Abstract

A novel low-threshold amplification scheme for bichromatically coupling three upper states including a metastable state is investigated. Based on model calculations, it is possible to amplify coherent vacuum-ultraviolet emission in Kr gases without population inversion at the probed transition. In this system, therefore, media that are the same as those used for lasing (e.g., Kr) can be used as the incoherent pumping source. The low-threshold amplification is attained when the spontaneous emission at the probed transition is modulated through population trapping in the upper states by two intense coupling lasers. The possibility of continuous amplification of vacuum-ultraviolet emission in this model is discussed.

© 1998 Optical Society of America

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  1. S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989).
    [CrossRef] [PubMed]
  2. A. Imamoglu, J. E. Field, and S. E. Harris, Phys. Rev. Lett. 66, 1154 (1991).
    [CrossRef]
  3. Y. Zhu, Phys. Rev. A 45, R6149 (1992).
    [CrossRef]
  4. M. O. Scully, S.-Y. Zhu, and A. Gavrielides, Phys. Rev. Lett. 62, 2813 (1989).
    [CrossRef] [PubMed]
  5. K. M. Gheri and D. F. Walls, Phys. Rev. A 45, 6675 (1992).
    [CrossRef] [PubMed]
  6. P. Mandel and O. Kocharovskaya, Phys. Rev. A 46, 2700 (1992).
    [CrossRef] [PubMed]
  7. A. Nottleman, C. Peters, and W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
    [CrossRef]
  8. W. E. van der Veer, R. J. J. van Diest, A. Donszelmann, and H. B. van Linden van denHeuvell, Phys. Rev. Lett. 70, 3243 (1993).
    [CrossRef] [PubMed]
  9. A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, Phys. Rev. Lett. 75, 1499 (1995).
    [CrossRef] [PubMed]
  10. T. Nakata and F. Kannari, in Pacific Rim Conference on Lasers and Electro-Optics (CLEO/Pacific Rim) (Optical Society of America, Washington, D.C., 1995), paper ThM5 (1995).
  11. P. M. Radmore and P. L. Knight, J. Phys. B 15, 561 (1982).
    [CrossRef]
  12. O. A. Kocharovskaya, F. Mauri, and E. Arimondo, Opt. Commun. 84, 393 (1991).
    [CrossRef]
  13. M. Aymar and M. Coulombe, At. Data Nucl. Data Tables 21, 537 (1978).
    [CrossRef]

1995 (1)

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, Phys. Rev. Lett. 75, 1499 (1995).
[CrossRef] [PubMed]

1993 (2)

A. Nottleman, C. Peters, and W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef]

W. E. van der Veer, R. J. J. van Diest, A. Donszelmann, and H. B. van Linden van denHeuvell, Phys. Rev. Lett. 70, 3243 (1993).
[CrossRef] [PubMed]

1992 (3)

K. M. Gheri and D. F. Walls, Phys. Rev. A 45, 6675 (1992).
[CrossRef] [PubMed]

P. Mandel and O. Kocharovskaya, Phys. Rev. A 46, 2700 (1992).
[CrossRef] [PubMed]

Y. Zhu, Phys. Rev. A 45, R6149 (1992).
[CrossRef]

1991 (2)

A. Imamoglu, J. E. Field, and S. E. Harris, Phys. Rev. Lett. 66, 1154 (1991).
[CrossRef]

O. A. Kocharovskaya, F. Mauri, and E. Arimondo, Opt. Commun. 84, 393 (1991).
[CrossRef]

1989 (2)

S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989).
[CrossRef] [PubMed]

M. O. Scully, S.-Y. Zhu, and A. Gavrielides, Phys. Rev. Lett. 62, 2813 (1989).
[CrossRef] [PubMed]

1982 (1)

P. M. Radmore and P. L. Knight, J. Phys. B 15, 561 (1982).
[CrossRef]

1978 (1)

M. Aymar and M. Coulombe, At. Data Nucl. Data Tables 21, 537 (1978).
[CrossRef]

Arimondo, E.

O. A. Kocharovskaya, F. Mauri, and E. Arimondo, Opt. Commun. 84, 393 (1991).
[CrossRef]

Aymar, M.

M. Aymar and M. Coulombe, At. Data Nucl. Data Tables 21, 537 (1978).
[CrossRef]

Coulombe, M.

