Abstract

We optimized the two-photon fluorescence (TPF) of a Coumarin 30 dye by using a feedback-controlled femtosecond pulse shaping technique. For optimization we implemented an evolutionary algorithm with a liquid crystal phase-only pulse shaper in a folded 4f setup. The optimization procedure applied to the second harmonic generation, and TPF noticeably improved the output signals and demonstrated good convergence. In addition, signal ratios involving TPF and second harmonic generation (SHG) were successfully optimized. The correlation between TPF and SHG was studied, and it was found to decrease when the pulse shape was close to the optimum. These experimental results are of interest for potential applications of coherent control to complex molecular systems as well as in biomedical imaging.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. I. Pastrik, E. J. Brown, Q. Zhang, and M. Dantus, “Quantum control of the yield of a chemical reaction,” J. Chem. Phys. 108, 4375–4378 (1998).
    [CrossRef]
  4. I. Otake, S. S. Kano, and A. Wada, “Pulse shaping effect on two-photon excitation efficiency of α-perylene crystals and perylene in chloroform solution,” J. Chem. Phys. 124, 014501(2006).
    [CrossRef]
  5. R. Judson and H. Rabitz, “Teaching laser to control molecules,” Phys. Rev. Lett. 68, 1500–1504 (1992).
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  6. D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22, 1793–1795 (1997).
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  7. C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
    [CrossRef]
  8. R. Bartels, S. Backus, E. Zeek, L. Misoguti, P. Vdovin, I. Chistov, M. Murname, and H. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft-x-rays,” Nature 406, 164–166 (2000).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).
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    [CrossRef]

2010

2009

M. Roth, L. Guyon, J. Roslund, V. Boutou, F. Courvoisier, J. Wolf, and H. Rabitz, “Quantum control of tightly competitive product channels,” Phys. Rev. Lett. 102, 253001 (2009).
[CrossRef] [PubMed]

2006

I. Otake, S. S. Kano, and A. Wada, “Pulse shaping effect on two-photon excitation efficiency of α-perylene crystals and perylene in chloroform solution,” J. Chem. Phys. 124, 014501(2006).
[CrossRef]

M. Kauert, P. C. Stoller, M. Frenz, and J. Ricka, “Absolute measurement of molecular two-photon absorption cross-sections using a fluorescence saturation technique,” Opt. Express 14, 8434–8447 (2006).
[CrossRef] [PubMed]

2004

S. Santhilkumar, S. Nath, and H. Pal, “Photophysical properties of coumarin-30 dye in aprotic and protic solvents of varying polarities,” Photochem. Photobiol. 80, 104–111 (2004).
[CrossRef]

2003

T. Brixner, N. H. Damrauer, B. Kiefer, and G. Gerber, “Liquid-phase adaptive femtosecond quantum control: removing intrinsic intensity dependencies,” J. Chem. Phys. 118, 3692–3701 (2003).
[CrossRef]

T. Brixner and G. Gerber, “Quantum control of gas-phase and liquid-phase femtochemistry,” Chem. Phys. Chem. 4, 418–438(2003).
[CrossRef] [PubMed]

2002

S. H. Lee, K. H. Jung, J. H. Sung, K. H. Hong, and C. H. Nam, “Adaptive quantum control of DCM fluorescence in the liquid phase,” J. Chem. Phys. 117, 9858–9861 (2002).
[CrossRef]

B. Kovac and I. Novak, “Electronic structures of coumarins,” Spectrochim Acta Part A 58, 1483–1488 (2002).
[CrossRef]

J. L. Herek, W. Wohleben, R. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002).
[CrossRef] [PubMed]

2001

D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, 023420 (2001).
[CrossRef]

2000

F. Verluise, V. Laude, Z. Cheng, C. 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]

T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Porch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
[CrossRef]

R. Bartels, S. Backus, E. Zeek, L. Misoguti, P. Vdovin, I. Chistov, M. Murname, and H. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft-x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

1998

D. Meshulach and Y. Silberberg, “Quantum control of multi-photon transitions by shaped ultrashort optical pulses,” Nature 396, 239–242 (1998).
[CrossRef]

I. Pastrik, E. J. Brown, Q. Zhang, and M. Dantus, “Quantum control of the yield of a chemical reaction,” J. Chem. Phys. 108, 4375–4378 (1998).
[CrossRef]

1997

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22, 1793–1795 (1997).
[CrossRef]

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295(1997).
[CrossRef]

1992

R. Judson and H. Rabitz, “Teaching laser to control molecules,” Phys. Rev. Lett. 68, 1500–1504 (1992).
[CrossRef] [PubMed]

Backus, S.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, P. Vdovin, I. Chistov, M. Murname, and H. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft-x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Bardeen, C. J.

