Abstract

A model of a superradiant laser comprising of N three-level systems driven by two pumping lasers is considered in semiclassical approximation. Steady-state equations for density matrix elements are solved both analytically and numerically. Various properties of generated light are investigated. It is found that such a laser can exhibit both superradiance, when the intensity scales as N2, and subradiance when the intensity does not depend on N. The phase of the laser field is locked to the relative phase of the pumping lasers.

© 2011 Optical Society of America

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  1. R. H. Dicke, Phys. Rev. 93, 99 (1954).
    [CrossRef]
  2. M. Gross and S. Haroche, Phys. Rep. 93, 301 (1982).
    [CrossRef]
  3. F. Haake, M. I. Kolobov, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. Lett. 71, 995 (1993).
    [CrossRef] [PubMed]
  4. F. Haake, M. I. Kolobov, C. Seeger, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. A 54, 1625 (1996).
    [CrossRef] [PubMed]
  5. C. Seeger, M. I. Kolobov, M. Kuś, and F. Haake, Phys. Rev. A 54, 4440 (1996).
    [CrossRef] [PubMed]
  6. Y. M. Golubev, Theor. Math. Phys. 109, 1437 (1996).
    [CrossRef]
  7. D. Yu and J. Chen, Phys. Rev. A 81, 053809 (2010).
    [CrossRef]
  8. C. Wiele, F. Haake, and Y. M. Golubev, Phys. Rev. A 60, 4986 (1999).
    [CrossRef]
  9. J. H. Eberly, J. Phys. B 39, S599 (2006).
    [CrossRef]
  10. I. E. Mazets and G. Kurizki, J. Phys. B 40, F105 (2007).
    [CrossRef]
  11. M. O. Scully, E. S. Fry, C. H. R. Ooi, and K. Wódkiewicz, Phys. Rev. Lett. 96, 010501 (2006).
    [CrossRef] [PubMed]
  12. D. Braunstein and R. Shuker, Phys. Rev. A 64, 053812(2001).
    [CrossRef]
  13. C. R. Stroud, J. H. Eberly, W. L. Lama, and L. Mandel, Phys. Rev. A 5, 1094 (1972).
    [CrossRef]
  14. G. A. Koganov and R. Shuker, Laser Phys. 21, 1260 (2011).
    [CrossRef]

2011 (1)

G. A. Koganov and R. Shuker, Laser Phys. 21, 1260 (2011).
[CrossRef]

2010 (1)

D. Yu and J. Chen, Phys. Rev. A 81, 053809 (2010).
[CrossRef]

2007 (1)

I. E. Mazets and G. Kurizki, J. Phys. B 40, F105 (2007).
[CrossRef]

2006 (2)

M. O. Scully, E. S. Fry, C. H. R. Ooi, and K. Wódkiewicz, Phys. Rev. Lett. 96, 010501 (2006).
[CrossRef] [PubMed]

J. H. Eberly, J. Phys. B 39, S599 (2006).
[CrossRef]

2001 (1)

D. Braunstein and R. Shuker, Phys. Rev. A 64, 053812(2001).
[CrossRef]

1999 (1)

C. Wiele, F. Haake, and Y. M. Golubev, Phys. Rev. A 60, 4986 (1999).
[CrossRef]

1996 (3)

F. Haake, M. I. Kolobov, C. Seeger, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. A 54, 1625 (1996).
[CrossRef] [PubMed]

C. Seeger, M. I. Kolobov, M. Kuś, and F. Haake, Phys. Rev. A 54, 4440 (1996).
[CrossRef] [PubMed]

Y. M. Golubev, Theor. Math. Phys. 109, 1437 (1996).
[CrossRef]

1993 (1)

F. Haake, M. I. Kolobov, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. Lett. 71, 995 (1993).
[CrossRef] [PubMed]

1982 (1)

M. Gross and S. Haroche, Phys. Rep. 93, 301 (1982).
[CrossRef]

1972 (1)

C. R. Stroud, J. H. Eberly, W. L. Lama, and L. Mandel, Phys. Rev. A 5, 1094 (1972).
[CrossRef]

1954 (1)

R. H. Dicke, Phys. Rev. 93, 99 (1954).
[CrossRef]

Braunstein, D.

D. Braunstein and R. Shuker, Phys. Rev. A 64, 053812(2001).
[CrossRef]

Chen, J.

D. Yu and J. Chen, Phys. Rev. A 81, 053809 (2010).
[CrossRef]

Dicke, R. H.

R. H. Dicke, Phys. Rev. 93, 99 (1954).
[CrossRef]

Eberly, J. H.

J. H. Eberly, J. Phys. B 39, S599 (2006).
[CrossRef]

C. R. Stroud, J. H. Eberly, W. L. Lama, and L. Mandel, Phys. Rev. A 5, 1094 (1972).
[CrossRef]

Fabre, C.

