Abstract

Wave mixing in a three-level quantum system induced by two-photon resonant pump and one-photon resonant coupling at lower transition has been studied theoretically and experimentally. Resonantly enhanced difference-frequency generation efficiency was observed clearly dependent on the time delay and its sign between the femtosecond pump and probe. The role of the atomic coherences on the amplification without inversion during different sequences of interaction in a closed three-level system has been also stressed. These findings were confirmed experimentally in atomic potassium, where strong parametric amplification, induced by the pump delayed with respect to the probe, has been observed for the first time.

© 2013 Optical Society of America

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  1. J. Mompart and R. Corbalan, J. Opt. B 2, R7 (2000).
    [CrossRef]
  2. M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
    [CrossRef]
  3. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
    [CrossRef]
  4. D. S. Bradshaw and D. L. Andrews, J Chem. Phys. 128, 144506 (2008).
    [CrossRef]
  5. A. Dogariu, J. B. Michael, M. O. Scully, and R. B. Miles, Science 331, 442 (2011).
    [CrossRef]
  6. A. J. Traverso, R. Sanchez-Gonzalez, L. Yuan, K. Wang, D. V. Voronine, A. M. Zheltikov, Y. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, S. W. North, and M. O. Scully, PNAS 109, 15185 (2012).
    [CrossRef]
  7. A. G. de Garcia, P. Meystre, and R. R. E. Salomaa, Phys. Rev. A 32, 1531 (1985).
    [CrossRef]
  8. E. Gaižauskas and G. Gedvilas, Opt. Commun. 91, 312 (1992).
    [CrossRef]
  9. C. S. Mullin, D. Kim, M. B. Feller, and Y. R. Shen, Phys. Rev. Lett. 74, 2678 (1995).
    [CrossRef]
  10. O. Kittelmann, J. Ringling, A. Nazarkin, G. Korn, and I. V. Hertel, Phys. Rev. Lett. 76, 2682 (1996).
    [CrossRef]
  11. A. Nazarkin, G. Korn, O. Kittelmann, J. Ringling, and I. V. Hertel, Phys. Rev. A 56, 671 (1997).
    [CrossRef]
  12. E. Gaizauskas and L. Valkunas, J. Phys. Chem. B 101, 7321 (1997).
    [CrossRef]
  13. I. Pop and L. Moorman, Phys. Rev. A 60, 678 (1999).
    [CrossRef]

2012 (1)

A. J. Traverso, R. Sanchez-Gonzalez, L. Yuan, K. Wang, D. V. Voronine, A. M. Zheltikov, Y. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, S. W. North, and M. O. Scully, PNAS 109, 15185 (2012).
[CrossRef]

2011 (1)

A. Dogariu, J. B. Michael, M. O. Scully, and R. B. Miles, Science 331, 442 (2011).
[CrossRef]

2008 (1)

D. S. Bradshaw and D. L. Andrews, J Chem. Phys. 128, 144506 (2008).
[CrossRef]

2001 (1)

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef]

2000 (1)

J. Mompart and R. Corbalan, J. Opt. B 2, R7 (2000).
[CrossRef]

1999 (2)

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

I. Pop and L. Moorman, Phys. Rev. A 60, 678 (1999).
[CrossRef]

1997 (2)

A. Nazarkin, G. Korn, O. Kittelmann, J. Ringling, and I. V. Hertel, Phys. Rev. A 56, 671 (1997).
[CrossRef]

E. Gaizauskas and L. Valkunas, J. Phys. Chem. B 101, 7321 (1997).
[CrossRef]

1996 (1)

O. Kittelmann, J. Ringling, A. Nazarkin, G. Korn, and I. V. Hertel, Phys. Rev. Lett. 76, 2682 (1996).
[CrossRef]

1995 (1)

C. S. Mullin, D. Kim, M. B. Feller, and Y. R. Shen, Phys. Rev. Lett. 74, 2678 (1995).
[CrossRef]

1992 (1)

E. Gaižauskas and G. Gedvilas, Opt. Commun. 91, 312 (1992).
[CrossRef]

1985 (1)

A. G. de Garcia, P. Meystre, and R. R. E. Salomaa, Phys. Rev. A 32, 1531 (1985).
[CrossRef]

Andrews, D. L.

