Abstract

On the basis of the results of numerical modeling, it is shown that dipole–dipole interactions among atoms in the active medium strongly influences the character of the associated superradiation. The main effect is to make the nuclear subsystem behave chaotically. Its strength increases with the atom density and leads to the suppression of distant collective correlations and superradiation. Near correlations between the atoms are established, causing a confinement effect: a shielding of radiation in the active medium.

© 2008 Optical Society of America

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References

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  1. R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99-110 (1954).
    [CrossRef]
  2. N. Skribanowitz, I. P. Herman, J. C. MacGillivray, and M. S. Feld, “Observation of Dicke superradiance in optically pumped HF gas,” Phys. Rev. Lett. 30, 309-312 (1973).
    [CrossRef]
  3. A. V. Gaponov, “Instability of a system of excited oscillators with respect to electromagnetic perturbations,” Sov. Phys. JETP 12, 232-298 (1960).
  4. A. V. Gaponov, M. I. Petelin, and V. K. Yulpatov, “The induced radiation of excited classical oscillators and its use in high-frequency electronics,” Radiophys. Quantum Electron. 10, 794-823 (1967).
    [CrossRef]
  5. M. Gross and S. Haroche, “Superradiance: an essay on the theory of collective spontaneous emission,” Phys. Rep. 93, 301-396 (1982).
    [CrossRef]
  6. S. Stenholm, “Quantum theory of electromagnetic fields interacting with atoms and molecules,” Phys. Rep. 6, 1-121 (1973).
    [CrossRef]
  7. L. I. Men'shikov, “Superradiance and related phenomena,” Sov. Phys. Usp. 42, 107-147 (1999).
  8. D. V. Sivukhin, General Course of Physics: Vol. 3: Electricity (Nauka-Fizmatlit, 1996).
  9. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  10. R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Limited superradiant damping of small samples,” Phys. Lett. A 40, 365-366 (1972).
    [CrossRef]
  11. R. Friedberg and S. R. Hartmann, “Temporal evolution of superradiance in a small sphere,” Phys. Rev. A 10, 1728-1739 (1974).
    [CrossRef]
  12. Yu. A. Il'inskii and N. S. Maslova, “The classical analog of superradiation in a system of interacting nonlinear oscillators,” Sov. Phys. JETP 94, 171-174 (1988).
  13. V. V. Berezovskii and L. I. Men'shikov, “Transverse cooling of electron beams,” JETP Lett. 86, 355-357 (2007).
    [CrossRef]
  14. L. D. Landau and E. M. Lifshiz, Course of Theoretical Physics: Vol. 2: the Classical Theory of Fields (Pergamon, 1975).
  15. S. V. Zaitsev, L. A. Graham, D. L. Huffaker, N. Yu. Gordeev, V. I. Kopchatov, L. Ya. Karachinsky, I. I. Novikov, and P. S. Kop'ev, “Superradiance in semiconductors,” Sov. Phys. Semicond. 33, 1309-1314 (1999).
  16. W. Pauli, Theory of Relativity (Dover, 1981).

2007

V. V. Berezovskii and L. I. Men'shikov, “Transverse cooling of electron beams,” JETP Lett. 86, 355-357 (2007).
[CrossRef]

1999

S. V. Zaitsev, L. A. Graham, D. L. Huffaker, N. Yu. Gordeev, V. I. Kopchatov, L. Ya. Karachinsky, I. I. Novikov, and P. S. Kop'ev, “Superradiance in semiconductors,” Sov. Phys. Semicond. 33, 1309-1314 (1999).

L. I. Men'shikov, “Superradiance and related phenomena,” Sov. Phys. Usp. 42, 107-147 (1999).

1988

Yu. A. Il'inskii and N. S. Maslova, “The classical analog of superradiation in a system of interacting nonlinear oscillators,” Sov. Phys. JETP 94, 171-174 (1988).

