Abstract

We consider a method for efficient parametric generation of a laser pulse. A single laser field is injected into a three-level medium that has two lower states and one excited state. The lower states are initially prepared in a position-dependent coherent superposition state. It is shown that, by proper choice of the position dependence of the superposition along the direction of propagation, the incoming field can be completely converted to a new field.

© 2002 Optical Society of America

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  1. M. D. Lukin, P. R. Hemmer, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 42, 347 (2000).
    [CrossRef]
  2. J. H. Eberly, A. Rahman, and R. Grobe, Phys. Rev. Lett. 76, 3687 (1996).
    [CrossRef] [PubMed]
  3. S. E. Harris and M. Jain, Opt. Lett. 22, 636 (1997).
    [CrossRef] [PubMed]
  4. W. Harshawardan and G. S. Agarwal, Phys. Rev. A 58, 598 (1998).
    [CrossRef]
  5. L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rev. A 58, 707 (1998).
    [CrossRef]
  6. S. H. Choi and G. Vemuri, Opt. Commun. 153, 257 (1998).
    [CrossRef]
  7. M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, Phys. Rev. Lett. 81, 2675 (1998).
    [CrossRef]
  8. E. A. Korsunsky and D. V. Kosachiov, Phys. Rev. A 60, 4996 (1999).
    [CrossRef]
  9. R. W. Boyd and M. O. Scully, Appl. Phys. Lett. 77, 3559 (2000).
    [CrossRef]
  10. E. Paspalakis and P. L. Knight, J. Mod. Opt. 49, 87 (2002).
    [CrossRef]
  11. E. Paspalakis, N. J. Kylstra, and P. L. Knight, Phys. Rev. A 65, 053808 (2002).
    [CrossRef]
  12. P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. Shahriar, and P. Kumar, Opt. Lett. 20, 982 (1995).
    [CrossRef]
  13. M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
    [CrossRef] [PubMed]
  14. A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24, 625 (1999).
    [CrossRef]
  15. A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
    [CrossRef] [PubMed]
  16. A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, Phys. Rev. A 63, 013802 (2001).
    [CrossRef]
  17. J. R. Csesznegi and R. Grobe, Phys. Rev. Lett. 79, 3162 (1997).
    [CrossRef]
  18. J. R. Csesznegi, B. K. Clark, and R. Grobe, Phys. Rev. A 57, 4860 (1998).
    [CrossRef]
  19. M. O. Scully, Phys. Rev. Lett. 67, 1855 (1991).
    [CrossRef] [PubMed]
  20. K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
    [CrossRef]
  21. N. V. Vitanov, M. Fleischhauer, B. W. Shore, and K. Bergmann, Adv. Atom. Mol. Opt. Phys. 46, 55 (2001).
    [CrossRef]
  22. A. Messiah, Quantum Mechanics (Dover, New York, 2000).
  23. Usually adiabatic evolution refers to temporal evolution. Here, we use it for spatial evolution.

2002 (2)

E. Paspalakis and P. L. Knight, J. Mod. Opt. 49, 87 (2002).
[CrossRef]

E. Paspalakis, N. J. Kylstra, and P. L. Knight, Phys. Rev. A 65, 053808 (2002).
[CrossRef]

2001 (2)

A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, Phys. Rev. A 63, 013802 (2001).
[CrossRef]

N. V. Vitanov, M. Fleischhauer, B. W. Shore, and K. Bergmann, Adv. Atom. Mol. Opt. Phys. 46, 55 (2001).
[CrossRef]

2000 (3)

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

R. W. Boyd and M. O. Scully, Appl. Phys. Lett. 77, 3559 (2000).
[CrossRef]

M. D. Lukin, P. R. Hemmer, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 42, 347 (2000).
[CrossRef]

1999 (2)

1998 (6)

W. Harshawardan and G. S. Agarwal, Phys. Rev. A 58, 598 (1998).
[CrossRef]

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rev. A 58, 707 (1998).
[CrossRef]

