Abstract

Weak-field coherent phase control of atomic non-resonant multiphoton excitation induced by shaped femtosecond pulses is studied theoretically in the single-cycle regime. The carrier-envelope phase (CEP) of the pulse, which in the multi-cycle regime does not play any control role, is shown here to be a new effective control parameter that its effect is highly sensitive to the spectral position of the ultrabroad spectrum. Rationally chosen position of the ultrabroadband spectrum coherently induces several groups of multiphoton transitions from the ground state to the excited state of the system: transitions involving only absorbed photons as well as Raman transitions involving both absorbed and emitted photons. The intra-group interference is controlled by the relative spectral phase of the different frequency components of the pulse, while the inter-group interference is controlled jointly by the CEP and the relative spectral phase. Specifically, non-resonant two- and three-photon excitation is studied in a simple model system within the perturbative frequency-domain framework. The developed intuition is then applied to weak-field multiphoton excitation of atomic cesium (Cs), where the simplified model is verified by non-perturbative numerical solution of the time-dependent Schrödinger equation. We expect this work to serve as a basis for a new line of femtosecond coherent control experiments.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. J. Tannor, R. Kosloff, and S. A. Rice, “Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations,” J. Chem. Phys. 85(10), 5805 (1986).
    [CrossRef]
  2. M. Shapiro, and P. Brumer, Principles of the quantum control of molecular processes (Wiley, New Jersey, 2003).
  3. W. S. Warren, H. Rabitz, and D. Mahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259(5101), 1581–1589 (1993).
    [CrossRef] [PubMed]
  4. R. J. Gordon and S. A. Rice, “Active control of the dynamics of atoms and molecules,” Annu. Rev. Phys. Chem. 48(1), 601–641 (1997).
    [CrossRef] [PubMed]
  5. H. Rabitz, M. Motzkus, K. Kompa, and R. de. Vivie-Riedle, “Whither the future of controlling quantum phenomena?” Science 288(5467), 824–828 (2000).
    [CrossRef] [PubMed]
  6. M. Dantus and V. V. Lozovoy, “Experimental coherent laser control of physicochemical processes,” Chem. Rev. 104(4), 1813–1859 (2004).
    [CrossRef] [PubMed]
  7. Y. Silberberg, “Quantum coherent control for nonlinear spectroscopy and microscopy,” Annu. Rev. Phys. Chem. 60(1), 277–292 (2009) (and references therein).
    [CrossRef]
  8. P. Nuernberger, G. Vogt, T. Brixner, and G. Gerber, “Femtosecond quantum control of molecular dynamics in the condensed phase,” Phys. Chem. Chem. Phys. 9(20), 2470–2497 (2007) (and references therein).
    [CrossRef] [PubMed]
  9. Y. Silberberg and D. Meshulach, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396(6708), 239–242 (1998).
    [CrossRef]
  10. D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60(2), 1287–1292 (1999).
    [CrossRef]
  11. N. Dudovich, B. Dayan, Y. Silberberg, and S. M. G. Faeder, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86(1), 47–50 (2001).
    [CrossRef] [PubMed]
  12. N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
    [CrossRef] [PubMed]
  13. H. U. Stauffer, J. B. Ballard, Z. Amitay, and S. R. Leone, “Simultaneous phase control of Li2 wave packets in two electronic states,” J. Chem. Phys. 116(3), 946 (2002).
    [CrossRef]
  14. B. Chatel, J. Degert, S. Stock, and B. Girard, “Competition between sequential and direct paths in a two-photon transition,” Phys. Rev. A 68(4), 041402 (2003).
    [CrossRef]
  15. B. Chatel, J. Degert, and B. Girard, “Role of quadratic and cubic spectral phases in ladder climbing with ultrashort pulses,” Phys. Rev. A 70(5), 053414 (2004).
    [CrossRef]
  16. A. Präkelt, M. Wollenhaupt, C. Sarpe-Tudoran, and T. Baumert, “Phase control of a two-photon transition with shaped femtosecond laser-pulse sequences,” Phys. Rev. A 70(6), 063407 (2004).
    [CrossRef]
  17. S. H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72(4), 041803 (2005).
    [CrossRef]
  18. X. Dai, E. W. Lerch, and S. R. Leone, “Coherent control through near-resonant Raman transitions,” Phys. Rev. A 73(2), 023404 (2006).
    [CrossRef]
  19. B. von Vacano and M. Motzkus, “Time-resolving molecular vibration for microanalytics: single laser beam nonlinear Raman spectroscopy in simulation and experiment,” Phys. Chem. Chem. Phys. 10(5), 681–691 (2008).
    [CrossRef] [PubMed]
  20. A. Gandman, L. Chuntonov, L. Rybak, and Z. Amitay, “Coherent phase control of resonance-mediated (2 + 1) three-photon absorption,” Phys. Rev. A 75(3), 031401 (2007).
    [CrossRef]
  21. L. Chuntonov, L. Rybak, A. Gandman, and Z. Amitay, “Enhancement of intermediate-field two-photon absorption by rationally shaped femtosecond pulses,” Phys. Rev. A 77(2), 021403 (2008).
    [CrossRef]
  22. L. Chuntonov, L. Rybak, A. Gandman, and Z. Amitay, “Frequency-domain coherent control of femtosecond two-photon absorption: intermediate-field versus weak-field regime,” J. Phys. At. Mol. Opt. Phys. 41(3), 035504 (2008).
    [CrossRef]
  23. Z. Amitay, A. Gandman, L. Chuntonov, and L. Rybak, “Multichannel selective femtosecond coherent control based on symmetry properties,” Phys. Rev. Lett. 100(19), 193002 (2008).
    [CrossRef] [PubMed]
  24. L. Rybak, L. Chuntonov, A. Gandman, N. Shakour, and Z. Amitay, “NIR femtosecond phase control of resonance-mediated generation of coherent UV radiation,” Opt. Express 16(26), 21738–21745 (2008).
    [CrossRef] [PubMed]
  25. N. T. Form, B. J. Whitaker, and C. Meier, “Enhancing the probability of three-photon absorption in iodine through pulse shaping,” J. Phys. B 41(7), 074011 (2008).
    [CrossRef]
  26. N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, “Simple route to strong-field coherent control,” Phys. Rev. Lett. 94(8), 083002 (2005).
    [CrossRef] [PubMed]
  27. M. Wollenhaupt, A. Präkelt, C. Sarpe-Tudoran, D. Liese, T. Bayer, and T. Baumert, “Femtosecond strong-field quantum control with sinusoidally phase-modulated pulses,” Phys. Rev. A 73(6), 063409 (2006).
    [CrossRef]
  28. C. Trallero-Herrero, J. L. Cohen, and T. Weinacht, “Strong-field atomic phase matching,” Phys. Rev. Lett. 96(6), 063603 (2006).
    [CrossRef] [PubMed]
  29. S. D. Clow, C. Trallero-Herrero, T. Bergeman, and T. Weinacht, “Strong field multiphoton inversion of a three-level system using shaped ultrafast laser pulses,” Phys. Rev. Lett. 100(23), 233603 (2008).
    [CrossRef] [PubMed]
  30. A. Lindinger, C. Lupulescu, M. Plewicki, F. Vetter, A. Merli, S. M. Weber, and L. Wöste, “Isotope selective ionization by optimal control using shaped femtosecond laser pulses,” Phys. Rev. Lett. 93(3), 033001 (2004).
    [CrossRef] [PubMed]
  31. W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
    [CrossRef]
  32. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929 (2000).
    [CrossRef]
  33. T. Brixner and G. Gerber, “Femtosecond polarization pulse shaping,” Opt. Lett. 26(8), 557–559 (2001).
    [CrossRef]
  34. M. Wollenhaupt, A. Assion, and T. Baumert, “Femtosecond laser pulses: linear properties, manipulation, generation and measurement”, Handbook of Lasers and Optics, ed. F. Träger, p. 937 (Springer, New York, 2007).
  35. P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” N. J. Phys. 6, 39 (2004).
    [CrossRef]
  36. E. Matsubara, K. Yamane, T. Sekikawa, and M. Yamashita, “Generation of 2.6 fs optical pulses using induced-phase modulation in a gas-filled hollow fiber,” J. Opt. Soc. Am. B 24(4), 985 (2007).
    [CrossRef]
  37. S. Akturk, C. D'Amico, and A. Mysyrowicz, “Measuring ultrashort pulses in the single-cycle regime using frequency-resolved optical gating,” J. Opt. Soc. Am. B 25(6), A63 (2008).
    [CrossRef]
  38. S. Rausch, T. Binhammer, A. Harth, J. Kim, R. Ell, F. X. Kärtner, and U. Morgner, “Controlled waveforms on the single-cycle scale from a femtosecond oscillator,” Opt. Express 16(13), 9739–9745 (2008).
    [CrossRef] [PubMed]
  39. A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
    [CrossRef]
  40. B. Xu, Y. Coello, V. V. Lozovoy, D. A. Harris, and M. Dantus, “Pulse shaping of octave spanning femtosecond laser pulses,” Opt. Express 14(22), 10939–10944 (2006).
    [CrossRef] [PubMed]
  41. B. von Vacano, W. Wohlleben, and M. Motzkus, “Actively shaped supercontinuum from a photonic crystal fiber for nonlinear coherent microspectroscopy,” Opt. Lett. 31(3), 413–415 (2006).
    [CrossRef] [PubMed]
  42. T. Nakajima and S. Watanabe, “Phase-dependent excitation and ionization in the multiphoton ionization regime,” Opt. Lett. 31(12), 1920–1922 (2006).
    [CrossRef] [PubMed]
  43. T. Nakajima and S. Watanabe, “Effects of the carrier-envelope phase in the multiphoton ionization regime,” Phys. Rev. Lett. 96(21), 213001 (2006).
    [CrossRef] [PubMed]
  44. A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92(7), 073902 (2004).
    [CrossRef] [PubMed]
  45. A. J. Verhoef, A. Fernández, M. Lezius, K. O’Keeffe, M. Uiberacker, and F. Krausz, “Few-cycle carrier envelope phase-dependent stereo detection of electrons,” Opt. Lett. 31(23), 3520–3522 (2006).
    [CrossRef] [PubMed]
  46. Y. Wu and X. Yang, “Carrier-envelope phase-dependent atomic coherence and quantum beats,” Phys. Rev. A 76(1), 013832 (2007).
    [CrossRef]
  47. S. Chelkowski and A. D. Bandrauk, “Sensitivity of spatial photoelectron distributions to the absolute phase of an ultrashort intense laser pulse,” Phys. Rev. A 65(6), 061802 (2002).
    [CrossRef]
  48. M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasovic, T. Uphues, D. B. Milosevic, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” N. J. Phys. 10(2), 025024 (2008).
    [CrossRef]
  49. M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. At. Mol. Opt. Phys. 42(7), 075601 (2009).
    [CrossRef]
  50. N. I. S. T. Atomic Spectra Database, (NIST, Gaithersburg, MD) available at http://physics.nist.gov/asd .
  51. S. A. Blundell, W. R. Johnson, and J. Sapirstein, “Relativistic all-order calculations of energies and matrix elements in cesium,” Phys. Rev. A 43(7), 3407–3418 (1991).
    [CrossRef] [PubMed]
  52. M. S. Safronova, W. R. Johnson, and A. Derevianko, “Relativistic many-body calculations of energy levels, hyperfine constants, electric-dipole matrix elements, and static polarizabilities for alkali-metal atoms,” Phys. Rev. A 60(6), 4476–4487 (1999).
    [CrossRef]
  53. M. S. Safronova and C. W. Clark, “Inconsistencies between lifetime and polarizability measurements in Cs,” Phys. Rev. A 69(4), 040501 (2004).
    [CrossRef]