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Bartels, R.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, P. Vdovin, I. Chistov, M. Murname, and H. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft-x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Boutou, V.

M. Roth, L. Guyon, J. Roslund, V. Boutou, F. Courvoisier, J. Wolf, and H. Rabitz, “Quantum control of tightly competitive product channels,” Phys. Rev. Lett. 102, 253001 (2009).
[CrossRef] [PubMed]

Brixner, T.

T. Brixner, N. H. Damrauer, B. Kiefer, and G. Gerber, “Liquid-phase adaptive femtosecond quantum control: removing intrinsic intensity dependencies,” J. Chem. Phys. 118, 3692–3701 (2003).
[CrossRef]

T. Brixner and G. Gerber, “Quantum control of gas-phase and liquid-phase femtochemistry,” Chem. Phys. Chem. 4, 418–438(2003).
[CrossRef] [PubMed]

Brown, E. J.

I. Pastrik, E. J. Brown, Q. Zhang, and M. Dantus, “Quantum control of the yield of a chemical reaction,” J. Chem. Phys. 108, 4375–4378 (1998).
[CrossRef]

Carpenter, S. D.

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Cheng, Z.

Chistov, I.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, P. Vdovin, I. Chistov, M. Murname, and H. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft-x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Cogdell, R.

J. L. Herek, W. Wohleben, R. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002).
[CrossRef] [PubMed]

Courvoisier, F.

M. Roth, L. Guyon, J. Roslund, V. Boutou, F. Courvoisier, J. Wolf, and H. Rabitz, “Quantum control of tightly competitive product channels,” Phys. Rev. Lett. 102, 253001 (2009).
[CrossRef] [PubMed]

Damrauer, N. H.

T. Brixner, N. H. Damrauer, B. Kiefer, and G. Gerber, “Liquid-phase adaptive femtosecond quantum control: removing intrinsic intensity dependencies,” J. Chem. Phys. 118, 3692–3701 (2003).
[CrossRef]

Dantus, M.

I. Pastrik, E. J. Brown, Q. Zhang, and M. Dantus, “Quantum control of the yield of a chemical reaction,” J. Chem. Phys. 108, 4375–4378 (1998).
[CrossRef]

Delong, K. W.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295(1997).
[CrossRef]

Fittinghoff, D. N.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295(1997).
[CrossRef]

Frenz, M.

Frey, S.

D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, 023420 (2001).
[CrossRef]

Gerber, G.

T. Brixner, N. H. Damrauer, B. Kiefer, and G. Gerber, “Liquid-phase adaptive femtosecond quantum control: removing intrinsic intensity dependencies,” J. Chem. Phys. 118, 3692–3701 (2003).
[CrossRef]

T. Brixner and G. Gerber, “Quantum control of gas-phase and liquid-phase femtochemistry,” Chem. Phys. Chem. 4, 418–438(2003).
[CrossRef] [PubMed]

Guyon, L.

M. Roth, L. Guyon, J. Roslund, V. Boutou, F. Courvoisier, J. Wolf, and H. Rabitz, “Quantum control of tightly competitive product channels,” Phys. Rev. Lett. 102, 253001 (2009).
[CrossRef] [PubMed]

Herek, J. L.

J. L. Herek, W. Wohleben, R. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002).
[CrossRef] [PubMed]

Hong, K. H.

S. H. Lee, K. H. Jung, J. H. Sung, K. H. Hong, and C. H. Nam, “Adaptive quantum control of DCM fluorescence in the liquid phase,” J. Chem. Phys. 117, 9858–9861 (2002).
[CrossRef]

Hornung, T.

T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Porch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
[CrossRef]

Judson, R.

R. Judson and H. Rabitz, “Teaching laser to control molecules,” Phys. Rev. Lett. 68, 1500–1504 (1992).
[CrossRef] [PubMed]

Jung, K. H.

S. H. Lee, K. H. Jung, J. H. Sung, K. H. Hong, and C. H. Nam, “Adaptive quantum control of DCM fluorescence in the liquid phase,” J. Chem. Phys. 117, 9858–9861 (2002).
[CrossRef]

Kano, S. S.

