Abstract

We show analytically and numerically that a double-Λ system, characterized by parametric amplification of cross-coupled probe and four-wave mixing pulses, is an excellent medium for producing both slow and stored light. Moreover, this system can compensate for the absorption and broadening processes that usually occur without destroying the coherent properties of the medium. The stored probe signal pulse is written by means of a simple Λ system and is retrieved and amplified, at the same frequency, by a double-Λ system that also produces a pulse at the four-wave mixing frequency.

© 2008 Optical Society of America

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  1. S. E. Harris, Phys. Today 50, 36 (1997).
    [CrossRef]
  2. M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
    [CrossRef] [PubMed]
  3. A. Raczynski, J. Zaremba, and S. Zielinska-Kaniasty, Phys. Rev. A 69, 043801 (2004).
    [CrossRef]
  4. V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
    [CrossRef] [PubMed]
  5. I. Novikova, D. F. Phillips, and R. L. Walsworth, Phys. Rev. Lett. 99, 173604 (2007).
    [CrossRef] [PubMed]
  6. K. Y. Song, M. G. Herraez, and L. Thevenaz, Phys. Rev. A 75, 013810 (2007).
    [CrossRef]
  7. J. T. Mok and B. J. Eggleton, Nature 433, 811 (2005).
    [CrossRef] [PubMed]
  8. A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Opt. Commun. 277, 186 (2007).
    [CrossRef]
  9. M. D. Eisaman, “Generation, storage, and retrieval of nonclassical states of light using atomic ensembles,” Ph.D. dissertation (Harvard University, 2006).
  10. M. D. Lukin, P. R. Hemmer, M. Loffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998).
    [CrossRef]
  11. A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 73, 053805 (2006).
    [CrossRef]
  12. H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 70, 063814 (2004).
    [CrossRef]
  13. C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
    [CrossRef] [PubMed]

2007 (4)

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

I. Novikova, D. F. Phillips, and R. L. Walsworth, Phys. Rev. Lett. 99, 173604 (2007).
[CrossRef] [PubMed]

K. Y. Song, M. G. Herraez, and L. Thevenaz, Phys. Rev. A 75, 013810 (2007).
[CrossRef]

A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Opt. Commun. 277, 186 (2007).
[CrossRef]

2006 (1)

A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 73, 053805 (2006).
[CrossRef]

2005 (1)

J. T. Mok and B. J. Eggleton, Nature 433, 811 (2005).
[CrossRef] [PubMed]

2004 (2)

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 70, 063814 (2004).
[CrossRef]

A. Raczynski, J. Zaremba, and S. Zielinska-Kaniasty, Phys. Rev. A 69, 043801 (2004).
[CrossRef]

2003 (1)

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

2000 (1)

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef] [PubMed]

1998 (1)

M. D. Lukin, P. R. Hemmer, M. Loffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998).
[CrossRef]

1997 (1)

S. E. Harris, Phys. Today 50, 36 (1997).
[CrossRef]

Andre, A.

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

Arimondo, E.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

Boyer, V.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

Eggleton, B. J.

J. T. Mok and B. J. Eggleton, Nature 433, 811 (2005).
[CrossRef] [PubMed]

Eilam, A.

A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Opt. Commun. 277, 186 (2007).
[CrossRef]

A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 73, 053805 (2006).
[CrossRef]

Eisaman, M. D.

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

M. D. Eisaman, “Generation, storage, and retrieval of nonclassical states of light using atomic ensembles,” Ph.D. dissertation (Harvard University, 2006).

Fleischhauer, M.

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef] [PubMed]

Friedmann, H.

A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Opt. Commun. 277, 186 (2007).
[CrossRef]

A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 73, 053805 (2006).
[CrossRef]

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 70, 063814 (2004).
[CrossRef]

Harris, S. E.

S. E. Harris, Phys. Today 50, 36 (1997).
[CrossRef]

Hemmer, P. R.

M. D. Lukin, P. R. Hemmer, M. Loffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998).
[CrossRef]

Herraez, M. G.

K. Y. Song, M. G. Herraez, and L. Thevenaz, Phys. Rev. A 75, 013810 (2007).
[CrossRef]

Lett, P. D.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

Loffler, M.

M. D. Lukin, P. R. Hemmer, M. Loffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998).
[CrossRef]

Lukin, M. D.

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef] [PubMed]

M. D. Lukin, P. R. Hemmer, M. Loffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998).
[CrossRef]

McCormick, C. F.

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

Mok, J. T.

J. T. Mok and B. J. Eggleton, Nature 433, 811 (2005).
[CrossRef] [PubMed]

Novikova, I.

I. Novikova, D. F. Phillips, and R. L. Walsworth, Phys. Rev. Lett. 99, 173604 (2007).
[CrossRef] [PubMed]

Phillips, D. F.

I. Novikova, D. F. Phillips, and R. L. Walsworth, Phys. Rev. Lett. 99, 173604 (2007).
[CrossRef] [PubMed]

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

Raczynski, A.

A. Raczynski, J. Zaremba, and S. Zielinska-Kaniasty, Phys. Rev. A 69, 043801 (2004).
[CrossRef]

Scully, M. O.

M. D. Lukin, P. R. Hemmer, M. Loffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998).
[CrossRef]

Shpaisman, H.

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 70, 063814 (2004).
[CrossRef]

Song, K. Y.

K. Y. Song, M. G. Herraez, and L. Thevenaz, Phys. Rev. A 75, 013810 (2007).
[CrossRef]

Thevenaz, L.

K. Y. Song, M. G. Herraez, and L. Thevenaz, Phys. Rev. A 75, 013810 (2007).
[CrossRef]

van der Wal, C. H.

