Abstract

We have considered an analytical control of two-photon absorption process of atoms in the strong-field interaction regime. The experiment was performed on gaseous cesium atoms strongly interacting with a shaped laser-pulse from a femtosecond laser amplifier and a programmable pulse-shaper. When this shaped laser-pulse transfers the atomic population from the 6s ground state to the 8s excited state, we have found that both positively- and negatively-chirped laser pulses, compared with a Gaussian pulse, enhance this excitation in the strong-field regime of laser-atom interaction. This unusual phenomena is explained because the temporal shape of the laser intensity compensates the effect of dynamic Stark shift for the two-photon resonant condition to be optimally maintained. We provide analytic calculations using the strong-field phase matching, which show good agreement with the experiment.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  5. R. S. Judson and H. Rabitz, "Teaching lasers to control molecules," Phys. Rev. Lett. 68, 1500-1503 (1992).
    [CrossRef] [PubMed]
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    [CrossRef]
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  8. H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, "Whither the future of controlling quantum phenomena?" Science 288, 824-828 (2000).
    [CrossRef] [PubMed]
  9. N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, "Transform-limited pulses are not optimal for resonant multiphoton transitions," Phys. Rev. Lett. 86, 47-50 (2001).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2008

Z. Amitay, A. Gandman, L. Chuntonov, and L. Rybak, "Multichannel selective femtosecond coherent control based on symmetry properties," Phys. Rev. Lett. 100, 193002 (2008).
[CrossRef] [PubMed]

H. Suchowski, A. Natan,B. D. Bruner, and Y. Silberberg, "Spatio-temporal coherent control of atomic systems: weak to strong field transition and breaking of symmetry in 2D maps," J. Phys. B 41, 074008 (2008).
[CrossRef]

2007

P. Fendel, S. D. Bergeson, Th. Udem, and T. W. Hänsch, "Two-photon frequency comb spectroscopy of the 6s-8s transition in cesium," Opt. Lett. 32, 701-703 (2007).
[CrossRef] [PubMed]

P. Nuernberger, G. Vogt, T. Brixner, and G. Gerber, "Femtosecond quantum control of molecular dynamics in the condensed phase," Phys. Chem. Chem. Phys. 9, 2470-2497 (2007).
[CrossRef] [PubMed]

2006

A. Monmayrant, B. Chatel, and B. Girard, "Quantum state measurement using coherent transients," Phys. Rev. Lett. 96, 103002 (2006).
[CrossRef] [PubMed]

C. Trallero-Herrero, J.L. Cohen, and T. Weinacht, "Strong-field atomic phase matching," Phys. Rev. Lett. 96, 063603 (2006).
[CrossRef] [PubMed]

2005

N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, "Simple route to strong-field coherent control," Phys. Rev. Lett. 94, 083002 (2005).
[CrossRef] [PubMed]

2004

A. Sieradzan, M. D. Havey, and M. S. Safronova, "Combined experimentl and theoretical study of the 6p2Pj ? 8s2S1/2 relative transiton matrix elements in atomic Cs," Phys. Rev. A 69, 022502 (2004).
[CrossRef]

2001

R. J. Levis, G. M. Menkir, ande H. Rabits, "Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulses," Science 292, 709-713 (2001).
[CrossRef] [PubMed]

N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, "Transform-limited pulses are not optimal for resonant multiphoton transitions," Phys. Rev. Lett. 86, 47-50 (2001).
[CrossRef] [PubMed]

2000

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, "Whither the future of controlling quantum phenomena?" Science 288, 824-828 (2000).
[CrossRef] [PubMed]

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

F. Verluise, V. Laude, Z. Cheng, Ch. Spielmann, and P. Tournois, "Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter: pulse compression and shaping," Opt. Lett. 25, 575-577 (2000).
[CrossRef]

1999

T. C. Weinacht, J. Ahn, and P. H. Bucksbaum, "Controlling the shape of a quantum wavefunction," Nature 397, 233-235 (1999).
[CrossRef]

