Abstract

We present an experimental demonstration of condensation in a many-light-pulse system in a loss trap (loss well) in a one-dimensional laser cavity. The route to condensation is similar to Bose–Einstein condensation in a potential trap (potential well), but classical. The pulses, their loss levels, and the noise-induced power distribution take the role of “particles”, “energy” levels, and quantum-thermal population-statistics, respectively. The multipulse system is formed by high harmonic active mode-locking modulation and the trap by an envelope modulation. The experiment is done with an erbium-doped fiber laser. Condensation is shown to occur when the loss trap has near the lowest-loss pulse a power law dependence with exponent smaller than 1, as the theory predicts.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  15. A. Gordon, B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
    [Crossref]
  16. B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, B. Fischer, Phys. Rev. Lett. 93, 0153901 (2004).
    [Crossref]
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    [Crossref]
  18. A. Schwartz, B. Fischer, Opt. Express 21, 6196 (2013).
    [Crossref]
  19. B. Fischer, A. Bekker, Opt. Photon. News 24, 40 (2013).
    [Crossref]

2013 (2)

A. Schwartz, B. Fischer, Opt. Express 21, 6196 (2013).
[Crossref]

B. Fischer, A. Bekker, Opt. Photon. News 24, 40 (2013).
[Crossref]

2012 (2)

B. Fischer, R. Weill, Opt. Express 20, 26704 (2012).
[Crossref]

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, J. W. Fleischer, Nat. Phys. 8, 470 (2012).
[Crossref]

2010 (5)

R. Weill, B. Fischer, O. Gat, Phys. Rev. Lett. 104, 173901 (2010).
[Crossref]

R. Weill, B. Levit, A. Bekker, O. Gat, B. Fischer, Opt. Express 18, 16520 (2010).
[Crossref]

J. Klaers, J. Schmitt, F. Vewinger, M. Weitz, Nature 468, 545 (2010).
[Crossref]

A. Fratalocchi, Nat. Photonics 4, 502 (2010).
[Crossref]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, B. Fischer, Phys. Rev. Lett. 105, 013905 (2010).
[Crossref]

2008 (1)

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[Crossref]

2007 (1)

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, K. West, Science 316, 1007 (2007).
[Crossref]

2006 (1)

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Segre, B. Hillerbrands, A. N. Slavin, Nature 443, 430 (2006).
[Crossref]

2005 (1)

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
[Crossref]

2004 (1)

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, B. Fischer, Phys. Rev. Lett. 93, 0153901 (2004).
[Crossref]

2002 (2)

A. Gordon, B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[Crossref]

H. Deng, G. Weihs, C. Santori, J. Bloch, Y. Yamamoto, Science 298, 199 (2002).
[Crossref]

2001 (1)

A. J. Leggett, Rev. Mod. Phys. 73, 307 (2001).
[Crossref]

1995 (1)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Weiman, E. A. Cornell, Science 269, 198 (1995).
[Crossref]

1991 (1)

V. Bagnato, D. Kleppner, Phys. Rev. A 44, 7439 (1991).
[Crossref]

Anderson, M. H.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Weiman, E. A. Cornell, Science 269, 198 (1995).
[Crossref]

Angelani, L.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[Crossref]

Bagnato, V.

V. Bagnato, D. Kleppner, Phys. Rev. A 44, 7439 (1991).
[Crossref]

Balili, R.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, K. West, Science 316, 1007 (2007).
[Crossref]

Barsi, C.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, J. W. Fleischer, Nat. Phys. 8, 470 (2012).
[Crossref]

Bekker, A.

B. Fischer, A. Bekker, Opt. Photon. News 24, 40 (2013).
[Crossref]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, B. Fischer, Phys. Rev. Lett. 105, 013905 (2010).
[Crossref]

R. Weill, B. Levit, A. Bekker, O. Gat, B. Fischer, Opt. Express 18, 16520 (2010).
[Crossref]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, B. Fischer, Phys. Rev. Lett. 93, 0153901 (2004).
[Crossref]

Bloch, J.