S. H. Choi and G. Vemuri, Opt. Commun. 153, 257 (1998).
[CrossRef]

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

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

J. R. Csesznegi, B. K. Clark, and R. Grobe, Phys. Rev. A 57, 4860 (1998).
[CrossRef]

1997 (2)

S. E. Harris and M. Jain, Opt. Lett. 22, 636 (1997).
[CrossRef] [PubMed]

J. R. Csesznegi and R. Grobe, Phys. Rev. Lett. 79, 3162 (1997).
[CrossRef]

1996 (2)

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

J. H. Eberly, A. Rahman, and R. Grobe, Phys. Rev. Lett. 76, 3687 (1996).
[CrossRef] [PubMed]

1995 (1)

1991 (1)

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

Agarwal, G. S.

W. Harshawardan and G. S. Agarwal, Phys. Rev. A 58, 598 (1998).
[CrossRef]

Bergmann, K.

N. V. Vitanov, M. Fleischhauer, B. W. Shore, and K. Bergmann, Adv. Atom. Mol. Opt. Phys. 46, 55 (2001).
[CrossRef]

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

Boyd, R. W.

R. W. Boyd and M. O. Scully, Appl. Phys. Lett. 77, 3559 (2000).
[CrossRef]

Choi, S. H.

S. H. Choi and G. Vemuri, Opt. Commun. 153, 257 (1998).
[CrossRef]

Clark, B. K.

J. R. Csesznegi, B. K. Clark, and R. Grobe, Phys. Rev. A 57, 4860 (1998).
[CrossRef]

Cronin-Golomb, M.

Csesznegi, J. R.

J. R. Csesznegi, B. K. Clark, and R. Grobe, Phys. Rev. A 57, 4860 (1998).
[CrossRef]

J. R. Csesznegi and R. Grobe, Phys. Rev. Lett. 79, 3162 (1997).
[CrossRef]

Deng, L.

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rev. A 58, 707 (1998).
[CrossRef]

Donoghue, J.

Eberly, J. H.

J. H. Eberly, A. Rahman, and R. Grobe, Phys. Rev. Lett. 76, 3687 (1996).
[CrossRef] [PubMed]

Fleischhauer, M.

N. V. Vitanov, M. Fleischhauer, B. W. Shore, and K. Bergmann, Adv. Atom. Mol. Opt. Phys. 46, 55 (2001).
[CrossRef]

Garrett, W. R.

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rev. A 58, 707 (1998).
[CrossRef]

Grobe, R.

J. R. Csesznegi, B. K. Clark, and R. Grobe, Phys. Rev. A 57, 4860 (1998).
[CrossRef]

J. R. Csesznegi and R. Grobe, Phys. Rev. Lett. 79, 3162 (1997).
[CrossRef]

J. H. Eberly, A. Rahman, and R. Grobe, Phys. Rev. Lett. 76, 3687 (1996).
[CrossRef] [PubMed]

Harris, S. E.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24, 625 (1999).
[CrossRef]

S. E. Harris and M. Jain, Opt. Lett. 22, 636 (1997).
[CrossRef] [PubMed]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Harshawardan, W.

W. Harshawardan and G. S. Agarwal, Phys. Rev. A 58, 598 (1998).
[CrossRef]

Hemmer, P. R.

M. D. Lukin, P. R. Hemmer, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 42, 347 (2000).
[CrossRef]

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

P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. Shahriar, and P. Kumar, Opt. Lett. 20, 982 (1995).
[CrossRef]

Huss, A. F.

A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, Phys. Rev. A 63, 013802 (2001).
[CrossRef]

Jain, M.

S. E. Harris and M. Jain, Opt. Lett. 22, 636 (1997).
[CrossRef] [PubMed]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Katz, D. P.

Knight, P. L.

