## Zeptosecond precision pulse shaping |

Optics Express, Vol. 19, Issue 12, pp. 11638-11653 (2011)

http://dx.doi.org/10.1364/OE.19.011638

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### Abstract

We investigate the temporal precision in the generation of ultrashort laser pulse pairs by pulse shaping techniques. To this end, we combine a femtosecond polarization pulse shaper with a polarizer and employ two linear spectral phase masks to mimic an ultrastable common-path interferometer. In an all-optical experiment we study the interference signal resulting from two temporally delayed pulses. Our results show a 2*σ*-precision of 300 zs = 300 × 10^{−21} s in pulse-to-pulse delay. The standard deviation of the mean is 11 zs. The obtained precision corresponds to a variation of the arm’s length in conventional delay stage based interferometers of 0.45 Å. We apply these precisely generated pulse pairs to a strong-field quantum control experiment. Coherent control of ultrafast electron dynamics via photon locking by temporal phase discontinuities on a few attosecond timescale is demonstrated.

© 2011 OSA

## 1. Introduction

*Tannor-Kosloff-Rice*scheme [2] are based on precisely timed pulse pairs to exert control on molecular dynamics on the femtosecond timescale. Double pulses have also been used to control

*electron*dynamics, e.g. atomic excitation in weak fields [3, 4], interference of ultrashort free electron wave packets [5

5. M. Wollenhaupt, A. Assion, D. Liese, Ch. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, “Interferences of ultrashort free electron wave packets,” Phys. Rev. Lett. **89**, 173001 (2002). [PubMed]

7. M. Wollenhaupt, V. Engel, and T. Baumert, “Femtosecond laser photoelectron spectroscopy on atoms and small molecules: prototype studies in quantum control,” Annu. Rev. Phys. Chem. **56**, 25–56 (2005). [PubMed]

8. Th. Ergler, A. Rudenko, B. Feuerstein, K. Zrost, C. D Schröter, R. Moshammer, and J. Ullrich, “Time-resolved imaging and manipulation of H_{2} fragmentation in intense laser fields,” Phys. Rev. Lett. **95**, 093001 (2005). [PubMed]

10. K. Ohmori, “Wave-packet and coherent control dynamics,” Annu. Rev. Phys. Chem. **60**, 487–511 (2009). [PubMed]

12. M. Chini, H. Mashiko, H. Wang, S. Chen, C. Yun, S. Scott, S. Gilbertson, and Z. Chang, “Delay control in attosecond pump-probe experiments,” Opt. Express **17**, 21459–21464 (2009). [PubMed]

24. M. T. Seidel, S. Yan, and H.-S. Tan, “Mid-infrared polarization pulse shaping by parametric transfer,” Opt. Lett. **35**, 478–480 (2010). [PubMed]

*σ*-precision of 300 zs = 300 × 10

^{−21}s in pulse-to-pulse delay. The observed standard deviation of the mean is 11 zs. So far, pulse shaping with sub-attosecond accuracy has not been shown experimentally. Our results demonstrate an improvement on the precision of interferometrically stable generation of pulse pairs by two orders of magnitude.

*σ*-precision of 300 zs is presented and discussed in Sect. 3. In Sect. 4 we demonstrate the application of precisely generated double pulses to coherent electronic excitation. An application to attosecond pump-probe experiments is proposed in Sect. 5. We end this article with a brief summary and conclusions in Sect. 6. In the appendix details about the data evaluation of the all-optical experiment are given.

