Abstract

We propose a novel method that uses the oscillation of an atomic excited wave packet observed through a pump–probe technique to accurately determine the zero time delay between a pair of ultrashort laser pulses. This physically based approach provides an easy fix for the intractable problem of synchronizing two different femtosecond laser pulses in a practical experimental environment, especially where an in situ time zero measurement with high accuracy is required.

© 2008 Optical Society of America

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References

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  1. M. Shapiro and P. Brumer, Principles of the Quantum Control of Molecular Processes (Wiley, 2003).
  2. N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 763 (2001).
    [CrossRef] [PubMed]
  3. M. Shapiro and P. Brumer, Phys. Rep. 425, 195 (2006).
    [CrossRef]
  4. P. Kral, I. Thanopulos, and M. Shapiro, Rev. Mod. Phys. 79, 53 (2007).
    [CrossRef]
  5. E. A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro, Phys. Rev. Lett. 99, 033002 (2007).
    [CrossRef] [PubMed]
  6. S. Zhdanovich, E. A. Shapiro, M. Shapiro, J. W. Hepburn, and V. Milner, Phys. Rev. Lett. 100, 103004 (2007).
    [CrossRef]
  7. K. Bergmann, H. Theuer, and B. W. Shore, Rev. Mod. Phys. 70, 1003 (1998).
    [CrossRef]
  8. N. V. Vitanov, M. Fleischhauer, B. W. Shore, and K. Bergmann, Adv. At. Mol. Opt. Phys. 46, 55 (2001).
    [CrossRef]
  9. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques, and Applications on a Femtosecond Time Scale (Academic, 1996).
  10. S. Zamith, M. A. Bouchene, E. Sokell, C. Nicole, V. Blanchet, and B. Girard, Eur. Phys. J. D 12, 255 (2000).
    [CrossRef]
  11. NIST Atomic Spectra Database (NIST, Gaithersburg, Md., 2008).
  12. C. Nicole, M. A. Bouchene, S. Zamith, N. Melikechi, and B. Girard, Phys. Rev. A 60, R1755 (1999).
    [CrossRef]

2007

P. Kral, I. Thanopulos, and M. Shapiro, Rev. Mod. Phys. 79, 53 (2007).
[CrossRef]

E. A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro, Phys. Rev. Lett. 99, 033002 (2007).
[CrossRef] [PubMed]

S. Zhdanovich, E. A. Shapiro, M. Shapiro, J. W. Hepburn, and V. Milner, Phys. Rev. Lett. 100, 103004 (2007).
[CrossRef]

2006

M. Shapiro and P. Brumer, Phys. Rep. 425, 195 (2006).
[CrossRef]

2001

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 763 (2001).
[CrossRef] [PubMed]

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

2000

S. Zamith, M. A. Bouchene, E. Sokell, C. Nicole, V. Blanchet, and B. Girard, Eur. Phys. J. D 12, 255 (2000).
[CrossRef]

1999

C. Nicole, M. A. Bouchene, S. Zamith, N. Melikechi, and B. Girard, Phys. Rev. A 60, R1755 (1999).
[CrossRef]

1998

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

Bergmann, K.

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 763 (2001).
[CrossRef] [PubMed]

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

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

Blanchet, V.

S. Zamith, M. A. Bouchene, E. Sokell, C. Nicole, V. Blanchet, and B. Girard, Eur. Phys. J. D 12, 255 (2000).
[CrossRef]

Bouchene, M. A.

S. Zamith, M. A. Bouchene, E. Sokell, C. Nicole, V. Blanchet, and B. Girard, Eur. Phys. J. D 12, 255 (2000).
[CrossRef]

C. Nicole, M. A. Bouchene, S. Zamith, N. Melikechi, and B. Girard, Phys. Rev. A 60, R1755 (1999).
[CrossRef]

Brumer, P.

M. Shapiro and P. Brumer, Phys. Rep. 425, 195 (2006).
[CrossRef]

M. Shapiro and P. Brumer, Principles of the Quantum Control of Molecular Processes (Wiley, 2003).

Diels, J.-C.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques, and Applications on a Femtosecond Time Scale (Academic, 1996).

Fleischhauer, M.

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

Girard, B.

S. Zamith, M. A. Bouchene, E. Sokell, C. Nicole, V. Blanchet, and B. Girard, Eur. Phys. J. D 12, 255 (2000).
[CrossRef]

C. Nicole, M. A. Bouchene, S. Zamith, N. Melikechi, and B. Girard, Phys. Rev. A 60, R1755 (1999).
[CrossRef]

Halfmann, T.

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 763 (2001).
[CrossRef] [PubMed]

Hepburn, J. W.

S. Zhdanovich, E. A. Shapiro, M. Shapiro, J. W. Hepburn, and V. Milner, Phys. Rev. Lett. 100, 103004 (2007).
[CrossRef]

Kral, P.

P. Kral, I. Thanopulos, and M. Shapiro, Rev. Mod. Phys. 79, 53 (2007).
[CrossRef]

Melikechi, N.

C. Nicole, M. A. Bouchene, S. Zamith, N. Melikechi, and B. Girard, Phys. Rev. A 60, R1755 (1999).
[CrossRef]

Menzel-Jones, C.

E. A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro, Phys. Rev. Lett. 99, 033002 (2007).
[CrossRef] [PubMed]

Milner, V.

E. A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro, Phys. Rev. Lett. 99, 033002 (2007).
[CrossRef] [PubMed]

S. Zhdanovich, E. A. Shapiro, M. Shapiro, J. W. Hepburn, and V. Milner, Phys. Rev. Lett. 100, 103004 (2007).
[CrossRef]

Nicole, C.