D. S. Bradshaw and D. L. Andrews, J Chem. Phys. 128, 144506 (2008).
[CrossRef]

Bradshaw, D. S.

D. S. Bradshaw and D. L. Andrews, J Chem. Phys. 128, 144506 (2008).
[CrossRef]

Corbalan, R.

J. Mompart and R. Corbalan, J. Opt. B 2, R7 (2000).
[CrossRef]

de Garcia, A. G.

A. G. de Garcia, P. Meystre, and R. R. E. Salomaa, Phys. Rev. A 32, 1531 (1985).
[CrossRef]

Dogariu, A.

A. Dogariu, J. B. Michael, M. O. Scully, and R. B. Miles, Science 331, 442 (2011).
[CrossRef]

Feller, M. B.

C. S. Mullin, D. Kim, M. B. Feller, and Y. R. Shen, Phys. Rev. Lett. 74, 2678 (1995).
[CrossRef]

Fleischhauer, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef]

Fry, E. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Gaizauskas, E.

E. Gaizauskas and L. Valkunas, J. Phys. Chem. B 101, 7321 (1997).
[CrossRef]

Gaižauskas, E.

E. Gaižauskas and G. Gedvilas, Opt. Commun. 91, 312 (1992).
[CrossRef]

Gedvilas, G.

E. Gaižauskas and G. Gedvilas, Opt. Commun. 91, 312 (1992).
[CrossRef]

Hertel, I. V.

A. Nazarkin, G. Korn, O. Kittelmann, J. Ringling, and I. V. Hertel, Phys. Rev. A 56, 671 (1997).
[CrossRef]

O. Kittelmann, J. Ringling, A. Nazarkin, G. Korn, and I. V. Hertel, Phys. Rev. Lett. 76, 2682 (1996).
[CrossRef]

Hollberg, L.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Kash, M. M.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Kim, D.

C. S. Mullin, D. Kim, M. B. Feller, and Y. R. Shen, Phys. Rev. Lett. 74, 2678 (1995).
[CrossRef]

Kittelmann, O.

A. Nazarkin, G. Korn, O. Kittelmann, J. Ringling, and I. V. Hertel, Phys. Rev. A 56, 671 (1997).
[CrossRef]

O. Kittelmann, J. Ringling, A. Nazarkin, G. Korn, and I. V. Hertel, Phys. Rev. Lett. 76, 2682 (1996).
[CrossRef]

Korn, G.

A. Nazarkin, G. Korn, O. Kittelmann, J. Ringling, and I. V. Hertel, Phys. Rev. A 56, 671 (1997).
[CrossRef]

O. Kittelmann, J. Ringling, A. Nazarkin, G. Korn, and I. V. Hertel, Phys. Rev. Lett. 76, 2682 (1996).
[CrossRef]

Lukin, M. D.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Mair, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef]

Meystre, P.

A. G. de Garcia, P. Meystre, and R. R. E. Salomaa, Phys. Rev. A 32, 1531 (1985).
[CrossRef]

Michael, J. B.

A. Dogariu, J. B. Michael, M. O. Scully, and R. B. Miles, Science 331, 442 (2011).
[CrossRef]

Miles, R. B.

A. Dogariu, J. B. Michael, M. O. Scully, and R. B. Miles, Science 331, 442 (2011).
[CrossRef]

Mompart, J.

J. Mompart and R. Corbalan, J. Opt. B 2, R7 (2000).
[CrossRef]

Moorman, L.

I. Pop and L. Moorman, Phys. Rev. A 60, 678 (1999).
[CrossRef]

Mullin, C. S.

C. S. Mullin, D. Kim, M. B. Feller, and Y. R. Shen, Phys. Rev. Lett. 74, 2678 (1995).
[CrossRef]

Nazarkin, A.