E. Paspalakis, N. J. Kylstra, and P. L. Knight, Phys. Rev. A 65, 053808 (2002).
[CrossRef]

E. Paspalakis and P. L. Knight, J. Mod. Opt. 49, 87 (2002).
[CrossRef]

Korsunsky, E. A.

A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, Phys. Rev. A 63, 013802 (2001).
[CrossRef]

E. A. Korsunsky and D. V. Kosachiov, Phys. Rev. A 60, 4996 (1999).
[CrossRef]

Kosachiov, D. V.

E. A. Korsunsky and D. V. Kosachiov, Phys. Rev. A 60, 4996 (1999).
[CrossRef]

Kumar, P.

Kylstra, N. J.

E. Paspalakis, N. J. Kylstra, and P. L. Knight, Phys. Rev. A 65, 053808 (2002).
[CrossRef]

Lammegger, R.

A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, Phys. Rev. A 63, 013802 (2001).
[CrossRef]

Löffler, M.

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

Lukin, M. D.

M. D. Lukin, P. R. Hemmer, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 42, 347 (2000).
[CrossRef]

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

Manuszak, D.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24, 625 (1999).
[CrossRef]

Merriam, A. J.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24, 625 (1999).
[CrossRef]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Messiah, A.

A. Messiah, Quantum Mechanics (Dover, New York, 2000).

Paspalakis, E.

E. Paspalakis and P. L. Knight, J. Mod. Opt. 49, 87 (2002).
[CrossRef]

E. Paspalakis, N. J. Kylstra, and P. L. Knight, Phys. Rev. A 65, 053808 (2002).
[CrossRef]

Payne, M. G.

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rev. A 58, 707 (1998).
[CrossRef]

Peer, N.

A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, Phys. Rev. A 63, 013802 (2001).
[CrossRef]

Rahman, A.

J. H. Eberly, A. Rahman, and R. Grobe, Phys. Rev. Lett. 76, 3687 (1996).
[CrossRef] [PubMed]

Scully, M. O.

M. D. Lukin, P. R. Hemmer, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 42, 347 (2000).
[CrossRef]

R. W. Boyd and M. O. Scully, Appl. Phys. Lett. 77, 3559 (2000).
[CrossRef]

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

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

Shahriar, M. S.

Sharpe, S. J.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24, 625 (1999).
[CrossRef]

Shore, B. W.

N. V. Vitanov, M. Fleischhauer, B. W. Shore, and K. Bergmann, Adv. Atom. Mol. Opt. Phys. 46, 55 (2001).
[CrossRef]

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

Shverdin, M.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

Theuer, H.

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

Vemuri, G.

S. H. Choi and G. Vemuri, Opt. Commun. 153, 257 (1998).
[CrossRef]

Vitanov, N. V.

N. V. Vitanov, M. Fleischhauer, B. W. Shore, and K. Bergmann, Adv. Atom. Mol. Opt. Phys. 46, 55 (2001).
[CrossRef]

Windholz, L.

A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, Phys. Rev. A 63, 013802 (2001).
[CrossRef]

Xia, H.

A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24, 625 (1999).
[CrossRef]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Yin, G. Y.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24, 625 (1999).
[CrossRef]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Adv. Atom. Mol. Opt. Phys. (2)

M. D. Lukin, P. R. Hemmer, and M. O. Scully, Adv. Atom. Mol. Opt. Phys. 42, 347 (2000).
[CrossRef]

N. V. Vitanov, M. Fleischhauer, B. W. Shore, and K. Bergmann, Adv. Atom. Mol. Opt. Phys. 46, 55 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

R. W. Boyd and M. O. Scully, Appl. Phys. Lett. 77, 3559 (2000).
[CrossRef]

J. Mod. Opt. (1)

E. Paspalakis and P. L. Knight, J. Mod. Opt. 49, 87 (2002).
[CrossRef]

Opt. Commun. (1)