2009 (2)

Y. Silberberg, “Quantum coherent control for nonlinear spectroscopy and microscopy,” Annu. Rev. Phys. Chem. 60(1), 277–292 (2009) (and references therein).
[CrossRef]

M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. At. Mol. Opt. Phys. 42(7), 075601 (2009).
[CrossRef]

2008 (10)

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasovic, T. Uphues, D. B. Milosevic, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” N. J. Phys. 10(2), 025024 (2008).
[CrossRef]

S. D. Clow, C. Trallero-Herrero, T. Bergeman, and T. Weinacht, “Strong field multiphoton inversion of a three-level system using shaped ultrafast laser pulses,” Phys. Rev. Lett. 100(23), 233603 (2008).
[CrossRef] [PubMed]

L. Chuntonov, L. Rybak, A. Gandman, and Z. Amitay, “Enhancement of intermediate-field two-photon absorption by rationally shaped femtosecond pulses,” Phys. Rev. A 77(2), 021403 (2008).
[CrossRef]

L. Chuntonov, L. Rybak, A. Gandman, and Z. Amitay, “Frequency-domain coherent control of femtosecond two-photon absorption: intermediate-field versus weak-field regime,” J. Phys. At. Mol. Opt. Phys. 41(3), 035504 (2008).
[CrossRef]

Z. Amitay, A. Gandman, L. Chuntonov, and L. Rybak, “Multichannel selective femtosecond coherent control based on symmetry properties,” Phys. Rev. Lett. 100(19), 193002 (2008).
[CrossRef] [PubMed]

L. Rybak, L. Chuntonov, A. Gandman, N. Shakour, and Z. Amitay, “NIR femtosecond phase control of resonance-mediated generation of coherent UV radiation,” Opt. Express 16(26), 21738–21745 (2008).
[CrossRef] [PubMed]

N. T. Form, B. J. Whitaker, and C. Meier, “Enhancing the probability of three-photon absorption in iodine through pulse shaping,” J. Phys. B 41(7), 074011 (2008).
[CrossRef]

B. von Vacano and M. Motzkus, “Time-resolving molecular vibration for microanalytics: single laser beam nonlinear Raman spectroscopy in simulation and experiment,” Phys. Chem. Chem. Phys. 10(5), 681–691 (2008).
[CrossRef] [PubMed]

S. Akturk, C. D'Amico, and A. Mysyrowicz, “Measuring ultrashort pulses in the single-cycle regime using frequency-resolved optical gating,” J. Opt. Soc. Am. B 25(6), A63 (2008).
[CrossRef]

S. Rausch, T. Binhammer, A. Harth, J. Kim, R. Ell, F. X. Kärtner, and U. Morgner, “Controlled waveforms on the single-cycle scale from a femtosecond oscillator,” Opt. Express 16(13), 9739–9745 (2008).
[CrossRef] [PubMed]

2007 (5)

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

A. Gandman, L. Chuntonov, L. Rybak, and Z. Amitay, “Coherent phase control of resonance-mediated (2 + 1) three-photon absorption,” Phys. Rev. A 75(3), 031401 (2007).
[CrossRef]

P. Nuernberger, G. Vogt, T. Brixner, and G. Gerber, “Femtosecond quantum control of molecular dynamics in the condensed phase,” Phys. Chem. Chem. Phys. 9(20), 2470–2497 (2007) (and references therein).
[CrossRef] [PubMed]

E. Matsubara, K. Yamane, T. Sekikawa, and M. Yamashita, “Generation of 2.6 fs optical pulses using induced-phase modulation in a gas-filled hollow fiber,” J. Opt. Soc. Am. B 24(4), 985 (2007).
[CrossRef]

Y. Wu and X. Yang, “Carrier-envelope phase-dependent atomic coherence and quantum beats,” Phys. Rev. A 76(1), 013832 (2007).
[CrossRef]

2006 (9)

A. J. Verhoef, A. Fernández, M. Lezius, K. O’Keeffe, M. Uiberacker, and F. Krausz, “Few-cycle carrier envelope phase-dependent stereo detection of electrons,” Opt. Lett. 31(23), 3520–3522 (2006).
[CrossRef] [PubMed]

W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
[CrossRef]

X. Dai, E. W. Lerch, and S. R. Leone, “Coherent control through near-resonant Raman transitions,” Phys. Rev. A 73(2), 023404 (2006).
[CrossRef]

M. Wollenhaupt, A. Präkelt, C. Sarpe-Tudoran, D. Liese, T. Bayer, and T. Baumert, “Femtosecond strong-field quantum control with sinusoidally phase-modulated pulses,” Phys. Rev. A 73(6), 063409 (2006).
[CrossRef]

C. Trallero-Herrero, J. L. Cohen, and T. Weinacht, “Strong-field atomic phase matching,” Phys. Rev. Lett. 96(6), 063603 (2006).
[CrossRef] [PubMed]

B. Xu, Y. Coello, V. V. Lozovoy, D. A. Harris, and M. Dantus, “Pulse shaping of octave spanning femtosecond laser pulses,” Opt. Express 14(22), 10939–10944 (2006).
[CrossRef] [PubMed]

B. von Vacano, W. Wohlleben, and M. Motzkus, “Actively shaped supercontinuum from a photonic crystal fiber for nonlinear coherent microspectroscopy,” Opt. Lett. 31(3), 413–415 (2006).
[CrossRef] [PubMed]