D. Meschulach, and Y. Silberberg, "Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses," Phy. Rev. A. 60, 1287-1292 (1999).
[CrossRef]

1998

K. Bergmann, H. Theuer, and B. W. Shore, "Coherent population transfer among quantum states of atoms and molecules," Rev. Mod. Phys. 70, 1003-1025 (1998).
[CrossRef]

D. Meshulach and Y. Silberberg, "Coherent quantum control of two-photon transitions by a femtosecond laser pulse," Nature 396, 239-242 (1998).
[CrossRef]

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Stehle, and G. Gerber, "Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses," Science 282, 919-922 (1998).
[CrossRef] [PubMed]

1992

R. S. Judson and H. Rabitz, "Teaching lasers to control molecules," Phys. Rev. Lett. 68, 1500-1503 (1992).
[CrossRef] [PubMed]

1986

M. Shapiro and P. Brumer, "Laser control of product quantum state populations in unimoleular reactions," J. Chem. Phys. 84, 4103-4104 (1986).
[CrossRef]

1985

D. J. Tanner and S. A. Rice, "Control of selectivity of chemical reaction via control of wavepacket evolution," J. Chem. Phys. 83, 5013-5018 (1985).
[CrossRef]

Ahn, J.

T. C. Weinacht, J. Ahn, and P. H. Bucksbaum, "Controlling the shape of a quantum wavefunction," Nature 397, 233-235 (1999).
[CrossRef]

Amitay, Z.

Z. Amitay, A. Gandman, L. Chuntonov, and L. Rybak, "Multichannel selective femtosecond coherent control based on symmetry properties," Phys. Rev. Lett. 100, 193002 (2008).
[CrossRef] [PubMed]

Assion, A.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Stehle, and G. Gerber, "Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses," Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Baumert, T.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Stehle, and G. Gerber, "Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses," Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Bergeson, S. D.

Bergmann, K.

K. Bergmann, H. Theuer, and B. W. Shore, "Coherent population transfer among quantum states of atoms and molecules," Rev. Mod. Phys. 70, 1003-1025 (1998).
[CrossRef]

Bergt, M.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Stehle, and G. Gerber, "Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses," Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Brixner, T.

P. Nuernberger, G. Vogt, T. Brixner, and G. Gerber, "Femtosecond quantum control of molecular dynamics in the condensed phase," Phys. Chem. Chem. Phys. 9, 2470-2497 (2007).
[CrossRef] [PubMed]

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Stehle, and G. Gerber, "Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses," Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Brumer, P.

M. Shapiro and P. Brumer, "Laser control of product quantum state populations in unimoleular reactions," J. Chem. Phys. 84, 4103-4104 (1986).
[CrossRef]

Bruner, B. D.

H. Suchowski, A. Natan,B. D. Bruner, and Y. Silberberg, "Spatio-temporal coherent control of atomic systems: weak to strong field transition and breaking of symmetry in 2D maps," J. Phys. B 41, 074008 (2008).
[CrossRef]

Bucksbaum, P. H.

T. C. Weinacht, J. Ahn, and P. H. Bucksbaum, "Controlling the shape of a quantum wavefunction," Nature 397, 233-235 (1999).
[CrossRef]

Chatel, B.

A. Monmayrant, B. Chatel, and B. Girard, "Quantum state measurement using coherent transients," Phys. Rev. Lett. 96, 103002 (2006).
[CrossRef] [PubMed]

Cheng, Z.

Chuntonov, L.

Z. Amitay, A. Gandman, L. Chuntonov, and L. Rybak, "Multichannel selective femtosecond coherent control based on symmetry properties," Phys. Rev. Lett. 100, 193002 (2008).
[CrossRef] [PubMed]

Cohen, J.L.

C. Trallero-Herrero, J.L. Cohen, and T. Weinacht, "Strong-field atomic phase matching," Phys. Rev. Lett. 96, 063603 (2006).
[CrossRef] [PubMed]

Dayan, B.