F. Haake, M. I. Kolobov, C. Seeger, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. A 54, 1625 (1996).
[CrossRef] [PubMed]

F. Haake, M. I. Kolobov, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. Lett. 71, 995 (1993).
[CrossRef] [PubMed]

Fry, E. S.

M. O. Scully, E. S. Fry, C. H. R. Ooi, and K. Wódkiewicz, Phys. Rev. Lett. 96, 010501 (2006).
[CrossRef] [PubMed]

Giacobino, E.

F. Haake, M. I. Kolobov, C. Seeger, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. A 54, 1625 (1996).
[CrossRef] [PubMed]

F. Haake, M. I. Kolobov, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. Lett. 71, 995 (1993).
[CrossRef] [PubMed]

Golubev, Y. M.

C. Wiele, F. Haake, and Y. M. Golubev, Phys. Rev. A 60, 4986 (1999).
[CrossRef]

Y. M. Golubev, Theor. Math. Phys. 109, 1437 (1996).
[CrossRef]

Gross, M.

M. Gross and S. Haroche, Phys. Rep. 93, 301 (1982).
[CrossRef]

Haake, F.

C. Wiele, F. Haake, and Y. M. Golubev, Phys. Rev. A 60, 4986 (1999).
[CrossRef]

C. Seeger, M. I. Kolobov, M. Kuś, and F. Haake, Phys. Rev. A 54, 4440 (1996).
[CrossRef] [PubMed]

F. Haake, M. I. Kolobov, C. Seeger, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. A 54, 1625 (1996).
[CrossRef] [PubMed]

F. Haake, M. I. Kolobov, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. Lett. 71, 995 (1993).
[CrossRef] [PubMed]

Haroche, S.

M. Gross and S. Haroche, Phys. Rep. 93, 301 (1982).
[CrossRef]

Koganov, G. A.

G. A. Koganov and R. Shuker, Laser Phys. 21, 1260 (2011).
[CrossRef]

Kolobov, M. I.

F. Haake, M. I. Kolobov, C. Seeger, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. A 54, 1625 (1996).
[CrossRef] [PubMed]

C. Seeger, M. I. Kolobov, M. Kuś, and F. Haake, Phys. Rev. A 54, 4440 (1996).
[CrossRef] [PubMed]

F. Haake, M. I. Kolobov, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. Lett. 71, 995 (1993).
[CrossRef] [PubMed]

Kurizki, G.

I. E. Mazets and G. Kurizki, J. Phys. B 40, F105 (2007).
[CrossRef]

Kus, M.

C. Seeger, M. I. Kolobov, M. Kuś, and F. Haake, Phys. Rev. A 54, 4440 (1996).
[CrossRef] [PubMed]

Lama, W. L.

C. R. Stroud, J. H. Eberly, W. L. Lama, and L. Mandel, Phys. Rev. A 5, 1094 (1972).
[CrossRef]

Mandel, L.

C. R. Stroud, J. H. Eberly, W. L. Lama, and L. Mandel, Phys. Rev. A 5, 1094 (1972).
[CrossRef]

Mazets, I. E.

I. E. Mazets and G. Kurizki, J. Phys. B 40, F105 (2007).
[CrossRef]

Ooi, C. H. R.

M. O. Scully, E. S. Fry, C. H. R. Ooi, and K. Wódkiewicz, Phys. Rev. Lett. 96, 010501 (2006).
[CrossRef] [PubMed]

Reynaud, S.

F. Haake, M. I. Kolobov, C. Seeger, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. A 54, 1625 (1996).
[CrossRef] [PubMed]

F. Haake, M. I. Kolobov, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. Lett. 71, 995 (1993).
[CrossRef] [PubMed]

Scully, M. O.

M. O. Scully, E. S. Fry, C. H. R. Ooi, and K. Wódkiewicz, Phys. Rev. Lett. 96, 010501 (2006).
[CrossRef] [PubMed]

Seeger, C.

F. Haake, M. I. Kolobov, C. Seeger, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. A 54, 1625 (1996).
[CrossRef] [PubMed]

C. Seeger, M. I. Kolobov, M. Kuś, and F. Haake, Phys. Rev. A 54, 4440 (1996).
[CrossRef] [PubMed]

Shuker, R.

G. A. Koganov and R. Shuker, Laser Phys. 21, 1260 (2011).
[CrossRef]

D. Braunstein and R. Shuker, Phys. Rev. A 64, 053812(2001).
[CrossRef]

Stroud, C. R.

C. R. Stroud, J. H. Eberly, W. L. Lama, and L. Mandel, Phys. Rev. A 5, 1094 (1972).
[CrossRef]

Wiele, C.

C. Wiele, F. Haake, and Y. M. Golubev, Phys. Rev. A 60, 4986 (1999).
[CrossRef]

Wódkiewicz, K.