T. Nakajima and S. Watanabe, “Phase-dependent excitation and ionization in the multiphoton ionization regime,” Opt. Lett. 31(12), 1920–1922 (2006).
[CrossRef] [PubMed]

T. Nakajima and S. Watanabe, “Effects of the carrier-envelope phase in the multiphoton ionization regime,” Phys. Rev. Lett. 96(21), 213001 (2006).
[CrossRef] [PubMed]

2005 (2)

N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, “Simple route to strong-field coherent control,” Phys. Rev. Lett. 94(8), 083002 (2005).
[CrossRef] [PubMed]

S. H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72(4), 041803 (2005).
[CrossRef]

2004 (7)

B. Chatel, J. Degert, and B. Girard, “Role of quadratic and cubic spectral phases in ladder climbing with ultrashort pulses,” Phys. Rev. A 70(5), 053414 (2004).
[CrossRef]

A. Präkelt, M. Wollenhaupt, C. Sarpe-Tudoran, and T. Baumert, “Phase control of a two-photon transition with shaped femtosecond laser-pulse sequences,” Phys. Rev. A 70(6), 063407 (2004).
[CrossRef]

M. Dantus and V. V. Lozovoy, “Experimental coherent laser control of physicochemical processes,” Chem. Rev. 104(4), 1813–1859 (2004).
[CrossRef] [PubMed]

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92(7), 073902 (2004).
[CrossRef] [PubMed]

A. Lindinger, C. Lupulescu, M. Plewicki, F. Vetter, A. Merli, S. M. Weber, and L. Wöste, “Isotope selective ionization by optimal control using shaped femtosecond laser pulses,” Phys. Rev. Lett. 93(3), 033001 (2004).
[CrossRef] [PubMed]

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” N. J. Phys. 6, 39 (2004).
[CrossRef]

M. S. Safronova and C. W. Clark, “Inconsistencies between lifetime and polarizability measurements in Cs,” Phys. Rev. A 69(4), 040501 (2004).
[CrossRef]

2003 (1)

B. Chatel, J. Degert, S. Stock, and B. Girard, “Competition between sequential and direct paths in a two-photon transition,” Phys. Rev. A 68(4), 041402 (2003).
[CrossRef]

2002 (3)

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

H. U. Stauffer, J. B. Ballard, Z. Amitay, and S. R. Leone, “Simultaneous phase control of Li2 wave packets in two electronic states,” J. Chem. Phys. 116(3), 946 (2002).
[CrossRef]

S. Chelkowski and A. D. Bandrauk, “Sensitivity of spatial photoelectron distributions to the absolute phase of an ultrashort intense laser pulse,” Phys. Rev. A 65(6), 061802 (2002).
[CrossRef]

2001 (2)

T. Brixner and G. Gerber, “Femtosecond polarization pulse shaping,” Opt. Lett. 26(8), 557–559 (2001).
[CrossRef]

N. Dudovich, B. Dayan, Y. Silberberg, and S. M. G. Faeder, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86(1), 47–50 (2001).
[CrossRef] [PubMed]

2000 (2)

H. Rabitz, M. Motzkus, K. Kompa, and R. de. Vivie-Riedle, “Whither the future of controlling quantum phenomena?” Science 288(5467), 824–828 (2000).
[CrossRef] [PubMed]

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929 (2000).
[CrossRef]

1999 (2)

M. S. Safronova, W. R. Johnson, and A. Derevianko, “Relativistic many-body calculations of energy levels, hyperfine constants, electric-dipole matrix elements, and static polarizabilities for alkali-metal atoms,” Phys. Rev. A 60(6), 4476–4487 (1999).
[CrossRef]

D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60(2), 1287–1292 (1999).
[CrossRef]

1998 (1)

Y. Silberberg and D. Meshulach, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396(6708), 239–242 (1998).
[CrossRef]

1997 (1)

R. J. Gordon and S. A. Rice, “Active control of the dynamics of atoms and molecules,” Annu. Rev. Phys. Chem. 48(1), 601–641 (1997).
[CrossRef] [PubMed]

1993 (1)

W. S. Warren, H. Rabitz, and D. Mahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259(5101), 1581–1589 (1993).
[CrossRef] [PubMed]

1991 (1)

S. A. Blundell, W. R. Johnson, and J. Sapirstein, “Relativistic all-order calculations of energies and matrix elements in cesium,” Phys. Rev. A 43(7), 3407–3418 (1991).
[CrossRef] [PubMed]

1986 (1)

D. J. Tannor, R. Kosloff, and S. A. Rice, “Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations,” J. Chem. Phys. 85(10), 5805 (1986).
[CrossRef]

Abel, M. J.

M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. At. Mol. Opt. Phys. 42(7), 075601 (2009).
[CrossRef]

Akturk, S.

Amitay, Z.

L. Chuntonov, L. Rybak, A. Gandman, and Z. Amitay, “Enhancement of intermediate-field two-photon absorption by rationally shaped femtosecond pulses,” Phys. Rev. A 77(2), 021403 (2008).
[CrossRef]

L. Chuntonov, L. Rybak, A. Gandman, and Z. Amitay, “Frequency-domain coherent control of femtosecond two-photon absorption: intermediate-field versus weak-field regime,” J. Phys. At. Mol. Opt. Phys. 41(3), 035504 (2008).
[CrossRef]

Z. Amitay, A. Gandman, L. Chuntonov, and L. Rybak, “Multichannel selective femtosecond coherent control based on symmetry properties,” Phys. Rev. Lett. 100(19), 193002 (2008).
[CrossRef] [PubMed]

L. Rybak, L. Chuntonov, A. Gandman, N. Shakour, and Z. Amitay, “NIR femtosecond phase control of resonance-mediated generation of coherent UV radiation,” Opt. Express 16(26), 21738–21745 (2008).
[CrossRef] [PubMed]

A. Gandman, L. Chuntonov, L. Rybak, and Z. Amitay, “Coherent phase control of resonance-mediated (2 + 1) three-photon absorption,” Phys. Rev. A 75(3), 031401 (2007).
[CrossRef]

H. U. Stauffer, J. B. Ballard, Z. Amitay, and S. R. Leone, “Simultaneous phase control of Li2 wave packets in two electronic states,” J. Chem. Phys. 116(3), 946 (2002).
[CrossRef]

Apolonski, A.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92(7), 073902 (2004).
[CrossRef] [PubMed]

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” N. J. Phys. 6, 39 (2004).
[CrossRef]

Ballard, J. B.

H. U. Stauffer, J. B. Ballard, Z. Amitay, and S. R. Leone, “Simultaneous phase control of Li2 wave packets in two electronic states,” J. Chem. Phys. 116(3), 946 (2002).
[CrossRef]

Bandrauk, A. D.

S. Chelkowski and A. D. Bandrauk, “Sensitivity of spatial photoelectron distributions to the absolute phase of an ultrashort intense laser pulse,” Phys. Rev. A 65(6), 061802 (2002).
[CrossRef]

Baumert, T.

M. Wollenhaupt, A. Präkelt, C. Sarpe-Tudoran, D. Liese, T. Bayer, and T. Baumert, “Femtosecond strong-field quantum control with sinusoidally phase-modulated pulses,” Phys. Rev. A 73(6), 063409 (2006).
[CrossRef]

A. Präkelt, M. Wollenhaupt, C. Sarpe-Tudoran, and T. Baumert, “Phase control of a two-photon transition with shaped femtosecond laser-pulse sequences,” Phys. Rev. A 70(6), 063407 (2004).
[CrossRef]

Bayer, T.

M. Wollenhaupt, A. Präkelt, C. Sarpe-Tudoran, D. Liese, T. Bayer, and T. Baumert, “Femtosecond strong-field quantum control with sinusoidally phase-modulated pulses,” Phys. Rev. A 73(6), 063409 (2006).
[CrossRef]

Bell, M. J.

M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. At. Mol. Opt. Phys. 42(7), 075601 (2009).
[CrossRef]

Bergeman, T.

S. D. Clow, C. Trallero-Herrero, T. Bergeman, and T. Weinacht, “Strong field multiphoton inversion of a three-level system using shaped ultrafast laser pulses,” Phys. Rev. Lett. 100(23), 233603 (2008).
[CrossRef] [PubMed]

Binhammer, T.

Blundell, S. A.

S. A. Blundell, W. R. Johnson, and J. Sapirstein, “Relativistic all-order calculations of energies and matrix elements in cesium,” Phys. Rev. A 43(7), 3407–3418 (1991).
[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(20), 2470–2497 (2007) (and references therein).
[CrossRef] [PubMed]

T. Brixner and G. Gerber, “Femtosecond polarization pulse shaping,” Opt. Lett. 26(8), 557–559 (2001).
[CrossRef]

Burgdörfer, J.