I. Otake, S. S. Kano, and A. Wada, “Pulse shaping effect on two-photon excitation efficiency of α-perylene crystals and perylene in chloroform solution,” J. Chem. Phys. 124, 014501(2006).
[CrossRef]

Kapteyn, H.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, P. Vdovin, I. Chistov, M. Murname, and H. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft-x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Kauert, M.

Kiefer, B.

T. Brixner, N. H. Damrauer, B. Kiefer, and G. Gerber, “Liquid-phase adaptive femtosecond quantum control: removing intrinsic intensity dependencies,” J. Chem. Phys. 118, 3692–3701 (2003).
[CrossRef]

Kolomenskii, A. A.

Kompa, K. L.

D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, 023420 (2001).
[CrossRef]

T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Porch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
[CrossRef]

Kovac, B.

B. Kovac and I. Novak, “Electronic structures of coumarins,” Spectrochim Acta Part A 58, 1483–1488 (2002).
[CrossRef]

Krumbugel, M. A.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295(1997).
[CrossRef]

Laude, V.

Lee, S. H.

S. H. Lee, K. H. Jung, J. H. Sung, K. H. Hong, and C. H. Nam, “Adaptive quantum control of DCM fluorescence in the liquid phase,” J. Chem. Phys. 117, 9858–9861 (2002).
[CrossRef]

Meier, R.

T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Porch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
[CrossRef]

Meshulach, D.

D. Meshulach and Y. Silberberg, “Quantum control of multi-photon transitions by shaped ultrashort optical pulses,” Nature 396, 239–242 (1998).
[CrossRef]

D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22, 1793–1795 (1997).
[CrossRef]

Misoguti, L.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, P. Vdovin, I. Chistov, M. Murname, and H. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft-x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Motzkus, M.

J. L. Herek, W. Wohleben, R. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002).
[CrossRef] [PubMed]

D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, 023420 (2001).
[CrossRef]

T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Porch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
[CrossRef]

Murname, M.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, P. Vdovin, I. Chistov, M. Murname, and H. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft-x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Nam, C. H.

S. H. Lee, K. H. Jung, J. H. Sung, K. H. Hong, and C. H. Nam, “Adaptive quantum control of DCM fluorescence in the liquid phase,” J. Chem. Phys. 117, 9858–9861 (2002).
[CrossRef]

Nath, S.

S. Santhilkumar, S. Nath, and H. Pal, “Photophysical properties of coumarin-30 dye in aprotic and protic solvents of varying polarities,” Photochem. Photobiol. 80, 104–111 (2004).
[CrossRef]

Novak, I.

B. Kovac and I. Novak, “Electronic structures of coumarins,” Spectrochim Acta Part A 58, 1483–1488 (2002).
[CrossRef]

Otake, I.

I. Otake, S. S. Kano, and A. Wada, “Pulse shaping effect on two-photon excitation efficiency of α-perylene crystals and perylene in chloroform solution,” J. Chem. Phys. 124, 014501(2006).
[CrossRef]

Pal, H.

S. Santhilkumar, S. Nath, and H. Pal, “Photophysical properties of coumarin-30 dye in aprotic and protic solvents of varying polarities,” Photochem. Photobiol. 80, 104–111 (2004).
[CrossRef]

Pastrik, I.

I. Pastrik, E. J. Brown, Q. Zhang, and M. Dantus, “Quantum control of the yield of a chemical reaction,” J. Chem. Phys. 108, 4375–4378 (1998).
[CrossRef]

Porch, D.

T. Hornung, R. Meier, D. Zeidler, K. L. Kompa, D. Porch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
[CrossRef]

Poudel, M. P.

Rabitz, H.

M. Roth, L. Guyon, J. Roslund, V. Boutou, F. Courvoisier, J. Wolf, and H. Rabitz, “Quantum control of tightly competitive product channels,” Phys. Rev. Lett. 102, 253001 (2009).
[CrossRef] [PubMed]

R. Judson and H. Rabitz, “Teaching laser to control molecules,” Phys. Rev. Lett. 68, 1500–1504 (1992).
[CrossRef] [PubMed]

Richman, B. A.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295(1997).
[CrossRef]

Ricka, J.

Roslund, J.

M. Roth, L. Guyon, J. Roslund, V. Boutou, F. Courvoisier, J. Wolf, and H. Rabitz, “Quantum control of tightly competitive product channels,” Phys. Rev. Lett. 102, 253001 (2009).
[CrossRef] [PubMed]

Roth, M.

