensation at η = 1 / 2 is finite, while for η = 2 it is near zero. The transition is not sharp due the finite size of the mode system. The large system (thermodynamic limit) theoretical graph is shown in the dashed lines.

Equations (2)

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d a m / d τ = ( g ε m ) a m + Γ m ,
P = m = N N p m = m = N N T ε m g P = T ε 0 g + T 0 ε N ρ ( ε ) d ε ε + ε 0 g ,

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