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” N. J. Phys. 6, 39 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92(7), 073902 (2004).
[CrossRef] [PubMed]

Caster, A. G.

S. H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72(4), 041803 (2005).
[CrossRef]

Cavalieri, A. L.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

Chatel, B.

B. Chatel, J. Degert, and B. Girard, “Role of quadratic and cubic spectral phases in ladder climbing with ultrashort pulses,” Phys. Rev. A 70(5), 053414 (2004).
[CrossRef]

B. Chatel, J. Degert, S. Stock, and B. Girard, “Competition between sequential and direct paths in a two-photon transition,” Phys. Rev. A 68(4), 041402 (2003).
[CrossRef]

Chelkowski, S.

S. Chelkowski and A. D. Bandrauk, “Sensitivity of spatial photoelectron distributions to the absolute phase of an ultrashort intense laser pulse,” Phys. Rev. A 65(6), 061802 (2002).
[CrossRef]

Chuntonov, L.

L. Chuntonov, L. Rybak, A. Gandman, and Z. Amitay, “Enhancement of intermediate-field two-photon absorption by rationally shaped femtosecond pulses,” Phys. Rev. A 77(2), 021403 (2008).
[CrossRef]

L. Chuntonov, L. Rybak, A. Gandman, and Z. Amitay, “Frequency-domain coherent control of femtosecond two-photon absorption: intermediate-field versus weak-field regime,” J. Phys. At. Mol. Opt. Phys. 41(3), 035504 (2008).
[CrossRef]

L. Rybak, L. Chuntonov, A. Gandman, N. Shakour, and Z. Amitay, “NIR femtosecond phase control of resonance-mediated generation of coherent UV radiation,” Opt. Express 16(26), 21738–21745 (2008).
[CrossRef] [PubMed]

Z. Amitay, A. Gandman, L. Chuntonov, and L. Rybak, “Multichannel selective femtosecond coherent control based on symmetry properties,” Phys. Rev. Lett. 100(19), 193002 (2008).
[CrossRef] [PubMed]

A. Gandman, L. Chuntonov, L. Rybak, and Z. Amitay, “Coherent phase control of resonance-mediated (2 + 1) three-photon absorption,” Phys. Rev. A 75(3), 031401 (2007).
[CrossRef]

Clark, C. W.

M. S. Safronova and C. W. Clark, “Inconsistencies between lifetime and polarizability measurements in Cs,” Phys. Rev. A 69(4), 040501 (2004).
[CrossRef]

Clow, S. D.

S. D. Clow, C. Trallero-Herrero, T. Bergeman, and T. Weinacht, “Strong field multiphoton inversion of a three-level system using shaped ultrafast laser pulses,” Phys. Rev. Lett. 100(23), 233603 (2008).
[CrossRef] [PubMed]

Coello, Y.

Cohen, J. L.

C. Trallero-Herrero, J. L. Cohen, and T. Weinacht, “Strong-field atomic phase matching,” Phys. Rev. Lett. 96(6), 063603 (2006).
[CrossRef] [PubMed]

Dai, X.

X. Dai, E. W. Lerch, and S. R. Leone, “Coherent control through near-resonant Raman transitions,” Phys. Rev. A 73(2), 023404 (2006).
[CrossRef]

D'Amico, C.

Dantus, M.

B. Xu, Y. Coello, V. V. Lozovoy, D. A. Harris, and M. Dantus, “Pulse shaping of octave spanning femtosecond laser pulses,” Opt. Express 14(22), 10939–10944 (2006).
[CrossRef] [PubMed]

M. Dantus and V. V. Lozovoy, “Experimental coherent laser control of physicochemical processes,” Chem. Rev. 104(4), 1813–1859 (2004).
[CrossRef] [PubMed]

Dayan, B.

N. Dudovich, B. Dayan, Y. Silberberg, and S. M. G. Faeder, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86(1), 47–50 (2001).
[CrossRef] [PubMed]

Degert, J.

B. Chatel, J. Degert, and B. Girard, “Role of quadratic and cubic spectral phases in ladder climbing with ultrashort pulses,” Phys. Rev. A 70(5), 053414 (2004).
[CrossRef]

B. Chatel, J. Degert, S. Stock, and B. Girard, “Competition between sequential and direct paths in a two-photon transition,” Phys. Rev. A 68(4), 041402 (2003).
[CrossRef]

Derevianko, A.

M. S. Safronova, W. R. Johnson, and A. Derevianko, “Relativistic many-body calculations of energy levels, hyperfine constants, electric-dipole matrix elements, and static polarizabilities for alkali-metal atoms,” Phys. Rev. A 60(6), 4476–4487 (1999).
[CrossRef]

Dombi, P.

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92(7), 073902 (2004).
[CrossRef] [PubMed]

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” N. J. Phys. 6, 39 (2004).
[CrossRef]

Dudovich, N.

N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, “Simple route to strong-field coherent control,” Phys. Rev. Lett. 94(8), 083002 (2005).
[CrossRef] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

N. Dudovich, B. Dayan, Y. Silberberg, and S. M. G. Faeder, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86(1), 47–50 (2001).
[CrossRef] [PubMed]

Ell, R.

Esparza, A. M.

W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
[CrossRef]

Faeder, S. M. G.

N. Dudovich, B. Dayan, Y. Silberberg, and S. M. G. Faeder, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86(1), 47–50 (2001).
[CrossRef] [PubMed]

Fernández, A.

Fieß, M.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

Form, N. T.

N. T. Form, B. J. Whitaker, and C. Meier, “Enhancing the probability of three-photon absorption in iodine through pulse shaping,” J. Phys. B 41(7), 074011 (2008).
[CrossRef]

Gandman, A.

L. Rybak, L. Chuntonov, A. Gandman, N. Shakour, and Z. Amitay, “NIR femtosecond phase control of resonance-mediated generation of coherent UV radiation,” Opt. Express 16(26), 21738–21745 (2008).
[CrossRef] [PubMed]

Z. Amitay, A. Gandman, L. Chuntonov, and L. Rybak, “Multichannel selective femtosecond coherent control based on symmetry properties,” Phys. Rev. Lett. 100(19), 193002 (2008).
[CrossRef] [PubMed]

L. Chuntonov, L. Rybak, A. Gandman, and Z. Amitay, “Enhancement of intermediate-field two-photon absorption by rationally shaped femtosecond pulses,” Phys. Rev. A 77(2), 021403 (2008).
[CrossRef]

L. Chuntonov, L. Rybak, A. Gandman, and Z. Amitay, “Frequency-domain coherent control of femtosecond two-photon absorption: intermediate-field versus weak-field regime,” J. Phys. At. Mol. Opt. Phys. 41(3), 035504 (2008).
[CrossRef]

A. Gandman, L. Chuntonov, L. Rybak, and Z. Amitay, “Coherent phase control of resonance-mediated (2 + 1) three-photon absorption,” Phys. Rev. A 75(3), 031401 (2007).
[CrossRef]

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(20), 2470–2497 (2007) (and references therein).
[CrossRef] [PubMed]

T. Brixner and G. Gerber, “Femtosecond polarization pulse shaping,” Opt. Lett. 26(8), 557–559 (2001).
[CrossRef]

Girard, B.

B. Chatel, J. Degert, and B. Girard, “Role of quadratic and cubic spectral phases in ladder climbing with ultrashort pulses,” Phys. Rev. A 70(5), 053414 (2004).
[CrossRef]

B. Chatel, J. Degert, S. Stock, and B. Girard, “Competition between sequential and direct paths in a two-photon transition,” Phys. Rev. A 68(4), 041402 (2003).
[CrossRef]

Gordon, R. J.

R. J. Gordon and S. A. Rice, “Active control of the dynamics of atoms and molecules,” Annu. Rev. Phys. Chem. 48(1), 601–641 (1997).
[CrossRef] [PubMed]

Goulielmakis, E.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

Hänsch, T. W.

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” N. J. Phys. 6, 39 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92(7), 073902 (2004).
[CrossRef] [PubMed]

Harris, D. A.

Harth, A.

Hasovic, E.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasovic, T. Uphues, D. B. Milosevic, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” N. J. Phys. 10(2), 025024 (2008).
[CrossRef]

Helml, W.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

Holzwarth, R.

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” N. J. Phys. 6, 39 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92(7), 073902 (2004).
[CrossRef] [PubMed]

Horvath, B.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

Johnson, W. R.