M. Aymar and M. Coulombe, At. Data Nucl. Data Tables 21, 537 (1978).
[CrossRef]

Donszelmann, A.

W. E. van der Veer, R. J. J. van Diest, A. Donszelmann, and H. B. van Linden van denHeuvell, Phys. Rev. Lett. 70, 3243 (1993).
[CrossRef] [PubMed]

Field, J. E.

A. Imamoglu, J. E. Field, and S. E. Harris, Phys. Rev. Lett. 66, 1154 (1991).
[CrossRef]

Gavrielides, A.

M. O. Scully, S.-Y. Zhu, and A. Gavrielides, Phys. Rev. Lett. 62, 2813 (1989).
[CrossRef] [PubMed]

Gheri, K. M.

K. M. Gheri and D. F. Walls, Phys. Rev. A 45, 6675 (1992).
[CrossRef] [PubMed]

Harris, S. E.

A. Imamoglu, J. E. Field, and S. E. Harris, Phys. Rev. Lett. 66, 1154 (1991).
[CrossRef]

S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989).
[CrossRef] [PubMed]

Hollberg, L.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, Phys. Rev. Lett. 75, 1499 (1995).
[CrossRef] [PubMed]

Imamoglu, A.

A. Imamoglu, J. E. Field, and S. E. Harris, Phys. Rev. Lett. 66, 1154 (1991).
[CrossRef]

Knight, P. L.

P. M. Radmore and P. L. Knight, J. Phys. B 15, 561 (1982).
[CrossRef]

Kocharovskaya, O.

P. Mandel and O. Kocharovskaya, Phys. Rev. A 46, 2700 (1992).
[CrossRef] [PubMed]

Kocharovskaya, O. A.

O. A. Kocharovskaya, F. Mauri, and E. Arimondo, Opt. Commun. 84, 393 (1991).
[CrossRef]

Lange, W.

A. Nottleman, C. Peters, and W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef]

Lukin, M. D.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, Phys. Rev. Lett. 75, 1499 (1995).
[CrossRef] [PubMed]

Mandel, P.

P. Mandel and O. Kocharovskaya, Phys. Rev. A 46, 2700 (1992).
[CrossRef] [PubMed]

Mauri, F.

O. A. Kocharovskaya, F. Mauri, and E. Arimondo, Opt. Commun. 84, 393 (1991).
[CrossRef]

Nikonov, D. E.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, Phys. Rev. Lett. 75, 1499 (1995).
[CrossRef] [PubMed]

Nottleman, A.

A. Nottleman, C. Peters, and W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef]

Peters, C.

A. Nottleman, C. Peters, and W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef]

Radmore, P. M.

P. M. Radmore and P. L. Knight, J. Phys. B 15, 561 (1982).
[CrossRef]

Robinson, H. G.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, Phys. Rev. Lett. 75, 1499 (1995).
[CrossRef] [PubMed]

Scully, M. O.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, Phys. Rev. Lett. 75, 1499 (1995).
[CrossRef] [PubMed]

M. O. Scully, S.-Y. Zhu, and A. Gavrielides, Phys. Rev. Lett. 62, 2813 (1989).
[CrossRef] [PubMed]

van der Veer, W. E.

W. E. van der Veer, R. J. J. van Diest, A. Donszelmann, and H. B. van Linden van denHeuvell, Phys. Rev. Lett. 70, 3243 (1993).
[CrossRef] [PubMed]

van Diest, R. J. J.

W. E. van der Veer, R. J. J. van Diest, A. Donszelmann, and H. B. van Linden van denHeuvell, Phys. Rev. Lett. 70, 3243 (1993).
[CrossRef] [PubMed]

van Linden van denHeuvell, H. B.

W. E. van der Veer, R. J. J. van Diest, A. Donszelmann, and H. B. van Linden van denHeuvell, Phys. Rev. Lett. 70, 3243 (1993).
[CrossRef] [PubMed]

Velichansky, V. L.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, Phys. Rev. Lett. 75, 1499 (1995).
[CrossRef] [PubMed]

Walls, D. F.

K. M. Gheri and D. F. Walls, Phys. Rev. A 45, 6675 (1992).
[CrossRef] [PubMed]

Zhu, S.-Y.

M. O. Scully, S.-Y. Zhu, and A. Gavrielides, Phys. Rev. Lett. 62, 2813 (1989).
[CrossRef] [PubMed]

Zhu, Y.