H. Deng, G. Weihs, C. Santori, J. Bloch, Y. Yamamoto, Science 298, 199 (2002).
[Crossref]

Connaughton, C.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
[Crossref]

Conti, C.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[Crossref]

Cornell, E. A.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Weiman, E. A. Cornell, Science 269, 198 (1995).
[Crossref]

Demidov, V. E.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Segre, B. Hillerbrands, A. N. Slavin, Nature 443, 430 (2006).
[Crossref]

Demokritov, S. O.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Segre, B. Hillerbrands, A. N. Slavin, Nature 443, 430 (2006).
[Crossref]

Deng, H.

H. Deng, G. Weihs, C. Santori, J. Bloch, Y. Yamamoto, Science 298, 199 (2002).
[Crossref]

Dzyapko, O.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Segre, B. Hillerbrands, A. N. Slavin, Nature 443, 430 (2006).
[Crossref]

Ensher, J. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Weiman, E. A. Cornell, Science 269, 198 (1995).
[Crossref]

Fischer, B.

A. Schwartz, B. Fischer, Opt. Express 21, 6196 (2013).
[Crossref]

B. Fischer, A. Bekker, Opt. Photon. News 24, 40 (2013).
[Crossref]

B. Fischer, R. Weill, Opt. Express 20, 26704 (2012).
[Crossref]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, B. Fischer, Phys. Rev. Lett. 105, 013905 (2010).
[Crossref]

R. Weill, B. Levit, A. Bekker, O. Gat, B. Fischer, Opt. Express 18, 16520 (2010).
[Crossref]

R. Weill, B. Fischer, O. Gat, Phys. Rev. Lett. 104, 173901 (2010).
[Crossref]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, B. Fischer, Phys. Rev. Lett. 93, 0153901 (2004).
[Crossref]

A. Gordon, B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[Crossref]

Fleischer, J. W.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, J. W. Fleischer, Nat. Phys. 8, 470 (2012).
[Crossref]

Fratalocchi, A.

A. Fratalocchi, Nat. Photonics 4, 502 (2010).
[Crossref]

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[Crossref]

Gat, O.

R. Weill, B. Fischer, O. Gat, Phys. Rev. Lett. 104, 173901 (2010).
[Crossref]

R. Weill, B. Levit, A. Bekker, O. Gat, B. Fischer, Opt. Express 18, 16520 (2010).
[Crossref]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, B. Fischer, Phys. Rev. Lett. 93, 0153901 (2004).
[Crossref]

Gordon, A.

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, B. Fischer, Phys. Rev. Lett. 93, 0153901 (2004).
[Crossref]

A. Gordon, B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[Crossref]

Hartwell, V.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, K. West, Science 316, 1007 (2007).
[Crossref]

Hillerbrands, B.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Segre, B. Hillerbrands, A. N. Slavin, Nature 443, 430 (2006).
[Crossref]

Jia, S.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, J. W. Fleischer, Nat. Phys. 8, 470 (2012).
[Crossref]

Josserand, C.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
[Crossref]

Klaers, J.

J. Klaers, J. Schmitt, F. Vewinger, M. Weitz, Nature 468, 545 (2010).
[Crossref]

Kleppner, D.

V. Bagnato, D. Kleppner, Phys. Rev. A 44, 7439 (1991).
[Crossref]

Leggett, A. J.

A. J. Leggett, Rev. Mod. Phys. 73, 307 (2001).
[Crossref]

Leonetti, M.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[Crossref]

Levit, B.