M. S. Safronova, W. R. Johnson, and A. Derevianko, “Relativistic many-body calculations of energy levels, hyperfine constants, electric-dipole matrix elements, and static polarizabilities for alkali-metal atoms,” Phys. Rev. A 60(6), 4476–4487 (1999).
[CrossRef]

S. A. Blundell, W. R. Johnson, and J. Sapirstein, “Relativistic all-order calculations of energies and matrix elements in cesium,” Phys. Rev. A 43(7), 3407–3418 (1991).
[CrossRef] [PubMed]

Jullien, A.

M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. At. Mol. Opt. Phys. 42(7), 075601 (2009).
[CrossRef]

Kakehata, M.

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92(7), 073902 (2004).
[CrossRef] [PubMed]

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” N. J. Phys. 6, 39 (2004).
[CrossRef]

Kärtner, F. X.

Kienberger, R.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

Kim, J.

Kling, M. F.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasovic, T. Uphues, D. B. Milosevic, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” N. J. Phys. 10(2), 025024 (2008).
[CrossRef]

Kompa, K.

H. Rabitz, M. Motzkus, K. Kompa, and R. de. Vivie-Riedle, “Whither the future of controlling quantum phenomena?” Science 288(5467), 824–828 (2000).
[CrossRef] [PubMed]

Kosloff, R.

D. J. Tannor, R. Kosloff, and S. A. Rice, “Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations,” J. Chem. Phys. 85(10), 5805 (1986).
[CrossRef]

Krausz, F.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

A. J. Verhoef, A. Fernández, M. Lezius, K. O’Keeffe, M. Uiberacker, and F. Krausz, “Few-cycle carrier envelope phase-dependent stereo detection of electrons,” Opt. Lett. 31(23), 3520–3522 (2006).
[CrossRef] [PubMed]

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92(7), 073902 (2004).
[CrossRef] [PubMed]

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” N. J. Phys. 6, 39 (2004).
[CrossRef]

Lemell, Ch.

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” N. J. Phys. 6, 39 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92(7), 073902 (2004).
[CrossRef] [PubMed]

Leone, S. R.

M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. At. Mol. Opt. Phys. 42(7), 075601 (2009).
[CrossRef]

X. Dai, E. W. Lerch, and S. R. Leone, “Coherent control through near-resonant Raman transitions,” Phys. Rev. A 73(2), 023404 (2006).
[CrossRef]

S. H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72(4), 041803 (2005).
[CrossRef]

H. U. Stauffer, J. B. Ballard, Z. Amitay, and S. R. Leone, “Simultaneous phase control of Li2 wave packets in two electronic states,” J. Chem. Phys. 116(3), 946 (2002).
[CrossRef]

Lerch, E. W.

X. Dai, E. W. Lerch, and S. R. Leone, “Coherent control through near-resonant Raman transitions,” Phys. Rev. A 73(2), 023404 (2006).
[CrossRef]

Lezius, M.

Liese, D.

M. Wollenhaupt, A. Präkelt, C. Sarpe-Tudoran, D. Liese, T. Bayer, and T. Baumert, “Femtosecond strong-field quantum control with sinusoidally phase-modulated pulses,” Phys. Rev. A 73(6), 063409 (2006).
[CrossRef]

Lim, S. H.

S. H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72(4), 041803 (2005).
[CrossRef]

Lindinger, A.

W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
[CrossRef]

A. Lindinger, C. Lupulescu, M. Plewicki, F. Vetter, A. Merli, S. M. Weber, and L. Wöste, “Isotope selective ionization by optimal control using shaped femtosecond laser pulses,” Phys. Rev. Lett. 93(3), 033001 (2004).
[CrossRef] [PubMed]

Lozovoy, V. V.

B. Xu, Y. Coello, V. V. Lozovoy, D. A. Harris, and M. Dantus, “Pulse shaping of octave spanning femtosecond laser pulses,” Opt. Express 14(22), 10939–10944 (2006).
[CrossRef] [PubMed]

M. Dantus and V. V. Lozovoy, “Experimental coherent laser control of physicochemical processes,” Chem. Rev. 104(4), 1813–1859 (2004).
[CrossRef] [PubMed]

Lupulescu, C.

A. Lindinger, C. Lupulescu, M. Plewicki, F. Vetter, A. Merli, S. M. Weber, and L. Wöste, “Isotope selective ionization by optimal control using shaped femtosecond laser pulses,” Phys. Rev. Lett. 93(3), 033001 (2004).
[CrossRef] [PubMed]

Mahleh, D.

W. S. Warren, H. Rabitz, and D. Mahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259(5101), 1581–1589 (1993).
[CrossRef] [PubMed]

Matsubara, E.

Meier, C.

N. T. Form, B. J. Whitaker, and C. Meier, “Enhancing the probability of three-photon absorption in iodine through pulse shaping,” J. Phys. B 41(7), 074011 (2008).
[CrossRef]

Merli, A.

W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
[CrossRef]

A. Lindinger, C. Lupulescu, M. Plewicki, F. Vetter, A. Merli, S. M. Weber, and L. Wöste, “Isotope selective ionization by optimal control using shaped femtosecond laser pulses,” Phys. Rev. Lett. 93(3), 033001 (2004).
[CrossRef] [PubMed]

Meshulach, D.

D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60(2), 1287–1292 (1999).
[CrossRef]

Y. Silberberg and D. Meshulach, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396(6708), 239–242 (1998).
[CrossRef]

Milosevic, D. B.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasovic, T. Uphues, D. B. Milosevic, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” N. J. Phys. 10(2), 025024 (2008).
[CrossRef]

Morgner, U.

Motzkus, M.

B. von Vacano and M. Motzkus, “Time-resolving molecular vibration for microanalytics: single laser beam nonlinear Raman spectroscopy in simulation and experiment,” Phys. Chem. Chem. Phys. 10(5), 681–691 (2008).
[CrossRef] [PubMed]

B. von Vacano, W. Wohlleben, and M. Motzkus, “Actively shaped supercontinuum from a photonic crystal fiber for nonlinear coherent microspectroscopy,” Opt. Lett. 31(3), 413–415 (2006).
[CrossRef] [PubMed]

H. Rabitz, M. Motzkus, K. Kompa, and R. de. Vivie-Riedle, “Whither the future of controlling quantum phenomena?” Science 288(5467), 824–828 (2000).
[CrossRef] [PubMed]

Muller, H. G.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasovic, T. Uphues, D. B. Milosevic, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” N. J. Phys. 10(2), 025024 (2008).
[CrossRef]

Mysyrowicz, A.

Nagel, P. M.

M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. At. Mol. Opt. Phys. 42(7), 075601 (2009).
[CrossRef]

Nakajima, T.

T. Nakajima and S. Watanabe, “Phase-dependent excitation and ionization in the multiphoton ionization regime,” Opt. Lett. 31(12), 1920–1922 (2006).
[CrossRef] [PubMed]

T. Nakajima and S. Watanabe, “Effects of the carrier-envelope phase in the multiphoton ionization regime,” Phys. Rev. Lett. 96(21), 213001 (2006).
[CrossRef] [PubMed]

Neumark, D. M.

M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. At. Mol. Opt. Phys. 42(7), 075601 (2009).
[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(20), 2470–2497 (2007) (and references therein).
[CrossRef] [PubMed]

O’Keeffe, K.

Oron, D.

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

Paulus, G. G.

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” N. J. Phys. 6, 39 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92(7), 073902 (2004).
[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(8), 083002 (2005).
[CrossRef] [PubMed]

Pervak, V.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

Pfeifer, T.

M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. At. Mol. Opt. Phys. 42(7), 075601 (2009).
[CrossRef]

Plewicki, M.

W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
[CrossRef]

A. Lindinger, C. Lupulescu, M. Plewicki, F. Vetter, A. Merli, S. M. Weber, and L. Wöste, “Isotope selective ionization by optimal control using shaped femtosecond laser pulses,” Phys. Rev. Lett. 93(3), 033001 (2004).
[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(8), 083002 (2005).
[CrossRef] [PubMed]

Poschinger, U.

W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
[CrossRef]

Präkelt, A.

M. Wollenhaupt, A. Präkelt, C. Sarpe-Tudoran, D. Liese, T. Bayer, and T. Baumert, “Femtosecond strong-field quantum control with sinusoidally phase-modulated pulses,” Phys. Rev. A 73(6), 063409 (2006).
[CrossRef]

A. Präkelt, M. Wollenhaupt, C. Sarpe-Tudoran, and T. Baumert, “Phase control of a two-photon transition with shaped femtosecond laser-pulse sequences,” Phys. Rev. A 70(6), 063407 (2004).
[CrossRef]

Rabitz, H.