## 2. Pulse shaper

### 2.1. General layout

*f*-zero dispersion compressor setup with a double layer Liquid Crystal-Spatial Light Modulator (LC-SLM) located in the Fourier plane. Instead of the transmission grating layout described in [20] we use a slightly modified version for the experiments discussed in this paper. Here, the 4

*f*-setup is equipped with 1480 grooves/mm gold-coated reflection gratings (

*HORIBA Jobin Yvon*) specifically designed for ultrashort laser pulse compression. The gratings are mounted in Littrow configuration with an angle of incidence of 36.3°. For p-polarized light they possess diffraction efficiencies of more than 85 % for all spectral components in the wavelength range from 700 nm to 900 nm. The efficiency values for s-polarized light lie at about 29 %. Cylindrical mirrors with silver coating and protection layer having a focal length of

*f*= 223 mm are used as focusing elements. The 2 x 640 pixel LC-SLM (

*Jenoptik SLM-S640d*) has two independent LC layers with preferential orientation axes at ∓45° (see Fig. 1). This allows for simultaneous and independent spectral phase modulation of two orthogonally polarized electric field components of the incident light. The existing LC configuration provides the possibility for phase and polarization pulse shaping [20] as well as phase and amplitude modulation by employing an additional polarizer [26

26. M. M. Wefers and K. A. Nelson, “Generation of high-fidelity programmable ultrafast optical waveforms,” Opt. Lett. **20**, 1047–1049 (1995). [PubMed]

29. F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys. **130**, 034302 (2009). [PubMed]

^{2}-intensity input beam diameter of more than 3.2 mm. For all wavelengths within the pulse shaper’s spectral transmission window this results in 1/e

^{2}-intensity beam diameters in the Fourier plane of less than 78 μm being well below the pixel width of 96.52 μm. In [27,29

29. F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys. **130**, 034302 (2009). [PubMed]

### 2.2. Mimicking an interferometer

30. B. von Vacano, T. Buckup, and M. Motzkus, “*In situ* broadband pulse compression for multiphoton microscopy using a shaper-assisted collinear SPIDER,” Opt. Lett. **31**, 1154–1156 (2006). [PubMed]

*f*-setup builds the basis for femtosecond pulse shaping. The incoming real temporal electric field

*E*

_{in}(

*t*) is transformed into its spectral counterpart

*Ẽ*

_{in}(

*ω*), to which a complex spectral transfer function

*M̃*(

*ω*) is applied, resulting in a modulated field Performing an inverse Fourier transform this spectral field is transformed back into the time domain to obtain the shaped pulse

*E*

_{out}(

*t*). In order to use a pulse shaper to mimic an interferometer, the temporal electric field

*τ*by the introduction of a reference frequency

*ω*

_{ref}, it reads Depending on the value of

*ω*

_{ref}either only the envelopes of the two pulses or both the envelopes and the relative phase between the two pulses are shifted upon scanning the pulse-to-pulse delay

*τ*. The first mode is achieved by the choice

*ω*

_{ref}=

*ω*

_{0}, where

*ω*

_{0}is the central frequency of the incoming laser pulses. The second mode describes the situation in a conventional interferometer. It is realized by setting

*ω*

_{ref}= 0. Generally, the required optical transfer functions are calculated employing Fourier techniques. In the following we present an alternative and intuitive approach to obtain the transfer function needed for pulse shaper based interferometry (cf. Eq. (2)). Our scheme builds on basic principles of spectral phase-only modulation.

*A*+

*B*≤ 1 must be calculated. Following our intuitive scheme, we make use of a different approach. Without changing the phase functions applied to the LC-SLM we tune the ratio of the pulse energies simply by changing the energy ratio of the two components

*Ẽ*

_{in,}

*(*

_{a}*ω*) and

*Ẽ*

_{in,}

*(*

_{b}*ω*) of the input field

*Ẽ*

_{in}(

*ω*). A rotation of the polarization plane of the linearly polarized input pulse employing a half-wave plate leads to an unequal energy distribution of the two components at ∓45°. Rotation angles of the polarization plane between −45° and +45° allow the realization of any desired pulse energy ratio. After rotation of its polarization plane, the incoming light is still linearly polarized for our reflection gratings, but it is not p-polarized any more. It is a superposition of p- and s-polarized components. Therefore, the difference between the grating efficiencies for p- and s-polarized light (cf. Subsection 2.1) has to be taken into account to determine the rotation angle of the half-wave plate needed for a certain energy ratio of the two pulses. The situation

*A*+

*B*< 1 corresponds to an additional attenuation reducing the total amount of energy contained in the pair of pulses.