N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, "Transform-limited pulses are not optimal for resonant multiphoton transitions," Phys. Rev. Lett. 86, 47-50 (2001).
[CrossRef] [PubMed]

de Vivie-Riedle, R.

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, "Whither the future of controlling quantum phenomena?" Science 288, 824-828 (2000).
[CrossRef] [PubMed]

Dudovich, N.

N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, "Simple route to strong-field coherent control," Phys. Rev. Lett. 94, 083002 (2005).
[CrossRef] [PubMed]

N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, "Transform-limited pulses are not optimal for resonant multiphoton transitions," Phys. Rev. Lett. 86, 47-50 (2001).
[CrossRef] [PubMed]

Fendel, P.

Gallagher Faeder, S. M.

N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, "Transform-limited pulses are not optimal for resonant multiphoton transitions," Phys. Rev. Lett. 86, 47-50 (2001).
[CrossRef] [PubMed]

Gandman, A.

Z. Amitay, A. Gandman, L. Chuntonov, and L. Rybak, "Multichannel selective femtosecond coherent control based on symmetry properties," Phys. Rev. Lett. 100, 193002 (2008).
[CrossRef] [PubMed]

Gerber, G.

P. Nuernberger, G. Vogt, T. Brixner, and G. Gerber, "Femtosecond quantum control of molecular dynamics in the condensed phase," Phys. Chem. Chem. Phys. 9, 2470-2497 (2007).
[CrossRef] [PubMed]

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Stehle, and G. Gerber, "Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses," Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Girard, B.

A. Monmayrant, B. Chatel, and B. Girard, "Quantum state measurement using coherent transients," Phys. Rev. Lett. 96, 103002 (2006).
[CrossRef] [PubMed]

Hänsch, T. W.

Havey, M. D.

A. Sieradzan, M. D. Havey, and M. S. Safronova, "Combined experimentl and theoretical study of the 6p2Pj ? 8s2S1/2 relative transiton matrix elements in atomic Cs," Phys. Rev. A 69, 022502 (2004).
[CrossRef]

Judson, R. S.

R. S. Judson and H. Rabitz, "Teaching lasers to control molecules," Phys. Rev. Lett. 68, 1500-1503 (1992).
[CrossRef] [PubMed]

Kiefer, B.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Stehle, and G. Gerber, "Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses," Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Kompa, K.

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, "Whither the future of controlling quantum phenomena?" Science 288, 824-828 (2000).
[CrossRef] [PubMed]

Laude, V.

Levis, R. J.

R. J. Levis, G. M. Menkir, ande H. Rabits, "Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulses," Science 292, 709-713 (2001).
[CrossRef] [PubMed]

Menkir, G. M.

R. J. Levis, G. M. Menkir, ande H. Rabits, "Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulses," Science 292, 709-713 (2001).
[CrossRef] [PubMed]

Meschulach, D.

D. Meschulach, and Y. Silberberg, "Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses," Phy. Rev. A. 60, 1287-1292 (1999).
[CrossRef]

Meshulach, D.

D. Meshulach and Y. Silberberg, "Coherent quantum control of two-photon transitions by a femtosecond laser pulse," Nature 396, 239-242 (1998).
[CrossRef]

Monmayrant, A.

A. Monmayrant, B. Chatel, and B. Girard, "Quantum state measurement using coherent transients," Phys. Rev. Lett. 96, 103002 (2006).
[CrossRef] [PubMed]

Motzkus, M.

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, "Whither the future of controlling quantum phenomena?" Science 288, 824-828 (2000).
[CrossRef] [PubMed]

Natan, A.

H. Suchowski, A. Natan,B. D. Bruner, and Y. Silberberg, "Spatio-temporal coherent control of atomic systems: weak to strong field transition and breaking of symmetry in 2D maps," J. Phys. B 41, 074008 (2008).
[CrossRef]

Nuernberger, P.