H. Rabitz, M. Motzkus, K. Kompa, and R. de. Vivie-Riedle, “Whither the future of controlling quantum phenomena?” Science 288(5467), 824–828 (2000).
[CrossRef] [PubMed]

W. S. Warren, H. Rabitz, and D. Mahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259(5101), 1581–1589 (1993).
[CrossRef] [PubMed]

Rausch, S.

Rauschenberger, J.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasovic, T. Uphues, D. B. Milosevic, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” N. J. Phys. 10(2), 025024 (2008).
[CrossRef]

Rice, S. A.

R. J. Gordon and S. A. Rice, “Active control of the dynamics of atoms and molecules,” Annu. Rev. Phys. Chem. 48(1), 601–641 (1997).
[CrossRef] [PubMed]

D. J. Tannor, R. Kosloff, and S. A. Rice, “Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations,” J. Chem. Phys. 85(10), 5805 (1986).
[CrossRef]

Rybak, L.

L. Chuntonov, L. Rybak, A. Gandman, and Z. Amitay, “Frequency-domain coherent control of femtosecond two-photon absorption: intermediate-field versus weak-field regime,” J. Phys. At. Mol. Opt. Phys. 41(3), 035504 (2008).
[CrossRef]

L. Chuntonov, L. Rybak, A. Gandman, and Z. Amitay, “Enhancement of intermediate-field two-photon absorption by rationally shaped femtosecond pulses,” Phys. Rev. A 77(2), 021403 (2008).
[CrossRef]

Z. Amitay, A. Gandman, L. Chuntonov, and L. Rybak, “Multichannel selective femtosecond coherent control based on symmetry properties,” Phys. Rev. Lett. 100(19), 193002 (2008).
[CrossRef] [PubMed]

L. Rybak, L. Chuntonov, A. Gandman, N. Shakour, and Z. Amitay, “NIR femtosecond phase control of resonance-mediated generation of coherent UV radiation,” Opt. Express 16(26), 21738–21745 (2008).
[CrossRef] [PubMed]

A. Gandman, L. Chuntonov, L. Rybak, and Z. Amitay, “Coherent phase control of resonance-mediated (2 + 1) three-photon absorption,” Phys. Rev. A 75(3), 031401 (2007).
[CrossRef]

Safronova, M. S.

M. S. Safronova and C. W. Clark, “Inconsistencies between lifetime and polarizability measurements in Cs,” Phys. Rev. A 69(4), 040501 (2004).
[CrossRef]

M. S. Safronova, W. R. Johnson, and A. Derevianko, “Relativistic many-body calculations of energy levels, hyperfine constants, electric-dipole matrix elements, and static polarizabilities for alkali-metal atoms,” Phys. Rev. A 60(6), 4476–4487 (1999).
[CrossRef]

Salzmann, W.

W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
[CrossRef]

Sapirstein, J.

S. A. Blundell, W. R. Johnson, and J. Sapirstein, “Relativistic all-order calculations of energies and matrix elements in cesium,” Phys. Rev. A 43(7), 3407–3418 (1991).
[CrossRef] [PubMed]

Sarpe-Tudoran, C.

M. Wollenhaupt, A. Präkelt, C. Sarpe-Tudoran, D. Liese, T. Bayer, and T. Baumert, “Femtosecond strong-field quantum control with sinusoidally phase-modulated pulses,” Phys. Rev. A 73(6), 063409 (2006).
[CrossRef]

A. Präkelt, M. Wollenhaupt, C. Sarpe-Tudoran, and T. Baumert, “Phase control of a two-photon transition with shaped femtosecond laser-pulse sequences,” Phys. Rev. A 70(6), 063407 (2004).
[CrossRef]

Sauer, F.

W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
[CrossRef]

Schultze, M.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

Sekikawa, T.

Shakour, N.

Silberberg, Y.

Y. Silberberg, “Quantum coherent control for nonlinear spectroscopy and microscopy,” Annu. Rev. Phys. Chem. 60(1), 277–292 (2009) (and references therein).
[CrossRef]

N. Dudovich, T. Polack, A. Pe’er, and Y. Silberberg, “Simple route to strong-field coherent control,” Phys. Rev. Lett. 94(8), 083002 (2005).
[CrossRef] [PubMed]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

N. Dudovich, B. Dayan, Y. Silberberg, and S. M. G. Faeder, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86(1), 47–50 (2001).
[CrossRef] [PubMed]

D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60(2), 1287–1292 (1999).
[CrossRef]

Y. Silberberg and D. Meshulach, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396(6708), 239–242 (1998).
[CrossRef]

Stauffer, H. U.

H. U. Stauffer, J. B. Ballard, Z. Amitay, and S. R. Leone, “Simultaneous phase control of Li2 wave packets in two electronic states,” J. Chem. Phys. 116(3), 946 (2002).
[CrossRef]

Stock, S.

B. Chatel, J. Degert, S. Stock, and B. Girard, “Competition between sequential and direct paths in a two-photon transition,” Phys. Rev. A 68(4), 041402 (2003).
[CrossRef]

Tannor, D. J.

D. J. Tannor, R. Kosloff, and S. A. Rice, “Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations,” J. Chem. Phys. 85(10), 5805 (1986).
[CrossRef]

Torizuka, K.

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” N. J. Phys. 6, 39 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92(7), 073902 (2004).
[CrossRef] [PubMed]

Trallero-Herrero, C.

S. D. Clow, C. Trallero-Herrero, T. Bergeman, and T. Weinacht, “Strong field multiphoton inversion of a three-level system using shaped ultrafast laser pulses,” Phys. Rev. Lett. 100(23), 233603 (2008).
[CrossRef] [PubMed]

C. Trallero-Herrero, J. L. Cohen, and T. Weinacht, “Strong-field atomic phase matching,” Phys. Rev. Lett. 96(6), 063603 (2006).
[CrossRef] [PubMed]

Udem, Th.

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” N. J. Phys. 6, 39 (2004).
[CrossRef]

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92(7), 073902 (2004).
[CrossRef] [PubMed]

Uiberacker, M.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

A. J. Verhoef, A. Fernández, M. Lezius, K. O’Keeffe, M. Uiberacker, and F. Krausz, “Few-cycle carrier envelope phase-dependent stereo detection of electrons,” Opt. Lett. 31(23), 3520–3522 (2006).
[CrossRef] [PubMed]

Uphues, T.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasovic, T. Uphues, D. B. Milosevic, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” N. J. Phys. 10(2), 025024 (2008).
[CrossRef]

Veisz, L.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

Verhoef, A. J.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasovic, T. Uphues, D. B. Milosevic, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” N. J. Phys. 10(2), 025024 (2008).
[CrossRef]

A. J. Verhoef, A. Fernández, M. Lezius, K. O’Keeffe, M. Uiberacker, and F. Krausz, “Few-cycle carrier envelope phase-dependent stereo detection of electrons,” Opt. Lett. 31(23), 3520–3522 (2006).
[CrossRef] [PubMed]

Vetter, F.

A. Lindinger, C. Lupulescu, M. Plewicki, F. Vetter, A. Merli, S. M. Weber, and L. Wöste, “Isotope selective ionization by optimal control using shaped femtosecond laser pulses,” Phys. Rev. Lett. 93(3), 033001 (2004).
[CrossRef] [PubMed]

Vivie-Riedle, R. de.

H. Rabitz, M. Motzkus, K. Kompa, and R. de. Vivie-Riedle, “Whither the future of controlling quantum phenomena?” Science 288(5467), 824–828 (2000).
[CrossRef] [PubMed]

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(20), 2470–2497 (2007) (and references therein).
[CrossRef] [PubMed]

von Vacano, B.

B. von Vacano and M. Motzkus, “Time-resolving molecular vibration for microanalytics: single laser beam nonlinear Raman spectroscopy in simulation and experiment,” Phys. Chem. Chem. Phys. 10(5), 681–691 (2008).
[CrossRef] [PubMed]

B. von Vacano, W. Wohlleben, and M. Motzkus, “Actively shaped supercontinuum from a photonic crystal fiber for nonlinear coherent microspectroscopy,” Opt. Lett. 31(3), 413–415 (2006).
[CrossRef] [PubMed]

Vrakking, M. J. J.

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasovic, T. Uphues, D. B. Milosevic, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” N. J. Phys. 10(2), 025024 (2008).
[CrossRef]

Warren, W. S.

W. S. Warren, H. Rabitz, and D. Mahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259(5101), 1581–1589 (1993).
[CrossRef] [PubMed]

Watanabe, S.