Y. Zhu, Phys. Rev. A 45, R6149 (1992).
[CrossRef]

Zibrov, A. S.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, Phys. Rev. Lett. 75, 1499 (1995).
[CrossRef] [PubMed]

At. Data Nucl. Data Tables (1)

M. Aymar and M. Coulombe, At. Data Nucl. Data Tables 21, 537 (1978).
[CrossRef]

J. Phys. B (1)

P. M. Radmore and P. L. Knight, J. Phys. B 15, 561 (1982).
[CrossRef]

Opt. Commun. (1)

O. A. Kocharovskaya, F. Mauri, and E. Arimondo, Opt. Commun. 84, 393 (1991).
[CrossRef]

Phys. Rev. A (3)

Y. Zhu, Phys. Rev. A 45, R6149 (1992).
[CrossRef]

K. M. Gheri and D. F. Walls, Phys. Rev. A 45, 6675 (1992).
[CrossRef] [PubMed]

P. Mandel and O. Kocharovskaya, Phys. Rev. A 46, 2700 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (6)

A. Nottleman, C. Peters, and W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef]

W. E. van der Veer, R. J. J. van Diest, A. Donszelmann, and H. B. van Linden van denHeuvell, Phys. Rev. Lett. 70, 3243 (1993).
[CrossRef] [PubMed]

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, Phys. Rev. Lett. 75, 1499 (1995).
[CrossRef] [PubMed]

M. O. Scully, S.-Y. Zhu, and A. Gavrielides, Phys. Rev. Lett. 62, 2813 (1989).
[CrossRef] [PubMed]

S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989).
[CrossRef] [PubMed]

A. Imamoglu, J. E. Field, and S. E. Harris, Phys. Rev. Lett. 66, 1154 (1991).
[CrossRef]

Other (1)

T. Nakata and F. Kannari, in Pacific Rim Conference on Lasers and Electro-Optics (CLEO/Pacific Rim) (Optical Society of America, Washington, D.C., 1995), paper ThM5 (1995).

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Figures (8)

Fig. 1
Fig. 1

Four-level atomic system.

Fig. 2
Fig. 2

Four-level system in the absorbing–nonabsorbing state basis.

Fig. 3
Fig. 3

Partial energy diagram of a Kr i atom: 5S[3/2]1, jl=3/2nl=5sK=3/2J=1; 5S[1/2]1, jl=1/2nl=5sK=1/2J=1 in |[(4p52Pjl, nl)K, 1/2]J.

Fig. 4
Fig. 4

Possible transition paths when polarized coupling fields are used.

Fig. 5
Fig. 5

Dependence of the VUV amplification gain on the intensity of two coupling lasers. (a) T21=10,000 K, T32=1000 K, T34=1000 K; (b) T21=15,000 K.

Fig. 6
Fig. 6

Saturation of the VUV amplification. I1=5 kW/cm2.

Fig. 7
Fig. 7

Dependence of the VUV gain on |3〉–|4〉 and |2〉–|3〉 incoherent pumping strength. I1=5 kW/cm2, I2=0.14 W/cm2. (a) T21=10,000 K, (b) T21=15,000 K.

Fig. 8
Fig. 8

Spectral profile of the peak VUV amplification of Fig. 5. (a), (b) T21=15,000 K, T32=T34=1000 K, I1=10 kW/cm2. (c) T21=15,000 K, I1=10 kW/cm2, 100 kW/cm2, 1 MW/cm2. (d) T21=25,000 K, I1=10 kW/cm2, 100 kW/cm2, 1 MW/cm2.  

Equations (33)