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, B. Fischer, Phys. Rev. Lett. 105, 013905 (2010).
[Crossref]

R. Weill, B. Levit, A. Bekker, O. Gat, B. Fischer, Opt. Express 18, 16520 (2010).
[Crossref]

Matthews, M. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Weiman, E. A. Cornell, Science 269, 198 (1995).
[Crossref]

Melkov, G. A.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Segre, B. Hillerbrands, A. N. Slavin, Nature 443, 430 (2006).
[Crossref]

Pfeiffer, L.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, K. West, Science 316, 1007 (2007).
[Crossref]

Picozzi, A.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, J. W. Fleischer, Nat. Phys. 8, 470 (2012).
[Crossref]

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
[Crossref]

Pomeau, Y.

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
[Crossref]

Rica, S.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, J. W. Fleischer, Nat. Phys. 8, 470 (2012).
[Crossref]

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
[Crossref]

Rosen, A.

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, B. Fischer, Phys. Rev. Lett. 105, 013905 (2010).
[Crossref]

Ruocco, G.

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[Crossref]

Santori, C.

H. Deng, G. Weihs, C. Santori, J. Bloch, Y. Yamamoto, Science 298, 199 (2002).
[Crossref]

Schmitt, J.

J. Klaers, J. Schmitt, F. Vewinger, M. Weitz, Nature 468, 545 (2010).
[Crossref]

Schwartz, A.

Segre, A. A.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Segre, B. Hillerbrands, A. N. Slavin, Nature 443, 430 (2006).
[Crossref]

Slavin, A. N.

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Segre, B. Hillerbrands, A. N. Slavin, Nature 443, 430 (2006).
[Crossref]

Smulakovsky, V.

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, B. Fischer, Phys. Rev. Lett. 105, 013905 (2010).
[Crossref]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, B. Fischer, Phys. Rev. Lett. 93, 0153901 (2004).
[Crossref]

Snoke, D.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, K. West, Science 316, 1007 (2007).
[Crossref]

Sun, C.

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, J. W. Fleischer, Nat. Phys. 8, 470 (2012).
[Crossref]

Vewinger, F.

J. Klaers, J. Schmitt, F. Vewinger, M. Weitz, Nature 468, 545 (2010).
[Crossref]

Vodonos, B.

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, B. Fischer, Phys. Rev. Lett. 93, 0153901 (2004).
[Crossref]

Weihs, G.

H. Deng, G. Weihs, C. Santori, J. Bloch, Y. Yamamoto, Science 298, 199 (2002).
[Crossref]

Weill, R.

B. Fischer, R. Weill, Opt. Express 20, 26704 (2012).
[Crossref]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, B. Fischer, Phys. Rev. Lett. 105, 013905 (2010).
[Crossref]

R. Weill, B. Fischer, O. Gat, Phys. Rev. Lett. 104, 173901 (2010).
[Crossref]

R. Weill, B. Levit, A. Bekker, O. Gat, B. Fischer, Opt. Express 18, 16520 (2010).
[Crossref]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, B. Fischer, Phys. Rev. Lett. 93, 0153901 (2004).
[Crossref]

Weiman, C. E.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Weiman, E. A. Cornell, Science 269, 198 (1995).
[Crossref]

Weitz, M.

J. Klaers, J. Schmitt, F. Vewinger, M. Weitz, Nature 468, 545 (2010).
[Crossref]

West, K.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, K. West, Science 316, 1007 (2007).
[Crossref]

Yamamoto, Y.

H. Deng, G. Weihs, C. Santori, J. Bloch, Y. Yamamoto, Science 298, 199 (2002).
[Crossref]

Nat. Photonics (1)

A. Fratalocchi, Nat. Photonics 4, 502 (2010).
[Crossref]

Nat. Phys. (1)

C. Sun, S. Jia, C. Barsi, S. Rica, A. Picozzi, J. W. Fleischer, Nat. Phys. 8, 470 (2012).
[Crossref]

Nature (2)

J. Klaers, J. Schmitt, F. Vewinger, M. Weitz, Nature 468, 545 (2010).
[Crossref]

S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Segre, B. Hillerbrands, A. N. Slavin, Nature 443, 430 (2006).
[Crossref]

Opt. Express (3)

Opt. Photon. News (1)