*τ*, any arbitrary phase modulation can be applied. Thus, the double layer LC-SLM based pulse shaper cannot only be used to mimic an interferometer, but it may serve as an interferometer with independent spectral phase modulators in both arms giving access to a large class of shaped pulse pairs.

## 3. All-optical experiment

### 3.1. Experimental

*S*of two temporally overlapping identical pulses was recorded as a function of the pulse-to-pulse delay

*τ*with a photodiode located directly behind the shaper to produce a 1st order interferometric autocorrelation. This signal was measured for different delay intervals with successively decreasing ranges and employing decreasing step sizes. In order to maximize the signal to noise ratio we chose a femtosecond oscillator as light source for this experiment. The used Ti:sapphire oscillator (

*Femtolasers Fusion Pro 400*) has a repetition rate of 75 MHz, a pulse energy of about 6.5 nJ and a spectral bandwidth of more than 80 nm Full-Width at Half Maximum (FWHM) centered at 800 nm. The latter results in a duration of less than 12 fs FWHM for the bandwidth-limited pulse.

### 3.2. Results and discussion

*τ*= −2.025 fs was selected and scanned with a delay step size of 0.1 as = 100 zs. Due to the small range of this interval, the relation between signal

*S*and pulse-to-pulse delay

*τ*is approximately linear. The result of this measurement is illustrated in Fig. 2(d). Minute deviations from perfect monotony appear revealing that this delay step size is beyond the highest possible temporal resolution.

*S*

_{fit}(see Eq. (7) in the appendix) to the 100 zs step size measurement data. The fit curve allows us to calculate the standard deviation

*σ*of the pulse-to-pulse delay

_{τ}*τ*. The evaluation procedure is described in detail in the appendix. Applying this procedure to the measurement with 100 zs delay step size, we obtain a standard deviation of the pulse-to-pulse delay of

*σ*≈ 140 zs. This leads to an estimation of the limit in minimum achievable delay step size of 2

_{τ}*σ*≈ 280 zs.

_{τ}*a*

_{0}= 0.529 Å. The resolution of 300 zs is equivalent to nearly 10000 measurement points per oscillation period, which is about 2.67 fs for our experimental conditions. Applying the aforementioned fit procedure to the 300 zs delay step size measurement data yields

*σ*≈ 150 zs for the standard deviation of the pulse-to-pulse delay. This confirms the value obtained from the measurement with 100 zs resolution.

_{τ}*δ*≈ 11 zs (cf. Eq. (10) in the appendix) is a meaningful quantity in our experiment, we consider the residuals for the optical interference measurement with 300 zs delay step size. They are the difference between the measured values and the linear fit to those data (cf. Eq. (7)). While in Fig. 4(a) the residuals are plotted, subfigure 4(b) is a histogram representation to reveal the nature of the residuals’ distribution. We find a non-quantized Gaussian distribution confirming the standard deviation of the mean is a meaningful quantity here.

_{τ}## 4. Coherent quantum control experiment

### 4.1. Experimental

38. T. Bayer, M. Wollenhaupt, C. Sarpe-Tudoran, and T. Baumert, “Robust photon locking,” Phys. Rev. Lett. **102**, 023004 (2009). [PubMed]

*Femtolasers Femtopower Pro*) pass a rotatable half-wave plate, the double layer LC-SLM based pulse shaper, and a polarizer. The laser pulses are attenuated to an energy of 0.5 μJ and focussed into a vacuum chamber by an

*f*= 300 mm lens. The focusing conditions correspond to a pulse intensity of about 5 × 10

^{11}W/cm

^{2}. The laser beam perpendicularly intersects a potassium atomic beam generated in an adjacent oven chamber. Photoelectrons released during the light-atom interaction are collected and detected by an energy-calibrated magnetic bottle Time Of Flight (TOF) spectrometer. A more detailed description of the atomic beam preparation and the energy resolution of the spectrometer is found elsewhere [37]. Prior to the actual measurements on potassium, residual phase compensation of the initial pulses was performed in situ by adaptively optimizing the multi-photon ionization of ground state xenon atoms in the interaction region of the photoelectron spectrometer. In order to ensure transform-limited pulses, the resulting compensation phase was always applied to the LC-SLM in addition to the phase functions needed to generate the pulse pair.