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i dρnndt=[Hat+Hint, ρnn]+l,lRnnllρll,
l,lRnnllρll=kn(wknρkk-wnkρnn)n=n-γnnρnnnn
w=0R2100Γ21+R210R3200Γ32+R320Γ34+R3400R340,
Rij=Γijnij=Γijexp(ωi-ωj)kbTij-1-1,
Hat=E1|11|+E2|22|+E3|33|+E4|44|,
Hint=-2 (Ω1|32|exp(-iΔ1t)+Ω2|34|exp(-iΔ2t)+ΩP|21|exp(-iΔPt)+c.c.),
Ωi=μFi,
Hint=20-ΩP*00-ΩP0-Ω1*00-Ω10-Ω2*00-Ω20.
R21>|Ω2|2|Ω1|2 Γ21|Ω2|2Γ32+|Ω1|2(Γ34+Γ21)|Ω2|2(Γ32-Γ21)+|Ω1|2Γ34,
R21Γ21>|Ω2|2|Ω1|21+Γ21Γ34.
|A=1W (Ω2*|4+Ω1*|2),
|NA=1W (Ω1|4-Ω2|2),
Hint=200-1W Ω2-1W Ω1000-W-1W Ω2*000-1W Ω1*-W00.
ΓA1=|Ω1|2W2 Γ21,ΓNA1=|Ω2|2W2 Γ21.
α=Kμ2N0Imρ12ΩP,
ρ˙120=-γ1202-iΔωPρ120+i2 ΩP*(ρ2020-ρ11)-i2 Ω1*(ρ13+1+ρ13-1),
ρ˙13+1=-γ13+12-i(ΔωP+Δω1)ρ13+1+i2 ΩP*×ρ203+1-i2 Ω1ρ120-i2 Ω2ρ14,
ρ˙13-1=-γ13-12-i(ΔωP+Δω1)ρ13-1+i2 ΩP*×ρ203-1-i2 Ω1ρ120-i2 Ω2ρ14,
ρ˙14=-γ142-i(ΔωP+Δω1-Δω2)ρ14+i2 ΩPρ204-i2 Ω2*(ρ13+1+ρ13-1),
ρ˙203+1=-γ203+12-iΔω1ρ203+1+i2 Ω1(ρ3+13+1+ρ3+13-1*-ρ2020)+i2 ΩP*ρ13+1-i2 Ω2ρ204,
ρ˙203-1=-γ203-12-iΔω1ρ203-1+i2 Ω1(ρ3+13-1+ρ3-13-1-ρ2020)+i2 ΩP*ρ13-1-i2 Ω2ρ204,
ρ˙3+13-1=-γ3+13-12 ρ3+13-1+i2 Ω1*ρ203-1-i2 Ω1×ρ203+1*+i2 Ω2*ρ3-14*-i2 Ω2ρ3+14,
ρ˙204=-γ2042-i(Δω1-Δω2)ρ204+i2 ΩP*ρ14+i2 Ω1(ρ3+14+ρ3-14)-i2 Ω2*(ρ203+1+ρ203-1),
ρ˙3+14=-γ3+142+iΔω2ρ3+14+i2 Ω1*ρ204-i2 Ω2*(ρ3+13+1+ρ3+13-1*-ρ44),
ρ˙3-14=-γ3-142+iΔω2ρ3-14+i2 Ω1*ρ204-i2 Ω2*(ρ3+13-1+ρ3-13-1*-ρ44),
ρ˙11=Γ21(ρ2020+ρ2±12±1)+Γ31(ρ3+13+1+ρ3030+ρ3-13-1)+R21(ρ2020+ρ2±12±1-ρ11)-i2 (ΩP*ρ120-c.c.),
ρ˙2020=Γ32(ρ3+13+1+ρ3-13-1)-Γ21ρ2020-R21ρ2020+12 ρ11+R32(ρ3+13+1+ρ3-13-1-ρ2020)+i2 (ΩP*ρ12-c.c.)
-i2 [Ω1*(ρ203+1+ρ203-1)-c.c.],
ρ˙2±12±1=Γ32ρ3030-Γ21ρ2±12±1+12 R21ρ11-R32ρ2±12±1,
ρ˙3+13+1=-(Γ34+Γ32+Γ31)ρ3+13+1-R32ρ3+13+1-12 ρ2020-R34ρ3+13+1-12 ρ44+i2 (Ω203+1*-c.c.)-i2 (Ω2ρ3+14-c.c.),
ρ˙3-13-1=-(Γ34+Γ32+Γ31)ρ3-13-1-R32ρ3-13-1-12 ρ2020×R34ρ3-13-1-12 ρ44+i2 (Ω203-1*-c.c.)-i2 (Ω2ρ3-14-c.c.),
ρ˙3030=-(Γ34+Γ32+Γ31)ρ3030+R32ρ2±12±1,
ρ˙44=Γ34(ρ3+13+1+ρ3-13-1)+R34(ρ3+13+1+ρ3-13-1-ρ44)+i2 [Ω2(ρ3+14+ρ3-14)-c.c.].

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