1982

M. Gross and S. Haroche, “Superradiance: an essay on the theory of collective spontaneous emission,” Phys. Rep. 93, 301-396 (1982).
[CrossRef]

1974

R. Friedberg and S. R. Hartmann, “Temporal evolution of superradiance in a small sphere,” Phys. Rev. A 10, 1728-1739 (1974).
[CrossRef]

1973

S. Stenholm, “Quantum theory of electromagnetic fields interacting with atoms and molecules,” Phys. Rep. 6, 1-121 (1973).
[CrossRef]

N. Skribanowitz, I. P. Herman, J. C. MacGillivray, and M. S. Feld, “Observation of Dicke superradiance in optically pumped HF gas,” Phys. Rev. Lett. 30, 309-312 (1973).
[CrossRef]

1972

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Limited superradiant damping of small samples,” Phys. Lett. A 40, 365-366 (1972).
[CrossRef]

1967

A. V. Gaponov, M. I. Petelin, and V. K. Yulpatov, “The induced radiation of excited classical oscillators and its use in high-frequency electronics,” Radiophys. Quantum Electron. 10, 794-823 (1967).
[CrossRef]

1960

A. V. Gaponov, “Instability of a system of excited oscillators with respect to electromagnetic perturbations,” Sov. Phys. JETP 12, 232-298 (1960).

1954

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99-110 (1954).
[CrossRef]

JETP Lett.

V. V. Berezovskii and L. I. Men'shikov, “Transverse cooling of electron beams,” JETP Lett. 86, 355-357 (2007).
[CrossRef]

Phys. Lett. A

R. Friedberg, S. R. Hartmann, and J. T. Manassah, “Limited superradiant damping of small samples,” Phys. Lett. A 40, 365-366 (1972).
[CrossRef]

Phys. Rep.

M. Gross and S. Haroche, “Superradiance: an essay on the theory of collective spontaneous emission,” Phys. Rep. 93, 301-396 (1982).
[CrossRef]

S. Stenholm, “Quantum theory of electromagnetic fields interacting with atoms and molecules,” Phys. Rep. 6, 1-121 (1973).
[CrossRef]

Phys. Rev.

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99-110 (1954).
[CrossRef]

Phys. Rev. A

R. Friedberg and S. R. Hartmann, “Temporal evolution of superradiance in a small sphere,” Phys. Rev. A 10, 1728-1739 (1974).
[CrossRef]

Phys. Rev. Lett.

N. Skribanowitz, I. P. Herman, J. C. MacGillivray, and M. S. Feld, “Observation of Dicke superradiance in optically pumped HF gas,” Phys. Rev. Lett. 30, 309-312 (1973).
[CrossRef]

Radiophys. Quantum Electron.

A. V. Gaponov, M. I. Petelin, and V. K. Yulpatov, “The induced radiation of excited classical oscillators and its use in high-frequency electronics,” Radiophys. Quantum Electron. 10, 794-823 (1967).
[CrossRef]

Sov. Phys. JETP

A. V. Gaponov, “Instability of a system of excited oscillators with respect to electromagnetic perturbations,” Sov. Phys. JETP 12, 232-298 (1960).

Yu. A. Il'inskii and N. S. Maslova, “The classical analog of superradiation in a system of interacting nonlinear oscillators,” Sov. Phys. JETP 94, 171-174 (1988).

Sov. Phys. Semicond.

S. V. Zaitsev, L. A. Graham, D. L. Huffaker, N. Yu. Gordeev, V. I. Kopchatov, L. Ya. Karachinsky, I. I. Novikov, and P. S. Kop'ev, “Superradiance in semiconductors,” Sov. Phys. Semicond. 33, 1309-1314 (1999).

Sov. Phys. Usp.