S. Zamith, M. A. Bouchene, E. Sokell, C. Nicole, V. Blanchet, and B. Girard, Eur. Phys. J. D 12, 255 (2000).
[CrossRef]

C. Nicole, M. A. Bouchene, S. Zamith, N. Melikechi, and B. Girard, Phys. Rev. A 60, R1755 (1999).
[CrossRef]

Rudolph, W.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques, and Applications on a Femtosecond Time Scale (Academic, 1996).

Shapiro, E. A.

E. A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro, Phys. Rev. Lett. 99, 033002 (2007).
[CrossRef] [PubMed]

S. Zhdanovich, E. A. Shapiro, M. Shapiro, J. W. Hepburn, and V. Milner, Phys. Rev. Lett. 100, 103004 (2007).
[CrossRef]

Shapiro, M.

S. Zhdanovich, E. A. Shapiro, M. Shapiro, J. W. Hepburn, and V. Milner, Phys. Rev. Lett. 100, 103004 (2007).
[CrossRef]

E. A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro, Phys. Rev. Lett. 99, 033002 (2007).
[CrossRef] [PubMed]

P. Kral, I. Thanopulos, and M. Shapiro, Rev. Mod. Phys. 79, 53 (2007).
[CrossRef]

M. Shapiro and P. Brumer, Phys. Rep. 425, 195 (2006).
[CrossRef]

M. Shapiro and P. Brumer, Principles of the Quantum Control of Molecular Processes (Wiley, 2003).

Shore, B. W.

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 763 (2001).
[CrossRef] [PubMed]

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

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

Sokell, E.

S. Zamith, M. A. Bouchene, E. Sokell, C. Nicole, V. Blanchet, and B. Girard, Eur. Phys. J. D 12, 255 (2000).
[CrossRef]

Thanopulos, I.

P. Kral, I. Thanopulos, and M. Shapiro, Rev. Mod. Phys. 79, 53 (2007).
[CrossRef]

Theuer, H.

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

Vitanov, N. V.

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

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 763 (2001).
[CrossRef] [PubMed]

Zamith, S.

S. Zamith, M. A. Bouchene, E. Sokell, C. Nicole, V. Blanchet, and B. Girard, Eur. Phys. J. D 12, 255 (2000).
[CrossRef]

C. Nicole, M. A. Bouchene, S. Zamith, N. Melikechi, and B. Girard, Phys. Rev. A 60, R1755 (1999).
[CrossRef]

Zhdanovich, S.

S. Zhdanovich, E. A. Shapiro, M. Shapiro, J. W. Hepburn, and V. Milner, Phys. Rev. Lett. 100, 103004 (2007).
[CrossRef]

Adv. At. Mol. Opt. Phys.

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

Annu. Rev. Phys. Chem.

N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu. Rev. Phys. Chem. 52, 763 (2001).
[CrossRef] [PubMed]

Eur. Phys. J. D

S. Zamith, M. A. Bouchene, E. Sokell, C. Nicole, V. Blanchet, and B. Girard, Eur. Phys. J. D 12, 255 (2000).
[CrossRef]

Phys. Rep.

M. Shapiro and P. Brumer, Phys. Rep. 425, 195 (2006).
[CrossRef]

Phys. Rev. A

C. Nicole, M. A. Bouchene, S. Zamith, N. Melikechi, and B. Girard, Phys. Rev. A 60, R1755 (1999).
[CrossRef]

Phys. Rev. Lett.

E. A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro, Phys. Rev. Lett. 99, 033002 (2007).
[CrossRef] [PubMed]

S. Zhdanovich, E. A. Shapiro, M. Shapiro, J. W. Hepburn, and V. Milner, Phys. Rev. Lett. 100, 103004 (2007).
[CrossRef]

Rev. Mod. Phys.

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

P. Kral, I. Thanopulos, and M. Shapiro, Rev. Mod. Phys. 79, 53 (2007).
[CrossRef]

Other

NIST Atomic Spectra Database (NIST, Gaithersburg, Md., 2008).

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques, and Applications on a Femtosecond Time Scale (Academic, 1996).

M. Shapiro and P. Brumer, Principles of the Quantum Control of Molecular Processes (Wiley, 2003).

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Figures (3)

Fig. 1
Fig. 1

Pump-probe scheme on the 3 s 3 p 3 d ladder system of atomic sodium. The left part represents the stationary state description, while the right part represents the bright–dark states description. See discussions in the text.

Fig. 2
Fig. 2

Pump–probe results in the sodium 3 p manifold (circles, experimental data; solid curve, cosine function fit; dashed curve, extrapolated from the fitted curve). The quantum beats period ( 1.94 ps ) derived from the fit corresponds to the fine structure splitting ( 17.2 cm 1 ) of the 3 p state. The positive time delays correspond to the pump pulse (centered at 593 nm ) preceding the Stokes (probe) pulse (centered at 812 nm ). The τ = 0 on the abscissa is a nominal value derived from an ex situ SFM-CC measurement. The actual time zero determined in this Letter is indicated by the vertical solid line.

Fig. 3
Fig. 3

Expanded view of the time delay range [ 400 , 200 fs ] in Fig. 2. The actual time zero (corresponding to a nominal τ = 98 fs ) is indicated by the vertical solid line. The inset shows the result of an ex situ SFM-CC measurement, which yields the nominal τ = 0 given on the abscissa.

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