Abstract

We present a five-level atomic system in which the index of refraction of a probe laser can be enhanced or reduced below unity with vanishing absorption in the region between pairs of absorption and gain lines formed by dressing of the atoms with a control laser and rf/microwave fields. By weak incoherent pumping of the population into a single metastable state, one can create several narrow amplifying resonances. At frequencies between these gain lines and additional absorption lines, there exist regions of vanishing absorption but resonantly enhanced index of refraction. In Rb vapors with density N in units of cm3, we predict an index of refraction up to n1+1.2×1014N for the D1 line, which is more than an order of magnitude larger than other proposals for index of refraction enhancement. Furthermore, the index can be readily reduced below 1 by simply changing the sign of the probe or rf field detunings. This enhancement is robust with respect to homogeneous and inhomogeneous broadening.

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  1. M. O. Scully, Phys. Rev. Lett. 67, 1855 (1991).
    [Crossref] [PubMed]
  2. A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, Phys. Rev. Lett. 76, 3935 (1996).
    [Crossref] [PubMed]
  3. D. D. Yavuz, Phys. Rev. Lett. 95, 223601 (2005).
    [Crossref] [PubMed]
  4. N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, Phys. Rev. Lett. 101, 147401 (2008).
    [Crossref] [PubMed]
  5. J. O. Weatherall and C. P. Search, Phys. Rev. A 81, 023806(2010).
    [Crossref]
  6. M. Fleishhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
    [Crossref]
  7. M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S. Y. Zhu, Phys. Rev. A 46, 1468 (1992).
    [Crossref] [PubMed]

2010 (1)

J. O. Weatherall and C. P. Search, Phys. Rev. A 81, 023806(2010).
[Crossref]

2008 (1)

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, Phys. Rev. Lett. 101, 147401 (2008).
[Crossref] [PubMed]

2005 (2)

D. D. Yavuz, Phys. Rev. Lett. 95, 223601 (2005).
[Crossref] [PubMed]

M. Fleishhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[Crossref]

1996 (1)

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, Phys. Rev. Lett. 76, 3935 (1996).
[Crossref] [PubMed]

1992 (1)

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S. Y. Zhu, Phys. Rev. A 46, 1468 (1992).
[Crossref] [PubMed]

1991 (1)

M. O. Scully, Phys. Rev. Lett. 67, 1855 (1991).
[Crossref] [PubMed]

Fleischhauer, M.

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S. Y. Zhu, Phys. Rev. A 46, 1468 (1992).
[Crossref] [PubMed]

Fleishhauer, M.

M. Fleishhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[Crossref]

Green, J. T.

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, Phys. Rev. Lett. 101, 147401 (2008).
[Crossref] [PubMed]

Hollberg, L.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, Phys. Rev. Lett. 76, 3935 (1996).
[Crossref] [PubMed]

Imamoglu, A.

M. Fleishhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[Crossref]

Keitel, C. H.

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S. Y. Zhu, Phys. Rev. A 46, 1468 (1992).
[Crossref] [PubMed]

Lukin, M. D.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, Phys. Rev. Lett. 76, 3935 (1996).
[Crossref] [PubMed]

Marangos, J. P.

M. Fleishhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[Crossref]

Nikonov, D. E.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, Phys. Rev. Lett. 76, 3935 (1996).
[Crossref] [PubMed]

Proite, N. A.

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, Phys. Rev. Lett. 101, 147401 (2008).
[Crossref] [PubMed]

Robinson, H. G.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, Phys. Rev. Lett. 76, 3935 (1996).
[Crossref] [PubMed]

Scully, M. O.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, Phys. Rev. Lett. 76, 3935 (1996).
[Crossref] [PubMed]

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S. Y. Zhu, Phys. Rev. A 46, 1468 (1992).
[Crossref] [PubMed]

M. O. Scully, Phys. Rev. Lett. 67, 1855 (1991).
[Crossref] [PubMed]

Search, C. P.

J. O. Weatherall and C. P. Search, Phys. Rev. A 81, 023806(2010).
[Crossref]

Su, C.

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S. Y. Zhu, Phys. Rev. A 46, 1468 (1992).
[Crossref] [PubMed]

Ulrich, B. T.

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S. Y. Zhu, Phys. Rev. A 46, 1468 (1992).
[Crossref] [PubMed]

Unks, B. E.

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, Phys. Rev. Lett. 101, 147401 (2008).
[Crossref] [PubMed]

Velichansky, V. L.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, Phys. Rev. Lett. 76, 3935 (1996).
[Crossref] [PubMed]

Weatherall, J. O.

J. O. Weatherall and C. P. Search, Phys. Rev. A 81, 023806(2010).
[Crossref]

Yavuz, D. D.

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, Phys. Rev. Lett. 101, 147401 (2008).
[Crossref] [PubMed]

D. D. Yavuz, Phys. Rev. Lett. 95, 223601 (2005).
[Crossref] [PubMed]

Zhu, S. Y.

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S. Y. Zhu, Phys. Rev. A 46, 1468 (1992).
[Crossref] [PubMed]

Zibrov, A. S.