M. Roth, L. Guyon, J. Roslund, V. Boutou, F. Courvoisier, J. Wolf, and H. Rabitz, “Quantum control of tightly competitive product channels,” Phys. Rev. Lett. 102, 253001 (2009).
[CrossRef] [PubMed]

Santhilkumar, S.

S. Santhilkumar, S. Nath, and H. Pal, “Photophysical properties of coumarin-30 dye in aprotic and protic solvents of varying polarities,” Photochem. Photobiol. 80, 104–111 (2004).
[CrossRef]

Schuessler, H. A.

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).

Silberberg, Y.

D. Meshulach and Y. Silberberg, “Quantum control of multi-photon transitions by shaped ultrashort optical pulses,” Nature 396, 239–242 (1998).
[CrossRef]

D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22, 1793–1795 (1997).
[CrossRef]

Spielmann, C.

Stoller, P. C.

Strohaber, J.

Sung, J. H.

S. H. Lee, K. H. Jung, J. H. Sung, K. H. Hong, and C. H. Nam, “Adaptive quantum control of DCM fluorescence in the liquid phase,” J. Chem. Phys. 117, 9858–9861 (2002).
[CrossRef]

Sweetser, J. N.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295(1997).
[CrossRef]

Tournois, P.

Trebino, R.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, and B. A. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295(1997).
[CrossRef]

Vdovin, P.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, P. Vdovin, I. Chistov, M. Murname, and H. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft-x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Verluise, F.

Wada, A.

I. Otake, S. S. Kano, and A. Wada, “Pulse shaping effect on two-photon excitation efficiency of α-perylene crystals and perylene in chloroform solution,” J. Chem. Phys. 124, 014501(2006).
[CrossRef]

Warren, W. S.

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Weber, P. M.

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Wilson, K. R.

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Wohleben, W.

J. L. Herek, W. Wohleben, R. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002).
[CrossRef] [PubMed]

Wolf, J.

M. Roth, L. Guyon, J. Roslund, V. Boutou, F. Courvoisier, J. Wolf, and H. Rabitz, “Quantum control of tightly competitive product channels,” Phys. Rev. Lett. 102, 253001 (2009).
[CrossRef] [PubMed]

Yakovlev, V. V.

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Yelin, D.

Zeek, E.

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup.

Fig. 2
Fig. 2

Schematic diagram of folded 4 f setup (top view).

Fig. 3
Fig. 3

Normalized absorption and emission spectra of Coumarin 30 shown by the solid and dashed curves, respectively. The insets show the chemical structure of the Coumarin 30 molecule and schematic of TPF transitions.

Fig. 4
Fig. 4

Convergence curves for optimization of the SHG signal. Three different curves show the best, worst, and mean SHG values.

Fig. 5
Fig. 5

Pulse images from GRENOUILLE: (a) before (pulse duration τ = 45 fs ) and (b) after ( τ = 33 fs ) the optimization of the SHG signal.

Fig. 6
Fig. 6

TPF spectra of Coumarin 30 measured before optimization (dashed curve) and after optimization (solid curve).

Fig. 7
Fig. 7

Typical convergence of the second-, third-, and fourth-order dispersion coefficients for TPF optimization.

Fig. 8
Fig. 8

Evolution of TPF, SHG, and their ratio during (TPF/SHG) optimization.

Fig. 9
Fig. 9

TPF, SHG, and their ratio [ ( TPF ) 2 / SHG ] during optimization of the latter.

Fig. 10
Fig. 10

Correlation analysis of the signals: (a) TPF and SHG signals for all individuals while SHG is optimized; (b) correlation between TPF and SHG (the deviation of maximum of the correlation function from 1 by δ = 0.23 is due to both the different nature of the two processes and the noise); and (c) correlation function of the SHG signals measured by two detection channels—in this case, the deviation of the maximum from 1, δ = 0.06 , is due to noise, and it is smaller than in Fig. 10b, showing a relatively small influence of the noise.

Equations (2)

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β ( ω ) = β 0 + β 1 ( ω ω 0 ) + 1 2 β 2 ( ω ω 0 ) 2 + 1 6 β 3 ( ω ω 0 ) 3 + 1 24 β 4 ( ω ω 0 ) 4 + ,
G norm ( Δ N ) = I 1 ( N ) I 2 ( N + Δ N ) [ I 1 2 ( N ) I 2 2 ( N ) ] ,

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