T. Nakajima and S. Watanabe, “Phase-dependent excitation and ionization in the multiphoton ionization regime,” Opt. Lett. 31(12), 1920–1922 (2006).
[CrossRef] [PubMed]

T. Nakajima and S. Watanabe, “Effects of the carrier-envelope phase in the multiphoton ionization regime,” Phys. Rev. Lett. 96(21), 213001 (2006).
[CrossRef] [PubMed]

Weber, S. M.

W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
[CrossRef]

A. Lindinger, C. Lupulescu, M. Plewicki, F. Vetter, A. Merli, S. M. Weber, and L. Wöste, “Isotope selective ionization by optimal control using shaped femtosecond laser pulses,” Phys. Rev. Lett. 93(3), 033001 (2004).
[CrossRef] [PubMed]

Weidemüller, M.

W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
[CrossRef]

Weinacht, T.

S. D. Clow, C. Trallero-Herrero, T. Bergeman, and T. Weinacht, “Strong field multiphoton inversion of a three-level system using shaped ultrafast laser pulses,” Phys. Rev. Lett. 100(23), 233603 (2008).
[CrossRef] [PubMed]

C. Trallero-Herrero, J. L. Cohen, and T. Weinacht, “Strong-field atomic phase matching,” Phys. Rev. Lett. 96(6), 063603 (2006).
[CrossRef] [PubMed]

Weiner, A. M.

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929 (2000).
[CrossRef]

Weise, F.

W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
[CrossRef]

Wester, R.

W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
[CrossRef]

Whitaker, B. J.

N. T. Form, B. J. Whitaker, and C. Meier, “Enhancing the probability of three-photon absorption in iodine through pulse shaping,” J. Phys. B 41(7), 074011 (2008).
[CrossRef]

Wohlleben, W.

Wollenhaupt, M.

M. Wollenhaupt, A. Präkelt, C. Sarpe-Tudoran, D. Liese, T. Bayer, and T. Baumert, “Femtosecond strong-field quantum control with sinusoidally phase-modulated pulses,” Phys. Rev. A 73(6), 063409 (2006).
[CrossRef]

A. Präkelt, M. Wollenhaupt, C. Sarpe-Tudoran, and T. Baumert, “Phase control of a two-photon transition with shaped femtosecond laser-pulse sequences,” Phys. Rev. A 70(6), 063407 (2004).
[CrossRef]

Wöste, L.

W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
[CrossRef]

A. Lindinger, C. Lupulescu, M. Plewicki, F. Vetter, A. Merli, S. M. Weber, and L. Wöste, “Isotope selective ionization by optimal control using shaped femtosecond laser pulses,” Phys. Rev. Lett. 93(3), 033001 (2004).
[CrossRef] [PubMed]

Wu, Y.

Y. Wu and X. Yang, “Carrier-envelope phase-dependent atomic coherence and quantum beats,” Phys. Rev. A 76(1), 013832 (2007).
[CrossRef]

Xu, B.

Yakovlev, V. S.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

Yamane, K.

Yamashita, M.

Yang, X.

Y. Wu and X. Yang, “Carrier-envelope phase-dependent atomic coherence and quantum beats,” Phys. Rev. A 76(1), 013832 (2007).
[CrossRef]

Annu. Rev. Phys. Chem. (2)

R. J. Gordon and S. A. Rice, “Active control of the dynamics of atoms and molecules,” Annu. Rev. Phys. Chem. 48(1), 601–641 (1997).
[CrossRef] [PubMed]

Y. Silberberg, “Quantum coherent control for nonlinear spectroscopy and microscopy,” Annu. Rev. Phys. Chem. 60(1), 277–292 (2009) (and references therein).
[CrossRef]

Chem. Rev. (1)

M. Dantus and V. V. Lozovoy, “Experimental coherent laser control of physicochemical processes,” Chem. Rev. 104(4), 1813–1859 (2004).
[CrossRef] [PubMed]

J. Chem. Phys. (2)

D. J. Tannor, R. Kosloff, and S. A. Rice, “Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations,” J. Chem. Phys. 85(10), 5805 (1986).
[CrossRef]

H. U. Stauffer, J. B. Ballard, Z. Amitay, and S. R. Leone, “Simultaneous phase control of Li2 wave packets in two electronic states,” J. Chem. Phys. 116(3), 946 (2002).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. At. Mol. Opt. Phys. (2)

L. Chuntonov, L. Rybak, A. Gandman, and Z. Amitay, “Frequency-domain coherent control of femtosecond two-photon absorption: intermediate-field versus weak-field regime,” J. Phys. At. Mol. Opt. Phys. 41(3), 035504 (2008).
[CrossRef]

M. J. Abel, T. Pfeifer, A. Jullien, P. M. Nagel, M. J. Bell, D. M. Neumark, and S. R. Leone, “Carrier-envelope phase-dependent quantum interferences in multiphoton ionization,” J. Phys. At. Mol. Opt. Phys. 42(7), 075601 (2009).
[CrossRef]

J. Phys. B (1)

N. T. Form, B. J. Whitaker, and C. Meier, “Enhancing the probability of three-photon absorption in iodine through pulse shaping,” J. Phys. B 41(7), 074011 (2008).
[CrossRef]

N. J. Phys. (3)

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, “Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua,” N. J. Phys. 9(7), 242 (2007).
[CrossRef]

P. Dombi, A. Apolonski, Ch. Lemell, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Direct measurement and analysis of the carrier-envelope phase in light pulses approaching the single-cycle regime,” N. J. Phys. 6, 39 (2004).
[CrossRef]

M. F. Kling, J. Rauschenberger, A. J. Verhoef, E. Hasovic, T. Uphues, D. B. Milosevic, H. G. Muller, and M. J. J. Vrakking, “Imaging of carrier-envelope phase effects in above-threshold ionization with intense few-cycle laser fields,” N. J. Phys. 10(2), 025024 (2008).
[CrossRef]

Nature (2)

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

Y. Silberberg and D. Meshulach, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396(6708), 239–242 (1998).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Phys. Chem. Chem. Phys. (2)

B. von Vacano and M. Motzkus, “Time-resolving molecular vibration for microanalytics: single laser beam nonlinear Raman spectroscopy in simulation and experiment,” Phys. Chem. Chem. Phys. 10(5), 681–691 (2008).
[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(20), 2470–2497 (2007) (and references therein).
[CrossRef] [PubMed]

Phys. Rev. A (15)

A. Gandman, L. Chuntonov, L. Rybak, and Z. Amitay, “Coherent phase control of resonance-mediated (2 + 1) three-photon absorption,” Phys. Rev. A 75(3), 031401 (2007).
[CrossRef]

L. Chuntonov, L. Rybak, A. Gandman, and Z. Amitay, “Enhancement of intermediate-field two-photon absorption by rationally shaped femtosecond pulses,” Phys. Rev. A 77(2), 021403 (2008).
[CrossRef]

D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60(2), 1287–1292 (1999).
[CrossRef]

B. Chatel, J. Degert, S. Stock, and B. Girard, “Competition between sequential and direct paths in a two-photon transition,” Phys. Rev. A 68(4), 041402 (2003).
[CrossRef]

B. Chatel, J. Degert, and B. Girard, “Role of quadratic and cubic spectral phases in ladder climbing with ultrashort pulses,” Phys. Rev. A 70(5), 053414 (2004).
[CrossRef]

A. Präkelt, M. Wollenhaupt, C. Sarpe-Tudoran, and T. Baumert, “Phase control of a two-photon transition with shaped femtosecond laser-pulse sequences,” Phys. Rev. A 70(6), 063407 (2004).
[CrossRef]

S. H. Lim, A. G. Caster, and S. R. Leone, “Single-pulse phase-control interferometric coherent anti-Stokes Raman scattering spectroscopy,” Phys. Rev. A 72(4), 041803 (2005).
[CrossRef]

X. Dai, E. W. Lerch, and S. R. Leone, “Coherent control through near-resonant Raman transitions,” Phys. Rev. A 73(2), 023404 (2006).
[CrossRef]

W. Salzmann, U. Poschinger, R. Wester, M. Weidemüller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, A. M. Esparza, L. Wöste, and A. Lindinger, “Coherent control with shaped femtosecond laser pulses applied to ultracold molecules,” Phys. Rev. A 73(2), 023414 (2006).
[CrossRef]

M. Wollenhaupt, A. Präkelt, C. Sarpe-Tudoran, D. Liese, T. Bayer, and T. Baumert, “Femtosecond strong-field quantum control with sinusoidally phase-modulated pulses,” Phys. Rev. A 73(6), 063409 (2006).
[CrossRef]

