Abstract

We demonstrate the preparation and probing of the coherence between the hyperfine ground states 5S12,F=1 and 5S12,F=2 of the Rb87 isotope. The effects of various coherence control techniques, i.e., fractional stimulated Raman adiabatic passage and coherent population return, on the coherence are investigated. These techniques are implemented using nearly degenerate pump and Stokes lasers at 795nm (Rb D1 transition), which couple the two hyperfine ground states via the excited state 5P12,F=1 through a resonant two-photon process in which a coherent superposition of the two hyperfine ground states is established. The medium is probed by an additional weak laser, which generates a four-wave mixing signal proportional to the ground state coherence and allows us to monitor its evolution in time. The experimental data are compared with numerical simulations.

© 2007 Optical Society of America

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  1. N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 764 (2001).
    [CrossRef]
  2. M. Jain and S. E. Harris, Opt. Lett. 22, 636 (1997).
    [CrossRef] [PubMed]
  3. F. Vewinger, M. Heinz, R. Garcia-Fernandez, N. V. Vitanov, and K. Bergmann, Phys. Rev. Lett. 91, 213001 (2003).
    [CrossRef] [PubMed]
  4. N. G. Kalugin and Y. V. Rostovtsev, Opt. Lett. 31, 969 (2006).
    [CrossRef] [PubMed]
  5. J. Volz, M. Weber, D. Schlenk, W. Rosenfeld, J. Vrana, K. Sauke, C. Kurtsiefer, and H. Weinfurter, Phys. Rev. Lett. 96, 030404 (2006).
    [CrossRef] [PubMed]
  6. A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24, 625 (2001).
    [CrossRef]
  7. M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, Phys. Rev. Lett. 77, 4326 (1996).
    [CrossRef] [PubMed]
  8. S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
    [CrossRef]
  9. A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
    [CrossRef] [PubMed]
  10. A. V. Sokolov, D. D. Yavuz, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. A 63, 051801 (2001).
    [CrossRef]
  11. S. E. Harris and A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
    [CrossRef]
  12. A. V. Sokolov, D. D. Yavuz, and S. E. Harris, Opt. Lett. 24, 557 (1999).
    [CrossRef]
  13. D. D. Yavuz, A. V. Sokolov, and S. E. Harris, Phys. Rev. Lett. 84, 75 (2000).
    [CrossRef] [PubMed]
  14. T. Halfmann, T. Rickes, N. V. Vitanov, and K. Bergmann, Opt. Commun. 220, 353 (2003).
    [CrossRef]
  15. N. V. Vitanov, K. A. Suominen, and B. W. Shore, J. Phys. B 32, 4535 (1999).
    [CrossRef]
  16. E. Figueroa, F. Vewinger, J. Appel, and A. I. Lvovsky, Opt. Lett. 31, 2625 (2006).
    [CrossRef] [PubMed]
  17. F. A. Franz and C. Volk, Phys. Rev. A 14, 1711 (1976).
    [CrossRef]

2006

N. G. Kalugin and Y. V. Rostovtsev, Opt. Lett. 31, 969 (2006).
[CrossRef] [PubMed]

J. Volz, M. Weber, D. Schlenk, W. Rosenfeld, J. Vrana, K. Sauke, C. Kurtsiefer, and H. Weinfurter, Phys. Rev. Lett. 96, 030404 (2006).
[CrossRef] [PubMed]

E. Figueroa, F. Vewinger, J. Appel, and A. I. Lvovsky, Opt. Lett. 31, 2625 (2006).
[CrossRef] [PubMed]

2003

T. Halfmann, T. Rickes, N. V. Vitanov, and K. Bergmann, Opt. Commun. 220, 353 (2003).
[CrossRef]

F. Vewinger, M. Heinz, R. Garcia-Fernandez, N. V. Vitanov, and K. Bergmann, Phys. Rev. Lett. 91, 213001 (2003).
[CrossRef] [PubMed]

2001

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 764 (2001).
[CrossRef]

A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24, 625 (2001).
[CrossRef]

A. V. Sokolov, D. D. Yavuz, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. A 63, 051801 (2001).
[CrossRef]

2000

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

D. D. Yavuz, A. V. Sokolov, and S. E. Harris, Phys. Rev. Lett. 84, 75 (2000).
[CrossRef] [PubMed]

1999

A. V. Sokolov, D. D. Yavuz, and S. E. Harris, Opt. Lett. 24, 557 (1999).
[CrossRef]

N. V. Vitanov, K. A. Suominen, and B. W. Shore, J. Phys. B 32, 4535 (1999).
[CrossRef]

1998

S. E. Harris and A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
[CrossRef]

1997

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

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

1996

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

1976

F. A. Franz and C. Volk, Phys. Rev. A 14, 1711 (1976).
[CrossRef]

Appel, J.

Bergmann, K.

T. Halfmann, T. Rickes, N. V. Vitanov, and K. Bergmann, Opt. Commun. 220, 353 (2003).
[CrossRef]

F. Vewinger, M. Heinz, R. Garcia-Fernandez, N. V. Vitanov, and K. Bergmann, Phys. Rev. Lett. 91, 213001 (2003).
[CrossRef] [PubMed]

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 764 (2001).
[CrossRef]

Figueroa, E.