*τ*(cf. Eqs. (2)–(5)) and the rotation angle of the half-wave plate, a pulse pair consisting of a pre-pulse (approximately 2.3 % of the main pulse’s intensity) and a much stronger main pulse is generated. The potassium transition 4

*p*← 4

*s*is strongly driven by this pulse pair (cf. Fig. 5). The first pulse prepares the system in a state of maximum coherence. The strong-field excitation gives rise to an energy splitting of the resonant state into two dressed states, i.e. eigenstates of the total system comprising the two-level system and the excitation laser field. In addition, the second pulse ionizes the excited atom in a perturbative two-photon process mapping both the energy and the population of the dressed states into the photoelectron spectrum. This spectrum reveals the Autler-Townes (AT) doublet resulting from the energy splitting of the resonant state. The relative population of the dressed states and thus the branching ratio of fast (high kinetic energy

*E*) and slow (low kinetic energy

_{F}*E*) photoelectrons represented by the two peaks of the AT doublet depends on the relative optical phase between the two pulses, which is controlled by their temporal separation. The underlying strong-field control mechanism has been termed Selective Population Of Dressed States (SPODS), in this case realized via photon locking by temporal phase discontinuities. A detailed description of this scenario including a spatiotemporal picture is given in [36, 37].

_{S}*F*and

*S*denote the integrated signals of fast and slow photoelectrons, respectively (cf. Fig. 5). This quantity is a measure for the asymmetry of the AT doublet and indicates the control exerted on the induced electron dynamics.

### 4.2. Results and discussion

*τ*= 120 fs. In a first scan this temporal separation was varied by an amount ranging from 0 fs to 3.69 fs in steps of 41.5 as. This corresponds to a relative phase shift between the two pulses from 0 rad to 8.81 rad. The photoelectron spectra acquired during this scan are displayed in Fig. 6(a). The curve of the AT contrast

*C*

_{AT}calculated by processing the recorded spectra according to Eq. (6) is plotted in Fig. 6(c) together with the laser power. The photoelectron spectra as well as the contrast curve show evidence of the periodic switching between fast and slow photoelectrons as it was observed and discussed previously [36, 37]. Focusing on the yellow-shaded area in subfigure 6(c), the strictly monotonic behavior expected from the signal within this parameter range is observed in the experiment. This demonstrates the controllability of the underlying electron dynamics on a temporal level of the applied step size of 41.5 as.

## 5. Application to attosecond pump-probe experiments

39. S. Rausch, T. Binhammer, A. Harth, F. X. Kärtner, and U. Morgner, “Few-cycle femtosecond field synthesizer,” Opt. Express **16**, 17410–17419 (2008). [PubMed]

## 6. Summary and conclusions

*σ*-precision of 300 zs = 300 × 10

^{−21}s in pulse-to-pulse delay with a standard deviation of the mean of 11 zs. In a coherent electronic excitation experiment we have applied precisely timed double pulses to strong-field quantum control with this technique. By steering population to different final quantum states with sub-10 as precision, we have shown efficient control of ultrafast electron dynamics in this temporal regime by employing our all-optical interferometer.

41. C. Ott, P. Raith, and T. Pfeifer, “Sub-cycle strong-field interferometry,” Opt. Express **18**, 24307–24315 (2010). [PubMed]

## Appendix

*σ*of the pulse-to-pulse delay for the measurement results shown in Figs. 2(d) and 3 in Subsect. 3.2 makes use of standard formulas of statistics. Here, they are recapitulated in detail for the sake of clarity.