A. Nazarkin, G. Korn, O. Kittelmann, J. Ringling, and I. V. Hertel, Phys. Rev. A 56, 671 (1997).
[CrossRef]

O. Kittelmann, J. Ringling, A. Nazarkin, G. Korn, and I. V. Hertel, Phys. Rev. Lett. 76, 2682 (1996).
[CrossRef]

North, S. W.

A. J. Traverso, R. Sanchez-Gonzalez, L. Yuan, K. Wang, D. V. Voronine, A. M. Zheltikov, Y. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, S. W. North, and M. O. Scully, PNAS 109, 15185 (2012).
[CrossRef]

Phillips, D. F.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef]

Pop, I.

I. Pop and L. Moorman, Phys. Rev. A 60, 678 (1999).
[CrossRef]

Ringling, J.

A. Nazarkin, G. Korn, O. Kittelmann, J. Ringling, and I. V. Hertel, Phys. Rev. A 56, 671 (1997).
[CrossRef]

O. Kittelmann, J. Ringling, A. Nazarkin, G. Korn, and I. V. Hertel, Phys. Rev. Lett. 76, 2682 (1996).
[CrossRef]

Rostovtsev, Y.

A. J. Traverso, R. Sanchez-Gonzalez, L. Yuan, K. Wang, D. V. Voronine, A. M. Zheltikov, Y. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, S. W. North, and M. O. Scully, PNAS 109, 15185 (2012).
[CrossRef]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Salomaa, R. R. E.

A. G. de Garcia, P. Meystre, and R. R. E. Salomaa, Phys. Rev. A 32, 1531 (1985).
[CrossRef]

Sanchez-Gonzalez, R.

A. J. Traverso, R. Sanchez-Gonzalez, L. Yuan, K. Wang, D. V. Voronine, A. M. Zheltikov, Y. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, S. W. North, and M. O. Scully, PNAS 109, 15185 (2012).
[CrossRef]

Sautenkov, V. A.

A. J. Traverso, R. Sanchez-Gonzalez, L. Yuan, K. Wang, D. V. Voronine, A. M. Zheltikov, Y. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, S. W. North, and M. O. Scully, PNAS 109, 15185 (2012).
[CrossRef]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Scully, M. O.

A. J. Traverso, R. Sanchez-Gonzalez, L. Yuan, K. Wang, D. V. Voronine, A. M. Zheltikov, Y. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, S. W. North, and M. O. Scully, PNAS 109, 15185 (2012).
[CrossRef]

A. Dogariu, J. B. Michael, M. O. Scully, and R. B. Miles, Science 331, 442 (2011).
[CrossRef]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Shen, Y. R.

C. S. Mullin, D. Kim, M. B. Feller, and Y. R. Shen, Phys. Rev. Lett. 74, 2678 (1995).
[CrossRef]

Sokolov, A. V.

A. J. Traverso, R. Sanchez-Gonzalez, L. Yuan, K. Wang, D. V. Voronine, A. M. Zheltikov, Y. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, S. W. North, and M. O. Scully, PNAS 109, 15185 (2012).
[CrossRef]

Traverso, A. J.

A. J. Traverso, R. Sanchez-Gonzalez, L. Yuan, K. Wang, D. V. Voronine, A. M. Zheltikov, Y. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, S. W. North, and M. O. Scully, PNAS 109, 15185 (2012).
[CrossRef]

Valkunas, L.

E. Gaizauskas and L. Valkunas, J. Phys. Chem. B 101, 7321 (1997).
[CrossRef]

Voronine, D. V.

A. J. Traverso, R. Sanchez-Gonzalez, L. Yuan, K. Wang, D. V. Voronine, A. M. Zheltikov, Y. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, S. W. North, and M. O. Scully, PNAS 109, 15185 (2012).
[CrossRef]

Walsworth, R. L.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef]

Wang, K.