P. Nuernberger, G. Vogt, T. Brixner, and G. Gerber, "Femtosecond quantum control of molecular dynamics in the condensed phase," Phys. Chem. Chem. Phys. 9, 2470-2497 (2007).
[CrossRef] [PubMed]

Pe’er, A.

N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, "Simple route to strong-field coherent control," Phys. Rev. Lett. 94, 083002 (2005).
[CrossRef] [PubMed]

Polack, T.

N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, "Simple route to strong-field coherent control," Phys. Rev. Lett. 94, 083002 (2005).
[CrossRef] [PubMed]

Rabitz, H.

H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, "Whither the future of controlling quantum phenomena?" Science 288, 824-828 (2000).
[CrossRef] [PubMed]

R. S. Judson and H. Rabitz, "Teaching lasers to control molecules," Phys. Rev. Lett. 68, 1500-1503 (1992).
[CrossRef] [PubMed]

Rice, S. A.

D. J. Tanner and S. A. Rice, "Control of selectivity of chemical reaction via control of wavepacket evolution," J. Chem. Phys. 83, 5013-5018 (1985).
[CrossRef]

Rybak, L.

Z. Amitay, A. Gandman, L. Chuntonov, and L. Rybak, "Multichannel selective femtosecond coherent control based on symmetry properties," Phys. Rev. Lett. 100, 193002 (2008).
[CrossRef] [PubMed]

Safronova, M. S.

A. Sieradzan, M. D. Havey, and M. S. Safronova, "Combined experimentl and theoretical study of the 6p2Pj ? 8s2S1/2 relative transiton matrix elements in atomic Cs," Phys. Rev. A 69, 022502 (2004).
[CrossRef]

Seyfried, V.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Stehle, and G. Gerber, "Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses," Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Shapiro, M.

M. Shapiro and P. Brumer, "Laser control of product quantum state populations in unimoleular reactions," J. Chem. Phys. 84, 4103-4104 (1986).
[CrossRef]

Shore, B. W.

K. Bergmann, H. Theuer, and B. W. Shore, "Coherent population transfer among quantum states of atoms and molecules," Rev. Mod. Phys. 70, 1003-1025 (1998).
[CrossRef]

Sieradzan, A.

A. Sieradzan, M. D. Havey, and M. S. Safronova, "Combined experimentl and theoretical study of the 6p2Pj ? 8s2S1/2 relative transiton matrix elements in atomic Cs," Phys. Rev. A 69, 022502 (2004).
[CrossRef]

Silberberg, Y.

H. Suchowski, A. Natan,B. D. Bruner, and Y. Silberberg, "Spatio-temporal coherent control of atomic systems: weak to strong field transition and breaking of symmetry in 2D maps," J. Phys. B 41, 074008 (2008).
[CrossRef]

N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, "Simple route to strong-field coherent control," Phys. Rev. Lett. 94, 083002 (2005).
[CrossRef] [PubMed]

N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, "Transform-limited pulses are not optimal for resonant multiphoton transitions," Phys. Rev. Lett. 86, 47-50 (2001).
[CrossRef] [PubMed]

D. Meschulach, and Y. Silberberg, "Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses," Phy. Rev. A. 60, 1287-1292 (1999).
[CrossRef]

D. Meshulach and Y. Silberberg, "Coherent quantum control of two-photon transitions by a femtosecond laser pulse," Nature 396, 239-242 (1998).
[CrossRef]

Spielmann, Ch.

Stehle, M.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Stehle, and G. Gerber, "Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses," Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Suchowski, H.

H. Suchowski, A. Natan,B. D. Bruner, and Y. Silberberg, "Spatio-temporal coherent control of atomic systems: weak to strong field transition and breaking of symmetry in 2D maps," J. Phys. B 41, 074008 (2008).
[CrossRef]

Tanner, D. J.

D. J. Tanner and S. A. Rice, "Control of selectivity of chemical reaction via control of wavepacket evolution," J. Chem. Phys. 83, 5013-5018 (1985).
[CrossRef]

Theuer, H.