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, Phys. Rev. Lett. 76, 3935 (1996).
[Crossref] [PubMed]

Phys. Rev. A (2)

J. O. Weatherall and C. P. Search, Phys. Rev. A 81, 023806(2010).
[Crossref]

M. Fleischhauer, C. H. Keitel, M. O. Scully, C. Su, B. T. Ulrich, and S. Y. Zhu, Phys. Rev. A 46, 1468 (1992).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

M. O. Scully, Phys. Rev. Lett. 67, 1855 (1991).
[Crossref] [PubMed]

A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, M. O. Scully, H. G. Robinson, and V. L. Velichansky, Phys. Rev. Lett. 76, 3935 (1996).
[Crossref] [PubMed]

D. D. Yavuz, Phys. Rev. Lett. 95, 223601 (2005).
[Crossref] [PubMed]

N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, Phys. Rev. Lett. 101, 147401 (2008).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

M. Fleishhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Diagram of DIGS level configuration. Such a five- level configuration could be realized in R b 87 by taking | a = | 5 P 1 / 2 , F = 2 , m f = 2 , | b = | 5 S 1 / 2 , F = 1 , m f = 1 , | b = | 5 S 1 / 2 , F = 1 , m f = 0 , | c = | 5 S 1 / 2 , F = 2 , m f = 1 , and | c = | 5 S 1 / 2 , F = 2 , m f = 2 where both probe and control lasers are σ + polarized.

Fig. 2
Fig. 2

(a)  [ χ ˜ ] and (b)  [ χ ˜ ] for Δ b = 0 and pumping values r b / r c = 0.0022 (red solid curve); r b / r c = 0.001 (blue dashed curve); r b / r c = 0.00022 (purple dotted curve). In (b), the zeros of [ χ ˜ ] are marked with dots located between the absorption lines centered at Δ p = ± Ω μ / 2 and the narrow gain lines at ± Ω b / 2 . In (a), the locations of the absorption zeros are marked by vertical lines with dots. Here Ω μ = 2 , Ω b = 0.65 , and Ω c = 0.15 , while the decay rates are γ a a = 2 , γ a b = γ a c = γ a c = 1 , γ C = γ C = γ b b = γ b b = γ c c = γ c c = γ c c = γ b b = 0.0001 . All parameters here and in the other figures are measured in units of the | a | b line width, γ a b . Insets show a larger range of Δ p .

Fig. 3
Fig. 3

(a) Location of the absorption zero [ χ ˜ ] = 0 in the range Δ p = Ω μ / 2 to Ω b / 2 and (b) value of [ χ ˜ ] at the absorption zero as a function of decoherence rate γ 1 = γ C = γ C . (c) Location of the absorption zero [ χ ˜ ] = 0 and (d) value of [ χ ˜ ] at the absorption zero as a function of Ω b . In (a)–(d), r b / r c = 0.0022 . (e) Location of absorption zero and (f) value of [ χ ˜ ] as a function of r b / r c . All other parameters are the same as in Fig. 1.

Fig. 4
Fig. 4

(a)  [ χ ˜ ] and (b)  [ χ ˜ ] . Clearly visible in (a) are the zeros of [ χ ˜ ] marked with dots. The values of [ χ ] in (b) where [ χ ˜ ] = 0 are marked with vertical lines. Parameters: r b / r c = 0.015 , Δ b = 0.01 (red curve); r b / r c = 0.01522 , Δ b = 0.01 (blue dashed curve); r b / r c = 0.0225 , Δ b = 0.01 (purple dashed curve); r b / r c = 0.01522 , Δ b = 0.01 (orange dotted curve); r b / r c = 0.015 , Δ b = 0.01 (green dotted curve); r b / r c = 0.0225 , Δ b = 0.01 (black dashed curve). Other parameters are identical to Fig. 1.

Equations (6)

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H = 2 ( Δ p | a a | + Δ p | c c | + Δ b | b b | + ( Δ p + Δ c ) | c c | Ω p | a b | Ω μ | a c | Ω b | b b | Ω c | c c | ) + h . c . ,
X + = η P B + ( i ϵ 1 + a + ) ( i ϵ 2 + a + ) c 2 ( P B + + cos 2 θ b ρ c c ) i ϵ 2 + a + ( i η + a + ) ( ( i ϵ 1 + a + ) ( i ϵ 2 + a + ) c 2 ) ,
X = η P B ( i ϵ 1 + a ) ( i ϵ 2 + a ) c 2 ( P B sin 2 θ b ρ c c ) i ϵ 2 + a ( i η + a ) ( ( i ϵ 1 + a ) ( i ϵ 2 + a ) c 2 ) ,
ρ c c = r c Ω μ 2 2 γ c a Ω c 2 + γ c c Ω μ 2 ,
ρ b b = r b ( 2 γ b b ( γ b b 2 + Δ b 2 ) + γ b b Ω b 2 ) 2 γ b b γ b b ( γ b b 2 + Δ b 2 ) + ( γ b b + γ b b ) γ b b Ω b 2 ,
ρ b b = r b γ b b ( i γ b b + Δ b ) Ω b 2 γ b b γ b b ( γ b b 2 + Δ b 2 ) + ( γ b b + γ b b ) γ b b Ω b 2 .

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