A. J. Traverso, R. Sanchez-Gonzalez, L. Yuan, K. Wang, D. V. Voronine, A. M. Zheltikov, Y. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, S. W. North, and M. O. Scully, PNAS 109, 15185 (2012).
[CrossRef]

Welch, G. R.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Yuan, L.

A. J. Traverso, R. Sanchez-Gonzalez, L. Yuan, K. Wang, D. V. Voronine, A. M. Zheltikov, Y. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, S. W. North, and M. O. Scully, PNAS 109, 15185 (2012).
[CrossRef]

Zheltikov, A. M.

A. J. Traverso, R. Sanchez-Gonzalez, L. Yuan, K. Wang, D. V. Voronine, A. M. Zheltikov, Y. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, S. W. North, and M. O. Scully, PNAS 109, 15185 (2012).
[CrossRef]

Zibrov, A. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

J Chem. Phys. (1)

D. S. Bradshaw and D. L. Andrews, J Chem. Phys. 128, 144506 (2008).
[CrossRef]

J. Opt. B (1)

J. Mompart and R. Corbalan, J. Opt. B 2, R7 (2000).
[CrossRef]

J. Phys. Chem. B (1)

E. Gaizauskas and L. Valkunas, J. Phys. Chem. B 101, 7321 (1997).
[CrossRef]

Opt. Commun. (1)

E. Gaižauskas and G. Gedvilas, Opt. Commun. 91, 312 (1992).
[CrossRef]

Phys. Rev. A (3)

A. G. de Garcia, P. Meystre, and R. R. E. Salomaa, Phys. Rev. A 32, 1531 (1985).
[CrossRef]

I. Pop and L. Moorman, Phys. Rev. A 60, 678 (1999).
[CrossRef]

A. Nazarkin, G. Korn, O. Kittelmann, J. Ringling, and I. V. Hertel, Phys. Rev. A 56, 671 (1997).
[CrossRef]

Phys. Rev. Lett. (4)

C. S. Mullin, D. Kim, M. B. Feller, and Y. R. Shen, Phys. Rev. Lett. 74, 2678 (1995).
[CrossRef]

O. Kittelmann, J. Ringling, A. Nazarkin, G. Korn, and I. V. Hertel, Phys. Rev. Lett. 76, 2682 (1996).
[CrossRef]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef]

PNAS (1)

A. J. Traverso, R. Sanchez-Gonzalez, L. Yuan, K. Wang, D. V. Voronine, A. M. Zheltikov, Y. Rostovtsev, V. A. Sautenkov, A. V. Sokolov, S. W. North, and M. O. Scully, PNAS 109, 15185 (2012).
[CrossRef]

Science (1)

A. Dogariu, J. B. Michael, M. O. Scully, and R. B. Miles, Science 331, 442 (2011).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Two- and one-photon resonant excitations in three-level configuration of potassium (K) atom. A strong laser pulse at 728 nm excites the two-photon transition 4S1/26S1/2(Δ0) and a weak probe at 404 nm drives the transition 4S1/25P3/2,1/2.

Fig. 2.
Fig. 2.

Normalized FWDFG efficiency near the transition 4S1/25P3/2,1/2 versus the delay time τD between pump and probe pulses in two photon resonant excited K vapor. Solid squares: experimentally measured points at an atomic density N=1016cm3 and pump wavelength of 726 nm. curves: rising and decaying exponentials with time constants T212=92ps and T213=35ps, respectively.

Equations (6)

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

tρ13=i[ΔΩS(t)]ρ13r13EL22n31ρ13T213,
tn31=2Im{r1322EL*2ρ13},
|Egen(z,τ)|2=ωPωns|ES(0,τ)|2G02G2sinh2(Gz),
tρ23=iΔΩ32ρ23iμ122EPρ13+iμr4EL*2ρ21ρ23T212,
|ρ23(τ)|2{|ΘP(ττD)ρ13(τD)|2,τD>0|ΘL(0)ρ12(τ)|2,τD<0.
|Ens(0,τD)|2{|ρ13(0)exp{τD/T213}|2,τD>0|ρ12(τD)exp{τD/T212}|2,τD<0.

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