Franz, F. A.

F. A. Franz and C. Volk, Phys. Rev. A 14, 1711 (1976).
[CrossRef]

Garcia-Fernandez, R.

F. Vewinger, M. Heinz, R. Garcia-Fernandez, N. V. Vitanov, and K. Bergmann, Phys. Rev. Lett. 91, 213001 (2003).
[CrossRef] [PubMed]

Halfmann, T.

T. Halfmann, T. Rickes, N. V. Vitanov, and K. Bergmann, Opt. Commun. 220, 353 (2003).
[CrossRef]

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 764 (2001).
[CrossRef]

Harris, S. E.

A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24, 625 (2001).
[CrossRef]

A. V. Sokolov, D. D. Yavuz, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. A 63, 051801 (2001).
[CrossRef]

D. D. Yavuz, A. V. Sokolov, and S. E. Harris, Phys. Rev. Lett. 84, 75 (2000).
[CrossRef] [PubMed]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

A. V. Sokolov, D. D. Yavuz, and S. E. Harris, Opt. Lett. 24, 557 (1999).
[CrossRef]

S. E. Harris and A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
[CrossRef]

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

M. Jain and S. E. Harris, 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]

Heinz, M.

F. Vewinger, M. Heinz, R. Garcia-Fernandez, N. V. Vitanov, and K. Bergmann, Phys. Rev. Lett. 91, 213001 (2003).
[CrossRef] [PubMed]

Jain, M.

M. Jain and S. E. Harris, 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]

Kalugin, N. G.

Kurtsiefer, C.

J. Volz, M. Weber, D. Schlenk, W. Rosenfeld, J. Vrana, K. Sauke, C. Kurtsiefer, and H. Weinfurter, Phys. Rev. Lett. 96, 030404 (2006).
[CrossRef] [PubMed]

Lvovsky, A. I.

Manuszak, D.

Merriam, A. J.

A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24, 625 (2001).
[CrossRef]

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

Rickes, T.

T. Halfmann, T. Rickes, N. V. Vitanov, and K. Bergmann, Opt. Commun. 220, 353 (2003).
[CrossRef]

Rosenfeld, W.

J. Volz, M. Weber, D. Schlenk, W. Rosenfeld, J. Vrana, K. Sauke, C. Kurtsiefer, and H. Weinfurter, Phys. Rev. Lett. 96, 030404 (2006).
[CrossRef] [PubMed]

Rostovtsev, Y. V.

Sauke, K.

J. Volz, M. Weber, D. Schlenk, W. Rosenfeld, J. Vrana, K. Sauke, C. Kurtsiefer, and H. Weinfurter, Phys. Rev. Lett. 96, 030404 (2006).
[CrossRef] [PubMed]

Schlenk, D.

J. Volz, M. Weber, D. Schlenk, W. Rosenfeld, J. Vrana, K. Sauke, C. Kurtsiefer, and H. Weinfurter, Phys. Rev. Lett. 96, 030404 (2006).
[CrossRef] [PubMed]

Sharpe, S. J.

Shore, B. W.

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 764 (2001).
[CrossRef]

N. V. Vitanov, K. A. Suominen, and B. W. Shore, J. Phys. B 32, 4535 (1999).
[CrossRef]

Sokolov, A. V.

A. V. Sokolov, D. D. Yavuz, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. A 63, 051801 (2001).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

D. D. Yavuz, A. V. Sokolov, and S. E. Harris, Phys. Rev. Lett. 84, 75 (2000).
[CrossRef] [PubMed]

A. V. Sokolov, D. D. Yavuz, and S. E. Harris, Opt. Lett. 24, 557 (1999).
[CrossRef]

S. E. Harris and A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
[CrossRef]

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

Suominen, K. A.

N. V. Vitanov, K. A. Suominen, and B. W. Shore, J. Phys. B 32, 4535 (1999).
[CrossRef]

Vewinger, F.

E. Figueroa, F. Vewinger, J. Appel, and A. I. Lvovsky, Opt. Lett. 31, 2625 (2006).
[CrossRef] [PubMed]

F. Vewinger, M. Heinz, R. Garcia-Fernandez, N. V. Vitanov, and K. Bergmann, Phys. Rev. Lett. 91, 213001 (2003).
[CrossRef] [PubMed]

Vitanov, N. V.

F. Vewinger, M. Heinz, R. Garcia-Fernandez, N. V. Vitanov, and K. Bergmann, Phys. Rev. Lett. 91, 213001 (2003).
[CrossRef] [PubMed]

T. Halfmann, T. Rickes, N. V. Vitanov, and K. Bergmann, Opt. Commun. 220, 353 (2003).
[CrossRef]

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 764 (2001).
[CrossRef]

N. V. Vitanov, K. A. Suominen, and B. W. Shore, J. Phys. B 32, 4535 (1999).
[CrossRef]

Volk, C.

F. A. Franz and C. Volk, Phys. Rev. A 14, 1711 (1976).
[CrossRef]

Volz, J.