K. Bergmann, H. Theuer, and B. W. Shore, "Coherent population transfer among quantum states of atoms and molecules," Rev. Mod. Phys. 70, 1003-1025 (1998).
[CrossRef]

Tournois, P.

Trallero-Herrero, C.

C. Trallero-Herrero, J.L. Cohen, and T. Weinacht, "Strong-field atomic phase matching," Phys. Rev. Lett. 96, 063603 (2006).
[CrossRef] [PubMed]

Udem, Th.

Verluise, F.

Vogt, G.

P. Nuernberger, G. Vogt, T. Brixner, and G. Gerber, "Femtosecond quantum control of molecular dynamics in the condensed phase," Phys. Chem. Chem. Phys. 9, 2470-2497 (2007).
[CrossRef] [PubMed]

Weinacht, T.

C. Trallero-Herrero, J.L. Cohen, and T. Weinacht, "Strong-field atomic phase matching," Phys. Rev. Lett. 96, 063603 (2006).
[CrossRef] [PubMed]

Weinacht, T. C.

T. C. Weinacht, J. Ahn, and P. H. Bucksbaum, "Controlling the shape of a quantum wavefunction," Nature 397, 233-235 (1999).
[CrossRef]

Weiner, A. M.

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929-1960 (2000).
[CrossRef]

J. Chem. Phys.

D. J. Tanner and S. A. Rice, "Control of selectivity of chemical reaction via control of wavepacket evolution," J. Chem. Phys. 83, 5013-5018 (1985).
[CrossRef]

M. Shapiro and P. Brumer, "Laser control of product quantum state populations in unimoleular reactions," J. Chem. Phys. 84, 4103-4104 (1986).
[CrossRef]

J. Phys. B

H. Suchowski, A. Natan,B. D. Bruner, and Y. Silberberg, "Spatio-temporal coherent control of atomic systems: weak to strong field transition and breaking of symmetry in 2D maps," J. Phys. B 41, 074008 (2008).
[CrossRef]

Nature

D. Meshulach and Y. Silberberg, "Coherent quantum control of two-photon transitions by a femtosecond laser pulse," Nature 396, 239-242 (1998).
[CrossRef]

T. C. Weinacht, J. Ahn, and P. H. Bucksbaum, "Controlling the shape of a quantum wavefunction," Nature 397, 233-235 (1999).
[CrossRef]

Opt. Lett.

Phy. Rev. A.

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[CrossRef]

Phys. Chem. Chem. Phys.

P. Nuernberger, G. Vogt, T. Brixner, and G. Gerber, "Femtosecond quantum control of molecular dynamics in the condensed phase," Phys. Chem. Chem. Phys. 9, 2470-2497 (2007).
[CrossRef] [PubMed]

Phys. Rev. A

A. Sieradzan, M. D. Havey, and M. S. Safronova, "Combined experimentl and theoretical study of the 6p2Pj ? 8s2S1/2 relative transiton matrix elements in atomic Cs," Phys. Rev. A 69, 022502 (2004).
[CrossRef]

Phys. Rev. Lett.

C. Trallero-Herrero, J.L. Cohen, and T. Weinacht, "Strong-field atomic phase matching," Phys. Rev. Lett. 96, 063603 (2006).
[CrossRef] [PubMed]

Z. Amitay, A. Gandman, L. Chuntonov, and L. Rybak, "Multichannel selective femtosecond coherent control based on symmetry properties," Phys. Rev. Lett. 100, 193002 (2008).
[CrossRef] [PubMed]

N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, "Simple route to strong-field coherent control," Phys. Rev. Lett. 94, 083002 (2005).
[CrossRef] [PubMed]

N. Dudovich, B. Dayan, S. M. Gallagher Faeder, and Y. Silberberg, "Transform-limited pulses are not optimal for resonant multiphoton transitions," Phys. Rev. Lett. 86, 47-50 (2001).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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Rev. Mod. Phys.