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

Walsworth, R. L.

I. Novikova, D. F. Phillips, and R. L. Walsworth, Phys. Rev. Lett. 99, 173604 (2007).
[CrossRef] [PubMed]

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

Wilson-Gordon, A. D.

A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Opt. Commun. 277, 186 (2007).
[CrossRef]

A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 73, 053805 (2006).
[CrossRef]

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 70, 063814 (2004).
[CrossRef]

Zaremba, J.

A. Raczynski, J. Zaremba, and S. Zielinska-Kaniasty, Phys. Rev. A 69, 043801 (2004).
[CrossRef]

Zibrov, A. S.

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

Zielinska-Kaniasty, S.

A. Raczynski, J. Zaremba, and S. Zielinska-Kaniasty, Phys. Rev. A 69, 043801 (2004).
[CrossRef]

Nature (1)

J. T. Mok and B. J. Eggleton, Nature 433, 811 (2005).
[CrossRef] [PubMed]

Opt. Commun. (1)

A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Opt. Commun. 277, 186 (2007).
[CrossRef]

Phys. Rev. A (4)

K. Y. Song, M. G. Herraez, and L. Thevenaz, Phys. Rev. A 75, 013810 (2007).
[CrossRef]

A. Raczynski, J. Zaremba, and S. Zielinska-Kaniasty, Phys. Rev. A 69, 043801 (2004).
[CrossRef]

A. Eilam, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 73, 053805 (2006).
[CrossRef]

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, Phys. Rev. A 70, 063814 (2004).
[CrossRef]

Phys. Rev. Lett. (4)

V. Boyer, C. F. McCormick, E. Arimondo, and P. D. Lett, Phys. Rev. Lett. 99, 143601 (2007).
[CrossRef] [PubMed]

I. Novikova, D. F. Phillips, and R. L. Walsworth, Phys. Rev. Lett. 99, 173604 (2007).
[CrossRef] [PubMed]

M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
[CrossRef] [PubMed]

M. D. Lukin, P. R. Hemmer, M. Loffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998).
[CrossRef]

Phys. Today (1)

S. E. Harris, Phys. Today 50, 36 (1997).
[CrossRef]

Science (1)

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

Other (1)

M. D. Eisaman, “Generation, storage, and retrieval of nonclassical states of light using atomic ensembles,” Ph.D. dissertation (Harvard University, 2006).

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Figures (3)

Fig. 1
Fig. 1

(a) Four-level double-Λ scheme for an atom interacting with copropagating resonant control and probe fields Ω 31 and Ω 32 , and detuned control and FWM fields Ω 42 and Ω 41 . The population remains in ∣2⟩ throughout. (b),(c) Time-dependence of (b) resonant control field Ω 31 = 10 [ 1 0.5 tanh ( γ 32 t 10 ) + 0.5 tanh ( γ 32 t 29 ) ] and initial probe pulse Ω 32 = 0.001 exp ( γ 32 t 10 ) (multiplied by 10 4 ), and (c) detuned control field Ω 42 = 5 [ 1 + tanh ( γ 32 t 29 ) ] . Ω i j = V i j γ 32 are dimensionless Rabi frequencies, and t is the retarded time.

Fig. 2
Fig. 2

Propagation of the probe and FWM pulses in the medium under the pulse sequence shown in Fig. 1, for Δ = 80 and γ 21 γ 32 = 10 3 . For α 0 z = α 0 L = 375 the probe and FWM relative peak intensities Ω 32 , 41 ( z ) 2 Ω 32 ( 0 ) 2 are 6.7 and 5.65 and their widths, relative to that of the initial probe, are 1 and 1.03.

Fig. 3
Fig. 3

Changes in retrieved probe and generated FWM pulses on propagation. (a) Peak intensities of probe (dotted curve) and FWM (solid curve); (b) width of probe (dotted curve) and FWM (solid curve) pulses, relative to the corresponding input probe parameters; and (c) delay between probe and FWM peaks in dimensionless units γ 32 Δ t . Parameters are the same as in Fig. 2.

Equations (7)

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ρ ̇ 21 = i ( V 42 * ρ 41 V 31 ρ 23 V 41 ρ 24 ) ( γ 21 + i Δ 31 i Δ 32 ) ρ 21 ,
ρ ̇ 23 = i ( V 31 * ρ 21 + V 32 * ) ( γ 32 i Δ 32 ) ρ 23 ,
ρ ̇ 41 = i V 42 ρ 21 ( γ 41 + i Δ 41 ) ρ 41 ,
ρ ̇ 24 = i V 41 * ρ 21 i V 42 * ( γ 42 i Δ 42 ) ρ 24 ,
ρ 32 = i Ω 42 2 Ω 32 ( x + i y ) x 2 + y 2 i Ω 42 Ω 41 * Γ * Γ 2 Ω 31 * + Ω ̇ 32 [ i ( γ x + Δ y ) + ( Δ x γ y ) ] x 2 + y 2 + 2 Ω 31 * Ω ̇ 31 * Ω 32 { i [ Δ 2 ( x 2 y 2 ) 4 Δ x y ] Δ 2 x y } ( x 2 + y 2 ) 2 + Ω ̇ 31 * Ω 32 [ i ( γ x + Δ y ) + ( Δ x γ y ) ] Ω 31 * ( x 2 + y 2 ) ,
ρ 41 = i Ω 42 Ω 32 * Ω 31 ( x i y ) x 2 + y 2 ,
( d d z + 1 c d d t ) Ω 32 , 41 = i α 0 ρ 32 , 41 ,

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