J. Volz, M. Weber, D. Schlenk, W. Rosenfeld, J. Vrana, K. Sauke, C. Kurtsiefer, and H. Weinfurter, Phys. Rev. Lett. 96, 030404 (2006).
[CrossRef] [PubMed]

Vrana, J.

J. Volz, M. Weber, D. Schlenk, W. Rosenfeld, J. Vrana, K. Sauke, C. Kurtsiefer, and H. Weinfurter, Phys. Rev. Lett. 96, 030404 (2006).
[CrossRef] [PubMed]

Walker, D. R.

A. V. Sokolov, D. D. Yavuz, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. A 63, 051801 (2001).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

Weber, M.

J. Volz, M. Weber, D. Schlenk, W. Rosenfeld, J. Vrana, K. Sauke, C. Kurtsiefer, and H. Weinfurter, Phys. Rev. Lett. 96, 030404 (2006).
[CrossRef] [PubMed]

Weinfurter, H.

J. Volz, M. Weber, D. Schlenk, W. Rosenfeld, J. Vrana, K. Sauke, C. Kurtsiefer, and H. Weinfurter, Phys. Rev. Lett. 96, 030404 (2006).
[CrossRef] [PubMed]

Xia, H.

A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24, 625 (2001).
[CrossRef]

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

Yavuz, D. D.

A. V. Sokolov, D. D. Yavuz, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. A 63, 051801 (2001).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (2000).
[CrossRef] [PubMed]

D. D. Yavuz, A. V. Sokolov, and S. E. Harris, Phys. Rev. Lett. 84, 75 (2000).
[CrossRef] [PubMed]

A. V. Sokolov, D. D. Yavuz, and S. E. Harris, Opt. Lett. 24, 557 (1999).
[CrossRef]

Yin, G. Y.

A. V. Sokolov, D. D. Yavuz, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. A 63, 051801 (2001).
[CrossRef]

A. J. Merriam, S. J. Sharpe, H. Xia, D. Manuszak, G. Y. Yin, and S. E. Harris, Opt. Lett. 24, 625 (2001).
[CrossRef]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (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]

Annu. Rev. Phys. Chem.

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 764 (2001).
[CrossRef]

J. Phys. B

N. V. Vitanov, K. A. Suominen, and B. W. Shore, J. Phys. B 32, 4535 (1999).
[CrossRef]

Opt. Commun.

T. Halfmann, T. Rickes, N. V. Vitanov, and K. Bergmann, Opt. Commun. 220, 353 (2003).
[CrossRef]

Opt. Lett.

Phys. Rev. A

S. E. Harris and A. V. Sokolov, Phys. Rev. A 55, R4019 (1997).
[CrossRef]

A. V. Sokolov, D. D. Yavuz, D. R. Walker, G. Y. Yin, and S. E. Harris, Phys. Rev. A 63, 051801 (2001).
[CrossRef]

F. A. Franz and C. Volk, Phys. Rev. A 14, 1711 (1976).
[CrossRef]

Phys. Rev. Lett.

S. E. Harris and A. V. Sokolov, Phys. Rev. Lett. 81, 2894 (1998).
[CrossRef]

D. D. Yavuz, A. V. Sokolov, and S. E. Harris, Phys. Rev. Lett. 84, 75 (2000).
[CrossRef] [PubMed]

A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 85, 562 (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]

J. Volz, M. Weber, D. Schlenk, W. Rosenfeld, J. Vrana, K. Sauke, C. Kurtsiefer, and H. Weinfurter, Phys. Rev. Lett. 96, 030404 (2006).
[CrossRef] [PubMed]

F. Vewinger, M. Heinz, R. Garcia-Fernandez, N. V. Vitanov, and K. Bergmann, Phys. Rev. Lett. 91, 213001 (2003).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Coupling scheme for the preparation and probing of the coherence ρ 13 in Rb 87 . The hyperfine splittings and detunings are exaggerated for clarity.

Fig. 2
Fig. 2

Fractional STIRAP process: FWM signal as a function of the probe laser delay Δ τ pr (triangles) and numerical simulation (filled circles). Inset, temporal shape of the pump (open circles) and Stokes pulses (filled rectangles).

Fig. 3
Fig. 3

Coherence during the CPR process: (a) measured FWM signal and (b) calculated coherence ρ 13 for different Stokes pulse intensities. The maximum Stokes Rabi frequencies (at t = 54.9 μ s ) are Ω S = 0.023 ns 1 (filled rectangles); Ω S = 0.033 ns 1 (open rectangles); Ω S = 0.05 ns 1 (stars); Ω S = 0.075 ns 1 (half-filled circles). The solid curve in (a) shows the temporal profile of the Stokes Rabi frequency (scale in arbitrary units).

Equations (4)

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

ds = cos θ ( t ) 1 sin θ ( t ) 3 ,
tan θ ( t ) = Ω P ( t ) Ω S ( t ) ,
ρ 13 ( t ) = cos θ ( t ) sin θ ( t )
z E FWM = π N ω FWM μ 12 μ 23 c ϵ 0 Δ pr ρ 13 E pr .

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