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[CrossRef]

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[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Schematics of strong-field two-photon excitations of ground-state atomic cesium with shaped laser pulses. The spectrograms of the laser pulses and of their second harmonics are depicted in red and blue, respectively. The magenta arrows indicate the excitation paths for the strong interaction cases, while the yellow arrows do for the weak interaction cases.

Fig. 2.
Fig. 2.

Schematic setup of a shaped-pulse two-photon absorption experiment in atomic cesium. A half-wave plate (HWP) and a polarization beam splitter (PBS) are used to vary the peak intensity for the range of 0 − 2 × 1011 W/cm2. The inset shows the energy levels of atomic cesium.

Fig. 3.
Fig. 3.

(a) Measured 7p−6s fluorescence signal induced by two-photon absorption in atomic cesium is plotted in color (red is the biggest) as a function of linear chirp rate a 2 and scaled TL peak intensity I 0/I c . The equi-signal levels are traced by contour lines which are reconstructed by a model calculation with best fit parameters. The typical behaviors of the signals are shown in the strong- and weak-field regimes in (b) and (c), respectively.

Fig. 4.
Fig. 4.

(a) Calculated 7p−6s fluorescence signals of atomic cesium in color (white is the biggest), plotted as a function of linear chirp rate and detuning. The TL intensity is I 0 = 1.43Ic . (b) Measured 7p−6s fluorescence as a function of chirp rate

Fig. 5.
Fig. 5.

Measured 7p−6s fluorescence signals in symbols as a function of detuning at various fixed peak intensities, compared with numerical fits in lines using Eq. (18).

Equations (18)

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H ( t ) = ( ω g ( S ) ( t ) χ * ( t ) e 1 [ δt ϕ ( t ) ] χ ( t ) e i [ δt ϕ ( t ) ] ω e ( S ) ( t ) ) ,
ω e , g ( S ) ( t ) = m μ { e , g } m 2 h ̄ 2 Ig ( t ) c ε 0 ω m { e , g } ω m { e , g } 2 Ω 2 ,
χ ( t ) = m μ em μ mg 2 h ̄ 2 Ig ( t ) c ε 0 1 ω mg Ω .
α ( t ) = t Δ ( t ) dt δt + ϕ ( t )
| χ ( t ) exp [ i α ( t ) ] d t | 2
α ( t ) π 2 Δτ [ 1 + ( t τ ) 1 3 ( t τ ) 3 + ] δt + β t 2 ,
P e χ 0 2 π τ 2 1 + β 2 τ 4 exp [ ( δ Δ π / 2 ) 2 τ 2 2 ( 1 + β 2 τ 4 ) ]
P e 1 1 + β 2 τ 4
P e 1 1 + β 2 τ 4 exp [ π Δ 2 τ 2 8 ( 1 + β 2 τ 4 ) ]
Φ ( ω ) = a 1 ( ω Ω ) + a 2 2 ( ω Ω ) 2 + a 3 6 ( ω Ω ) 3 + a 4 24 ( ω Ω ) 4 + ,
β τ 2 = 2 a 2 / τ 0 2 ,
Δτ = Δ 0 τ 0 ,
χ 0 τ = χ 0 ( 0 ) τ 0 ,
P e 1 1 + 4 a 2 2 / τ 0 4 exp [ 1 2 ( δ τ 0 π Δ 0 τ 0 2 1 + 4 a 2 2 / τ 0 4 ) 2 ] .
P e 1 1 + 4 a 2 2 / τ 0 4 exp [ π η 2 I 0 2 τ 0 2 8 ( 1 + 4 a 2 2 / τ 0 4 ) ] ,
P e [ 1 + 1 8 π η 2 τ 0 2 ( I 0 2 I c 2 ) ( 2 a 2 τ 0 2 ) 2 ] exp ( π η 2 τ 0 2 I 0 2 8 ) .
C = 1 2 X 2 π 4 η I 0 τ 0 2 X 2 Y + τ 0 2 2 Y 2 ,
P e exp ( ( δ Δ 0 π / 2 ) 2 τ 0 2 / 2 ) .

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