_{τ}*S*measured in dependence on the pulse-to-pulse delay

*τ*by a linear fit function This fit curve allows us to calculate the standard deviation

*σ*of the measured interference signal

_{S}*S*: where

*N*is the number of measurement points. The slope

*m*of the fit curve is associated with the standard deviation

*σ*of the interference signal

_{S}*S*from Eq. (8) as well as with the standard deviation

*σ*of the pulse-to-pulse delay

_{τ}*τ*by the equation This relation is schematically depicted in the inset in Fig. 3. Inserting the values previously calculated for

*m*and

*σ*, we finally use Eq. (9) to extract a value for

_{S}*σ*.

_{τ}## Acknowledgments

## References and links

1. | A. W. Albrecht, J. D. Hybl, S. M. Gallagher Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: Implications for femtosecond spectroscopy and coherent control of chemical reactions,” 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. |

3. | M. A. Bouchene, V. Blanchet, C. Nicole, N. Melikechi, B. Girard, H. Ruppe, S. Rutz, E. Schreiber, and L. Wöste, “Temporal coherent control induced by wave packet interferences in one and two photon atomic transitions,” Eur. Phys. J. D |

4. | 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 |

5. | M. Wollenhaupt, A. Assion, D. Liese, Ch. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, “Interferences of ultrashort free electron wave packets,” Phys. Rev. Lett. |

6. | M. Wollenhaupt, A. Assion, O. Bazhan, Ch. Horn, D. Liese, Ch. Sarpe-Tudoran, M. Winter, and T. Baumert, “Control of interferences in an Autler-Townes doublet: Symmetry of control parameters,” Phys. Rev. A |

7. | M. Wollenhaupt, V. Engel, and T. Baumert, “Femtosecond laser photoelectron spectroscopy on atoms and small molecules: prototype studies in quantum control,” Annu. Rev. Phys. Chem. |

8. | Th. Ergler, A. Rudenko, B. Feuerstein, K. Zrost, C. D Schröter, R. Moshammer, and J. Ullrich, “Time-resolved imaging and manipulation of H |

9. | K. Ohmori, “Development of ultrahigh-precision coherent control and its applications,” Proc. Jpn. Acad., Ser. B |

10. | K. Ohmori, “Wave-packet and coherent control dynamics,” Annu. Rev. Phys. Chem. |

11. | H. Katsuki, K. Hosaka, H. Chiba, and K. Ohmori, “Read and write amplitude and phase information by using high-precision molecular wave-packet interferometry,” Phys. Rev. A |

12. | M. Chini, H. Mashiko, H. Wang, S. Chen, C. Yun, S. Scott, S. Gilbertson, and Z. Chang, “Delay control in attosecond pump-probe experiments,” Opt. Express |

13. | A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. |

14. | A. Monmayrant, S. Weber, and B. Chatel, “A newcomer’s guide to ultrashort pulse shaping and characterization,” J. Phys. B |

15. | T. Brixner and G. Gerber, “Femtosecond polarization pulse shaping,” Opt. Lett. |

16. | T. Suzuki, S. Minemoto, T. Kanai, and H. Sakai, “Optimal control of multiphoton ionization processes in aligned I |

17. | T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, “Quantum control by ultrafast polarization shaping,” Phys. Rev. Lett. |

18. | L. Polachek, D. Oron, and Y. Silberberg, “Full control of the spectral polarization of ultrashort laser pulses,” Opt. Lett. |

19. | M. Ninck, A. Galler, T. Feurer, and T. Brixner, “Programmable common-path vector field synthesizer for femtosecond pulses,” Opt. Lett. |

20. | M. Wollenhaupt, M. Krug, J. Köhler, T. Bayer, C. Sarpe-Tudoran, and T. Baumert, “Photoelectron angular distributions from strong-field coherent electronic excitation,” Appl. Phys. B |

21. | D. Kupka, P. Schlup, and R. A. Bartels, “Simplified ultrafast pulse shaper for tailored polarization states using a birefringent prism,” Rev. Sci. Instrum. |