M. O. Scully, E. S. Fry, C. H. R. Ooi, and K. Wódkiewicz, Phys. Rev. Lett. 96, 010501 (2006).
[CrossRef] [PubMed]

Yu, D.

D. Yu and J. Chen, Phys. Rev. A 81, 053809 (2010).
[CrossRef]

J. Phys. B (2)

J. H. Eberly, J. Phys. B 39, S599 (2006).
[CrossRef]

I. E. Mazets and G. Kurizki, J. Phys. B 40, F105 (2007).
[CrossRef]

Laser Phys. (1)

G. A. Koganov and R. Shuker, Laser Phys. 21, 1260 (2011).
[CrossRef]

Phys. Rep. (1)

M. Gross and S. Haroche, Phys. Rep. 93, 301 (1982).
[CrossRef]

Phys. Rev. (1)

R. H. Dicke, Phys. Rev. 93, 99 (1954).
[CrossRef]

Phys. Rev. A (6)

D. Braunstein and R. Shuker, Phys. Rev. A 64, 053812(2001).
[CrossRef]

C. R. Stroud, J. H. Eberly, W. L. Lama, and L. Mandel, Phys. Rev. A 5, 1094 (1972).
[CrossRef]

F. Haake, M. I. Kolobov, C. Seeger, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. A 54, 1625 (1996).
[CrossRef] [PubMed]

C. Seeger, M. I. Kolobov, M. Kuś, and F. Haake, Phys. Rev. A 54, 4440 (1996).
[CrossRef] [PubMed]

D. Yu and J. Chen, Phys. Rev. A 81, 053809 (2010).
[CrossRef]

C. Wiele, F. Haake, and Y. M. Golubev, Phys. Rev. A 60, 4986 (1999).
[CrossRef]

Phys. Rev. Lett. (2)

M. O. Scully, E. S. Fry, C. H. R. Ooi, and K. Wódkiewicz, Phys. Rev. Lett. 96, 010501 (2006).
[CrossRef] [PubMed]

F. Haake, M. I. Kolobov, C. Fabre, E. Giacobino, and S. Reynaud, Phys. Rev. Lett. 71, 995 (1993).
[CrossRef] [PubMed]

Theor. Math. Phys. (1)

Y. M. Golubev, Theor. Math. Phys. 109, 1437 (1996).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Scheme of the system.

Fig. 2
Fig. 2

The number of photons n and populations of states as functions of the number of atoms N.

Fig. 3
Fig. 3

The number of photons n and populations of states ρ i i as functions of the ratio Ω a b / Ω b c between Rabi frequencies of the driving fields.

Equations (13)

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

H int = [ Ω a b e i ( Δ a b t + φ a b ) σ a b + Ω b c e i ( Δ b c t + φ b c ) σ b c + g b ^ e i Δ a c t σ a c ] + H . c . ,
ρ ˙ c c = ( γ c b + γ c a ) ρ c c + i Ω b c ( ρ c b e i φ b c ρ b c e i φ b c ) + i g * b ^ ρ c a i g b ^ ρ a c ,
ρ ˙ b b = γ c b ρ c c γ b a ρ b b + i Ω b c ( ρ b c e i φ b c ρ c b e i φ b c ) i Ω a b ( ρ a b e i φ a b ρ b a e i φ a b ) ,
ρ ˙ a a = γ c a ρ c c + γ b a ρ b b + i Ω a b ( ρ a b e i φ a b ρ b a e i φ a b ) + i g * b ^ ρ a c i g b ^ ρ c a ,
ρ ˙ b c = ( γ c a + γ c b + γ b a 2 i Δ b c ) ρ b c i Ω b c ( ρ c c ρ b b ) e i φ b c + i g * b ρ b a e i Δ 3 t i Ω a b ρ a c e i ( Δ 3 t φ a b ) ,
ρ ˙ a c = ( γ c a + γ c b 2 i ( Δ b c + Δ a b ) ) ρ a c i g * b ( ρ c c ρ a a ) + i Ω b c ρ a b e i ( Δ 3 t φ b c ) i Ω a b ρ b c e i ( Δ 3 t φ a b ) ,
ρ ˙ a b = ( γ b a 2 + i Δ a b ) ρ a b i Ω a b ( ρ b b ρ a a ) e i φ a b i g * b ρ c b e i Δ 3 t + i Ω b c ρ a c e i ( Δ 3 t φ b c ) ,
b ˙ = κ b + i j g ρ c a ,
b ˙ = κ b i j g ρ a c ,
n = ( 2 Ω a b Ω b c g γ ) 2 ( N N + N S ) 2 ,
φ = φ a b + φ b c π 2 ,
N S = 2 κ Ω b c 2 γ g 2 .
n ( g Ω a b κ Ω b c ) 2 N 2 ,

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