S. H. Choi and G. Vemuri, Opt. Commun. 153, 257 (1998).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (6)

A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, Phys. Rev. A 63, 013802 (2001).
[CrossRef]

J. R. Csesznegi, B. K. Clark, and R. Grobe, Phys. Rev. A 57, 4860 (1998).
[CrossRef]

W. Harshawardan and G. S. Agarwal, Phys. Rev. A 58, 598 (1998).
[CrossRef]

L. Deng, M. G. Payne, and W. R. Garrett, Phys. Rev. A 58, 707 (1998).
[CrossRef]

E. Paspalakis, N. J. Kylstra, and P. L. Knight, Phys. Rev. A 65, 053808 (2002).
[CrossRef]

E. A. Korsunsky and D. V. Kosachiov, Phys. Rev. A 60, 4996 (1999).
[CrossRef]

Phys. Rev. Lett. (6)

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

J. H. Eberly, A. Rahman, and R. Grobe, Phys. Rev. Lett. 76, 3687 (1996).
[CrossRef] [PubMed]

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

J. R. Csesznegi and R. Grobe, Phys. Rev. Lett. 79, 3162 (1997).
[CrossRef]

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 84, 5308 (2000).
[CrossRef] [PubMed]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
[CrossRef]

Other (2)

A. Messiah, Quantum Mechanics (Dover, New York, 2000).

Usually adiabatic evolution refers to temporal evolution. Here, we use it for spatial evolution.

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram of the system studied. The excited state |0 is coupled by two coherent laser pulses to the lower states, |1 and |2. In the calculations presented in Fig. 2, below, Ω1ζ,τ is the Rabi frequency of the incoming pulse and Ω2ζ,τ is the Rabi frequency of the generated pulse.

Fig. 2
Fig. 2

Normalized field intensities (a) Ω1ζ,τ2/Ω12 and (b) Ω2ζ,τ2/Ω12 as a function of τ for different values of ζ, with (solid curves) ζ=0, (dashed curves) ζ=100, and (dotted–dashed curves) ζ=200. In (c) we present the maximum of the normalized field intensities as a function of ζ for the incoming field (dashed curve) and the generated field (solid curve). The incident pulse is Ωτ=Ω1 sin2τπ/τp, with 0ττp. The parameters used in the calculations are a1=a2=1000,Ω1=0.01,τp=50, δ=0,γ=100,ζ0=100, and ζ¯=5. All quantities are in arbitrary units.

Equations (16)

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

iτbζ,τ=Hζ,τbζ,τ,
τΩnζ,τ=ianbnζ,τb0*ζ,τ,  n=1,2,
Hζ,τ=δ1-iγ2Ω1*ζ,τΩ2*ζ,τΩ1ζ,τ00Ω2ζ,τ0δ1-δ2
|ψζ,τ=0=b1ζ|1+b2ζ|2,
b1ζ,τb1ζ,    b2ζ,τb2ζ, b0ζ,τ-Ω1*ζ,τb1ζ+Ω2*ζ,τb2ζδ-iγ/2,
ζΩζ,τ=-iKζΩζ,τ,
Kζ=α1b1ζ2α1b1ζb2*ζα2b2ζb1*ζα2b2ζ2.
Ω1ζ,τ=b12exp-iαζ+b22Ωτ,
Ω2ζ,τ=b1*b2-1+exp-iαζΩτ.
vζα
vζ=ib1ζb2ζζ-b1ζζb2ζ.
Ω1ζ,τ=b20b2ζ*+exp-iαζb10*b1ζΩτ,
Ω2ζ,τ=-b20b1ζ*+exp-iαζb10*b2ζΩτ.
Ω1ζ,τ=0, Ω2ζ,τ=-expiϕ2-ϕ1Ωτ,
b1ζ=1/1+exp-ζ-ζ0/ζ¯1/2,
b2ζ=1/1+expζ+ζ0/ζ¯1/2,

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