22. | F. Weise and A. Lindinger, “Full control over the electric field using four liquid crystal arrays,” Opt. Lett. |

23. | C. T. Middleton, D. B. Strasfeld, and M. T. Zanni, “Polarization shaping in the mid-IR and polarization-based balanced heterodyne detection with application to 2D IR spectroscopy,” Opt. Express |

24. | M. T. Seidel, S. Yan, and H.-S. Tan, “Mid-infrared polarization pulse shaping by parametric transfer,” Opt. Lett. |

25. | A. Präkelt, M. Wollenhaupt, A. Assion, Ch. Horn, C. Sarpe-Tudoran, M. Winter, and T. Baumert, “Compact, robust, and flexible setup for femtosecond pulse shaping,” Rev. Sci. Instrum. |

26. | M. M. Wefers and K. A. Nelson, “Generation of high-fidelity programmable ultrafast optical waveforms,” Opt. Lett. |

27. | M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. |

28. | B. J. Sussman, R. Lausten, and A. Stolow, “Focusing of light following a 4- |

29. | F. Frei, A. Galler, and T. Feurer, “Space-time coupling in femtosecond pulse shaping and its effects on coherent control,” J. Chem. Phys. |

30. | B. von Vacano, T. Buckup, and M. Motzkus, “ |

31. | B. von Vacano, T. Buckup, and M. Motzkus, “Shaper-assisted collinear SPIDER: fast and simple broadband pulse compression in nonlinear microscopy,” J. Opt. Soc. Am. B |

32. | A. Galler and T. Feurer, “Pulse shaper assisted short laser pulse characterization,” Appl. Phys. B |

33. | M. Wollenhaupt, A. Assion, and T. Baumert, “Femtosecond laser pulses: linear properties, manipulation, generation and measurement,” in |

34. | R. N. Bracewell, |

35. | M. Wollenhaupt, D. Liese, A. Präkelt, C. Sarpe-Tudoran, and T. Baumert, “Quantum control by ultrafast dressed states tailoring,” Chem. Phys. Lett. |

36. | 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 |

37. | T. Bayer, M. Wollenhaupt, and T. Baumert, “Strong-field control landscapes of coherent electronic excitation,” J. Phys. B |

38. | T. Bayer, M. Wollenhaupt, C. Sarpe-Tudoran, and T. Baumert, “Robust photon locking,” Phys. Rev. Lett. |

39. | S. Rausch, T. Binhammer, A. Harth, F. X. Kärtner, and U. Morgner, “Few-cycle femtosecond field synthesizer,” Opt. Express |

40. | D. Oron, Y. Silberberg, N. Dudovich, and D. M. Villeneuve, “Efficient polarization gating of high-order harmonic generation by polarization-shaped ultrashort pulses,” Phys. Rev. A |

41. | C. Ott, P. Raith, and T. Pfeifer, “Sub-cycle strong-field interferometry,” Opt. Express |

**OCIS Codes**

(020.4180) Atomic and molecular physics : Multiphoton processes

(270.1670) Quantum optics : Coherent optical effects

(320.0320) Ultrafast optics : Ultrafast optics

(320.5540) Ultrafast optics : Pulse shaping

(320.7080) Ultrafast optics : Ultrafast devices

(320.7100) Ultrafast optics : Ultrafast measurements

(020.2649) Atomic and molecular physics : Strong field laser physics

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: April 4, 2011

Revised Manuscript: May 25, 2011

Manuscript Accepted: May 25, 2011

Published: June 1, 2011

**Virtual Issues**

Vol. 6, Iss. 7 *Virtual Journal for Biomedical Optics*

**Citation**

Jens Köhler, Matthias Wollenhaupt, Tim Bayer, Cristian Sarpe, and Thomas Baumert, "Zeptosecond precision pulse shaping," Opt. Express **19**, 11638-11653 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-12-11638