Y. Wu and X. Yang, “Carrier-envelope phase-dependent atomic coherence and quantum beats,” Phys. Rev. A 76(1), 013832 (2007).
[CrossRef]

S. Chelkowski and A. D. Bandrauk, “Sensitivity of spatial photoelectron distributions to the absolute phase of an ultrashort intense laser pulse,” Phys. Rev. A 65(6), 061802 (2002).
[CrossRef]

S. A. Blundell, W. R. Johnson, and J. Sapirstein, “Relativistic all-order calculations of energies and matrix elements in cesium,” Phys. Rev. A 43(7), 3407–3418 (1991).
[CrossRef] [PubMed]

M. S. Safronova, W. R. Johnson, and A. Derevianko, “Relativistic many-body calculations of energy levels, hyperfine constants, electric-dipole matrix elements, and static polarizabilities for alkali-metal atoms,” Phys. Rev. A 60(6), 4476–4487 (1999).
[CrossRef]

M. S. Safronova and C. W. Clark, “Inconsistencies between lifetime and polarizability measurements in Cs,” Phys. Rev. A 69(4), 040501 (2004).
[CrossRef]

Phys. Rev. Lett. (8)

T. Nakajima and S. Watanabe, “Effects of the carrier-envelope phase in the multiphoton ionization regime,” Phys. Rev. Lett. 96(21), 213001 (2006).
[CrossRef] [PubMed]

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of light-phase-sensitive photoemission from a metal,” Phys. Rev. Lett. 92(7), 073902 (2004).
[CrossRef] [PubMed]

C. Trallero-Herrero, J. L. Cohen, and T. Weinacht, “Strong-field atomic phase matching,” Phys. Rev. Lett. 96(6), 063603 (2006).
[CrossRef] [PubMed]

S. D. Clow, C. Trallero-Herrero, T. Bergeman, and T. Weinacht, “Strong field multiphoton inversion of a three-level system using shaped ultrafast laser pulses,” Phys. Rev. Lett. 100(23), 233603 (2008).
[CrossRef] [PubMed]

A. Lindinger, C. Lupulescu, M. Plewicki, F. Vetter, A. Merli, S. M. Weber, and L. Wöste, “Isotope selective ionization by optimal control using shaped femtosecond laser pulses,” Phys. Rev. Lett. 93(3), 033001 (2004).
[CrossRef] [PubMed]

Z. Amitay, A. Gandman, L. Chuntonov, and L. Rybak, “Multichannel selective femtosecond coherent control based on symmetry properties,” Phys. Rev. Lett. 100(19), 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(8), 083002 (2005).
[CrossRef] [PubMed]

N. Dudovich, B. Dayan, Y. Silberberg, and S. M. G. Faeder, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86(1), 47–50 (2001).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929 (2000).
[CrossRef]

Science (2)

W. S. Warren, H. Rabitz, and D. Mahleh, “Coherent control of quantum dynamics: the dream is alive,” Science 259(5101), 1581–1589 (1993).
[CrossRef] [PubMed]

H. Rabitz, M. Motzkus, K. Kompa, and R. de. Vivie-Riedle, “Whither the future of controlling quantum phenomena?” Science 288(5467), 824–828 (2000).
[CrossRef] [PubMed]

Other (3)

M. Shapiro, and P. Brumer, Principles of the quantum control of molecular processes (Wiley, New Jersey, 2003).

M. Wollenhaupt, A. Assion, and T. Baumert, “Femtosecond laser pulses: linear properties, manipulation, generation and measurement”, Handbook of Lasers and Optics, ed. F. Träger, p. 937 (Springer, New York, 2007).

N. I. S. T. Atomic Spectra Database, (NIST, Gaithersburg, MD) available at http://physics.nist.gov/asd .

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

(a) Two-photon excitation scheme in the femtosecond single-cycle regime. Indicated are the two-photon absorption transitions and two-photon Raman transitions. (b) Ultrabroad spectrum of single-cycle pulse centered at Ω f g that provides two absorbed photons of frequencies around Ω f g / 2 to the two-photon absorption transitions as well as two photons, one absorbed photon of frequency around 3 Ω f g / 2 and one emitted photon of frequency around Ω f g / 2 , to Raman transitions. (c) Temporal electric field of the TL single-cycle pulse with ω 0 =12500 cm−1 (800 nm) and different ϕ C E . (d) Relative population of the excited state | f induced by the TL single-cycle pulse with different values of ϕ C E and different carrier frequencies ω 0 (normalized to the case of ϕ C E = 0).

Fig. 2
Fig. 2

Coherent control of two-photon excitation in the model system: Excited state population induced by ultrabroadband pulses shaped with a spectral π phase step at different positions for several cases of carrier frequency ω 0 and CEP ϕ C E . Each trace is normalized by the population excited by the corresponding TL pulse having non-stabilized ϕ C E .

Fig. 3
Fig. 3

(a) Three-photon excitation scheme in the femtosecond single-cycle regime. Indicated are the three-photon absorption transitions and three-photon Raman transitions. (b) Ultrabroad spectrum of the single-cycle pulse centered at Ω f g /2 provides three absorbed photons of frequencies around Ω f g /3 to the three-photon absorption transitions as well as three photons, two absorbed photon of frequency around 2 Ω f g /3 and one emitted photon of frequency around Ω f g /3, to the Raman transitions. (c) Relative population of the excited state | f induced by the TL single-cycle pulse with different values of ϕ C E and different carrier frequencies ω 0 (normalized to the case of ϕ C E = 0).

Fig. 4
Fig. 4

Coherent control of three-photon excitation in the model system: Excited state population induced by ultrabroadband pulses shaped with a spectral π phase step at different positions for several cases of carrier frequency ω 0 and CEP ϕ C E . Each trace is normalized by the population excited by the corresponding TL pulse having non-stabilized ϕ C E .

Fig. 5
Fig. 5

Weak-field two-photon femtosecond coherent phase control of Cs in the single-cycle regime. Upper panel: Excitation scheme of Cs (fine structure splitting is not shown), with examples of two-photon absorption and Raman transitions. Panels (a) and (b): Relative population of the excited states 5d 3 / 2 [panel (a)] and 5d 5 / 2 [panel (b)] induced by TL single-cycle pulses of ω 0 = 16667 cm−1 ( Δ ω = 7350 cm−1) having different values of ϕ C E . Panels (c) and (d): Relative population of the excited states 5d 3 / 2 [panel (c)] and 5d 5 / 2 [panel (d)] induced by such ultrabroadband pulses applied with ϕ C E = 3.3 rad and shaped with a spectral π phase step at different positions. Indicated are the different state-to-state transitions associated with the different resonance-mediated enhancement peaks of the π-traces (see text).

Equations (8)

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

A f ( 2 ) ε 2 ( t ) exp ( i Ω f g t ) d t ,
ε ( t ) = 1 2 E ( t ) exp [ i ( ω 0 t + ϕ C E ) ] + c . c . ,
A f ( 2 ) = A a b s ( 2 ) + A R a m ( 2 ) ,
A a b s ( 2 ) = exp ( i 2 ϕ C E ) μ a b s 2 0 E ˜ ( ω ) E ˜ ( Ω f g ω ) d ω A R a m ( 2 ) = μ R a m , 1 2 Ω f g E ˜ ( ω ) E ˜ ( ω Ω f g ) d ω + μ R a m , 2 2 Ω f g E ˜ ( ω Ω f g ) E ˜ ( ω ) d ω ,
A f ( 3 ) ε 3 ( t ) exp ( i Ω f g t ) d t .
A f ( 3 ) = A a b s ( 3 ) + A R a m ( 3 ) ,
A a b s ( 3 ) = exp ( i 3 ϕ C E ) μ a b s 3 0 0 E ˜ ( ω 1 ) E ˜ ( ω 2 ) E ˜ ( Ω f g ω 1 ω 2 ) d ω 1 d ω 2
A R a m ( 3 ) = exp ( i ϕ C E ) [ μ R a m , 1 3 0 0 E ˜ ( ω 1 ) E ˜ ( ω 2 ) E ˜ ( ω 1 + ω 2 Ω f g ) d ω 1 d ω 2 + μ R a m , 2 3 0 0 E ˜ ( ω 1 + ω 2 Ω f g ) E ˜ ( ω 1 ) E ˜ ( ω 2 ) d ω 1 d ω 2 + μ R a m , 3 3 0 0 E ˜ ( ω 1 ) E ˜ ( ω 1 + ω 2 Ω f g ) E ˜ ( ω 2 ) d ω 1 d ω 2 ] ,

Metrics