L. I. Men'shikov, “Superradiance and related phenomena,” Sov. Phys. Usp. 42, 107-147 (1999).

Other

D. V. Sivukhin, General Course of Physics: Vol. 3: Electricity (Nauka-Fizmatlit, 1996).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

W. Pauli, Theory of Relativity (Dover, 1981).

L. D. Landau and E. M. Lifshiz, Course of Theoretical Physics: Vol. 2: the Classical Theory of Fields (Pergamon, 1975).

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Figures (7)

Fig. 1
Fig. 1

Time evolution of the phase distribution of oscillators. The dotted curve is a circle with unit radius. The number of oscillators is N = 5 × 10 3 . The concentration of oscillators n = 10 22 m 3 (curve 2 in Fig. 4). The x and y axes correspond to x a = ρ a cos φ a , y a = ρ a sin φ a , where ρ a and φ a were introduced above Eq. (5).

Fig. 2
Fig. 2

Time dependence of the radiation intensity for N = 5 × 10 3 (all values in arbitrary units).

Fig. 3
Fig. 3

Time evolution of the phase distribution of oscillators in systems with a strong dipole–dipole interaction. The dotted curve is a circle with unit radius. (a) and (b) correspond to the concentration of oscillators n = 8 × 10 22 m 3 (curve 4 in Fig. 4). (c) corresponds to n = 1.8 × 10 23 m 3 (curve 6 in Fig. 4). Notations are the same as in Fig. 1.

Fig. 4
Fig. 4

Intensity of radiation (arbitrary units) for systems with different oscillator concentrations n ( 10 22 m 3 ) : 0.083, 1.0, 2.3, 8.0, 12.13, 18.38, and 27.86 for curves 1–7, respectively. Units coincide with those of Fig. 2.

Fig. 5
Fig. 5

Radiation intensity (arbitrary units) versus time (arbitrary units) for classical systems with different oscillator concentrations n ( 10 22 m 3 ) : 0.083, 1.0, 2.3, 8.0, 12.13, 18.38, and 27.86 for curves 1–7, respectively. Case 1 is compared with the purely quantum result, which varies as sech 2 ( t t 0 ) . Units coincide with those of Fig. 2.

Fig. 6
Fig. 6

Dependence of a maximum of radiation intensity (arbitrary units) on oscillator density n (in 10 22 m 3 ).

Fig. 7
Fig. 7

Dependencies on the number of oscillators N, of (a) the ratio log 10 ( I max ) log 10 ( N ) , and (b) the peak of radiation intensity ( I max ) (the latter is in arbitrary units).

Equations (11)

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ξ ̈ a + ω 0 2 ( 1 + γ ξ a 2 ) ξ a + 2 e 2 ω 0 2 3 m c 3 ξ ̇ a = e 2 m b a a × ( a × ξ b ( t a b ) r a b ) .
ξ a = b [ F a ( t ) exp ( ι ω t ) + F a * ( t ) exp ( ι ω t ) ] ,
F ̇ a + ι δ ( F a 2 1 ) F a + 1 2 β 0 F a = ι β b a a × [ a exp ( ι k r a b ) r a b × F b ( t ) ] .
e B m c 1 v 2 c 2 e B m c ( 1 v 2 2 c 2 ) [ 14 ] .
F ̇ a + ι δ ( F a 2 1 ) F a = ι β b a 3 n a b ( n a b F b ) F b r a b 3 1 2 β 0 b F b ,
I = e 2 ω 4 b 2 3 c 3 a , b F a F b cos ( φ a φ b ) .
v a = ω ( ρ a ) × ρ a + f + b d ( ρ a , ρ b ; r a , r b ) .
I ( t ) = ω 0 4 μ τ N ( μ N + 1 ) 2 sech 2 ( t t 0 2 τ N ) ,
U ( ξ a ) = 1 2 m ω 0 2 ξ a 2 + 1 4 γ m ω 0 2 ξ 0 4 .
m ξ ̈ a + m ω 0 2 ( 1 + γ ξ 0 2 ) ξ a = e E ( r a , t ) .
E ( r , t ) = e b = 1 N r × [ r × ξ b ( t R b c ) R b ]

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