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### References

- A. W. Albrecht, J. D. Hybl, S. M. Gallagher Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: Implications for femtosecond spectroscopy and coherent control of chemical reactions,” J. Chem. Phys. 111, 10934–10956 (1999).
- 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, 5805–5820 (1986).
- M. A. Bouchene, V. Blanchet, C. Nicole, N. Melikechi, B. Girard, H. Ruppe, S. Rutz, E. Schreiber, and L. Wöste, “Temporal coherent control induced by wave packet interferences in one and two photon atomic transitions,” Eur. Phys. J. D 2, 131–141 (1998).
- 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, 063407 (2004).
- M. Wollenhaupt, A. Assion, D. Liese, Ch. Sarpe-Tudoran, T. Baumert, S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, and G. Gerber, “Interferences of ultrashort free electron wave packets,” Phys. Rev. Lett. 89, 173001 (2002). [PubMed]
- M. Wollenhaupt, A. Assion, O. Bazhan, Ch. Horn, D. Liese, Ch. Sarpe-Tudoran, M. Winter, and T. Baumert, “Control of interferences in an Autler-Townes doublet: Symmetry of control parameters,” Phys. Rev. A 68, 015401(R) (2003).
- M. Wollenhaupt, V. Engel, and T. Baumert, “Femtosecond laser photoelectron spectroscopy on atoms and small molecules: prototype studies in quantum control,” Annu. Rev. Phys. Chem. 56, 25–56 (2005). [PubMed]
- Th. Ergler, A. Rudenko, B. Feuerstein, K. Zrost, C. D Schröter, R. Moshammer, and J. Ullrich, “Time-resolved imaging and manipulation of H2 fragmentation in intense laser fields,” Phys. Rev. Lett. 95, 093001 (2005). [PubMed]
- K. Ohmori, “Development of ultrahigh-precision coherent control and its applications,” Proc. Jpn. Acad., Ser. B 84, 167–175 (2008).
- K. Ohmori, “Wave-packet and coherent control dynamics,” Annu. Rev. Phys. Chem. 60, 487–511 (2009). [PubMed]
- H. Katsuki, K. Hosaka, H. Chiba, and K. Ohmori, “Read and write amplitude and phase information by using high-precision molecular wave-packet interferometry,” Phys. Rev. A 76, 013403 (2007).
- M. Chini, H. Mashiko, H. Wang, S. Chen, C. Yun, S. Scott, S. Gilbertson, and Z. Chang, “Delay control in attosecond pump-probe experiments,” Opt. Express 17, 21459–21464 (2009). [PubMed]
- A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929–1960 (2000).
- A. Monmayrant, S. Weber, and B. Chatel, “A newcomer’s guide to ultrashort pulse shaping and characterization,” J. Phys. B 43, 103001 (2010).
- T. Brixner and G. Gerber, “Femtosecond polarization pulse shaping,” Opt. Lett. 26, 557–559 (2001).
- T. Suzuki, S. Minemoto, T. Kanai, and H. Sakai, “Optimal control of multiphoton ionization processes in aligned I2 molecules with time-dependent polarization pulses,” Phys. Rev. Lett. 92, 133005 (2004). [PubMed]
- T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt, O. Graefe, C. Horn, D. Liese, and T. Baumert, “Quantum control by ultrafast polarization shaping,” Phys. Rev. Lett. 92, 208301 (2004). [PubMed]
- L. Polachek, D. Oron, and Y. Silberberg, “Full control of the spectral polarization of ultrashort laser pulses,” Opt. Lett. 31, 631–633 (2006). [PubMed]
- M. Ninck, A. Galler, T. Feurer, and T. Brixner, “Programmable common-path vector field synthesizer for femtosecond pulses,” Opt. Lett. 32, 3379–3381 (2007). [PubMed]
- M. Wollenhaupt, M. Krug, J. Köhler, T. Bayer, C. Sarpe-Tudoran, and T. Baumert, “Photoelectron angular distributions from strong-field coherent electronic excitation,” Appl. Phys. B 95, 245–259 (2009).
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