B. Fischer, A. Bekker, Opt. Photon. News 24, 40 (2013).
[Crossref]

Phys. Rev. A (1)

V. Bagnato, D. Kleppner, Phys. Rev. A 44, 7439 (1991).
[Crossref]

Phys. Rev. Lett. (6)

A. Gordon, B. Fischer, Phys. Rev. Lett. 89, 103901 (2002).
[Crossref]

B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, B. Fischer, Phys. Rev. Lett. 93, 0153901 (2004).
[Crossref]

A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, B. Fischer, Phys. Rev. Lett. 105, 013905 (2010).
[Crossref]

C. Connaughton, C. Josserand, A. Picozzi, Y. Pomeau, S. Rica, Phys. Rev. Lett. 95, 263901 (2005).
[Crossref]

C. Conti, M. Leonetti, A. Fratalocchi, L. Angelani, G. Ruocco, Phys. Rev. Lett. 101, 143901 (2008).
[Crossref]

R. Weill, B. Fischer, O. Gat, Phys. Rev. Lett. 104, 173901 (2010).
[Crossref]

Rev. Mod. Phys. (1)

A. J. Leggett, Rev. Mod. Phys. 73, 307 (2001).
[Crossref]

Science (3)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Weiman, E. A. Cornell, Science 269, 198 (1995).
[Crossref]

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, K. West, Science 316, 1007 (2007).
[Crossref]

H. Deng, G. Weihs, C. Santori, J. Bloch, Y. Yamamoto, Science 298, 199 (2002).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1. Pulse system and the loss trap in the laser cavity. The loss trap is provided by an envelope modulation, shown for η=2,1,1/2, and the pulses by a harmonic modulation, here illustrated for a 15th order, that gives 15 pulse sites. Characteristic pulse forms are plotted in the cavity in each figure along with their power distributions, which are shown in the diagrams to the right. We note that in the experiments, the pulses in the cavity are much denser, and so are the loss states. In the present experiment, we had 51 pulses.
Fig. 2.
Fig. 2. Experimental setup. Ring fiber laser of length L404m, with a high harmonic AML, an envelope modulation (509 kHz), and a controllable noise injection. The wavelength was 1549nm. The system is composed of an erbium-doped fiber amplifier (EDFA), single mode fiber (SMF), wavelength division multiplexer (WDM), dispersion compensation fiber (DCF), bandpass filter (BPF), high pass filter (HPF), variable optical attenuator (VOA), polarization controller (PC), circulator (CIR), and fiber Bragg grating (FBG).
Fig. 3.
Fig. 3. Experimental and theoretical lowest-loss pulse power versus noise level normalized by power (T/P) for various η s. (a) Experimental results for 51 pulses in the cavity. The inset is a zoomed view of the transition region and the difference between the two regimes, below and above η=1. Theoretical graphs are shown for (b) 51 and (c) 501 pulses.
Fig. 4.
Fig. 4. Experimental and theoretical pulse power distribution. The experimental figures (left-hand side figures) are plotted from measurements of 51 equally spaced pulses in the cavity frame (L/2,L/2), as a function of the injected noise level T (in logarithmic scale and opposite direction), for various η s. The corresponding theoretical results are shown in the right-hand side figures. We can see the route to condensation for η<1 with a massive lowest-loss pulse population as T decreases. The power scale is the same as in Fig. 3.

Tables (1)

Tables Icon

Table 1. Analogy between BEC and Pulse/Mode Condensation

Equations (6)

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

(dam/dτ)=(gεm)am+Γm.
P=m=NNpm=m=NNTεmgP=Tε0g+T0εNρ(ε)dεε+ε0g,
fBE(ε)=1/{exp[(εμ)/kBT]1}[(εμ)/kBT]1kBT/(εμ)
p(ε)=T/(ε+ε0g)
N=n0+0ρ(ε)dεexp[(εμ)/kBT]1
P=p0+T0εNρ(ε)dεε+ε0g

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