Control and measurement of a non-resonant Raman wavepacket using a single ultrashort pulse

Chemical Physics 318 (2005) 163–169 www.elsevier.com/locate/chemphys

Control and measurement of a non-resonant Raman wavepacket using a single ultrashort pulse T. Polack *, D. Oron, Y. Silberberg Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel Received 8 December 2004; accepted 1 June 2005 Available online 7 July 2005

Abstract Using a single shaped femtosecond pulse, a molecular wavepacket is both tailored and monitored. Several toluene vibrational levels are excited in a controlled manner, both in amplitude and phase, through a quantum coherently controlled non-resonant Raman process. The entire coherent anti-Stokes Raman spectroscopy (CARS) process, that includes excitation and probing of the Raman-induced wavepacket, is enabled by polarization and phase shaping. We achieve a wavepacket detection sensitive to the modes relative phase and further extend the capabilities of the single-pulse CARS technique.
2005 Elsevier B.V. All rights reserved. PACS: 32.80.Qk; 42.65.Dr; 78.47.+p Keywords: Impulsive Raman scattering; CARS; Quantum coherent control; Single-pulse-CARS

1. Introduction 1.1. Coherent control Driving a quantum system toward a desired output state through its interaction with a shaped electric field is the substance of quantum coherent control. It applies when multiple coherent contributions – or quantum paths – lead to a same output state, the interference between these contributions being under the control of a designed electric field. Quantum coherent control first developed as a theoretical field [1,2]. Recently, due to the advance of femtosecond laser technology and pulse-shaping techniques, it has been successfully applied to various systems: atoms,

*

Corresponding author. Fax: +972 8 934 4109. E-mail addresses: [email protected] (T. Polack), [email protected] (D. Oron), [email protected] (Y. Silberberg). 0301-0104/$ - see front matter
2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2005.06.018

crystals, molecules in gas or liquid phase, or biological compounds. For complex systems, especially when subjected to strong electric fields, an analytical or numerical approach to the light–matter interaction is generally out of reach, forbidding a design of the electric field a priori. Consequently, the control of such systems is tackled by adaptive techniques in which a feedback algorithm optimizes the electric field shape according to a measured output quantity [3]. This strategy, known as optimal or closed-loop control, has been fruitfully applied, among others, to selective chemical bond breaking [4], high harmonic generation [5], and wave-function shaping [6]. A reverse approach consists in designing the electric field a priori. Since it requires a precise understanding of the interaction, it preferentially targets simple processes, which are either due to a simple enough system or a valid perturbative treatment. Hence, the investigation of the few-photon processes control such as coherent transients [7,8], non-resonant [9] and resonant [10] two-photon absorption, or stimulated Raman processes [11–20]. Such

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an approach, which is not limited to the perturbative limit, has led to a thorough understanding of important mechanisms at stake in coherent control and to the implementation of numerous coherent control schemes. Coherent control and pulse-shaping ideas and tools lead to new spectroscopic techniques; they also enhance existing ones, simplifying the experimental set-up and providing them with new capabilities. In this regard, the application of femtosecond pulse-shaping to coherent anti-Stokes Raman spectroscopy (CARS) is particularly interesting. CARS is a spectroscopy technique sensitive to rovibrational resonances. Since it does not require wavelength tuning to one-photon resonances, it aims at a broad range of molecular systems. To the conventional CARS technique, pulse-shaping adds a versatile mode selective excitation of rovibrational levels and a sharp probing of the excited modes [12,18]. 1.2. Stimulated Raman control and single-pulse CARS The overall third-order CARS process (shown in Fig. 1(a)) breaks up into a non-resonant two-photon excitation – a stimulated Raman process – followed by a linear probing process. In an impulsive Raman scattering process, an electric field pulse only efficiently excites the modes having a vibrational period longer than the pulse duration. Consequently, Fourier-transform limited femtosecond pulses of short duration access a large number of vibrational modes. However, they are not the best tool for CARS. First, their high peak power leads to non-resonant effects which smear the weaker resonant signals that possess a specific molecular information; second, their large bandwidth lead to a non-selective mode excitation. Even though femtosecond pulses have been used for multiplex CARS [29], these drawbacks caused CARS to remain a picosecond rather than a femtosecond technique. While retaining the femtosecond pulse large spectral bandwidth, pulse-shaping techniques overcome these a

b

Fig. 1. CARS process diagram and experimental set-up. (a) A pump– Stokes photon pair with frequencies x1 and x2 non-resonantly excite a Raman level with a frequency XR = x1
x2 lying within the bandwidth of the pulse. The successive scattering of an x3 probe photon leads to a CARS emission at frequency xCARS = x3 + XR. The pulse spectrum is, depicted on the upper-left side, is blocked at its high energy end so that the CARS frequency lies outside the spectrum of the incoming pulse. (b) Schematic drawing of the experimental configuration.

drawbacks. They allow to avoid undesired non-linear effects by reducing the pulse peak-power and to target a specific mode or a group of selected modes. Nonresonant Raman selective excitation has first been demonstrated using pulse sequences [11,21,22]. Since then, other pulse-shaping schemes have been used to achieve selective Raman excitation: spectral phase shaping [14,19], chirped pulses [23], pairs of chirped or Fouriertransform limited pulses [24–26] and even optimal control approaches [25,27]. Monitoring the two photon induced vibrational coherence via the spontaneous Raman scattering of an optical probe results in a CARS process. The picosecond CARS technique lately gave rise to several applications, notably in microscopy [28]. Its most stringent technical requirement is the synchronization of pulses of different color. This is circumvented by the single-pulse CARS technique [12] that derives the three photons involved in the process from a single femtosecond pulse. Elimination of non-resonant third-order competing processes – usually referred to as non-resonant background due to their spectrally broad character – as well as spectral selectivity are retrieved by femtosecond shaping techniques that exploit the coherence and tensorial properties of the third-order emission. So far, the control of the mode excitation only dealt with amplitude issues. In this article, using single-pulse CARS, we report the control in amplitude and phase over a vibrational wavepacket in liquid Toluene. The excited wavepacket is detected in a manner sensitive to the induced modes relative phases. Besides, we demonstrate and use improved probing techniques for non-resonant background rejection.

2. Theoretical analysis CARS is a third-order process. While two photons – pump and Stokes – account for the non-resonant Raman vibrational excitation, the Raman scattering of a third – probe – photon leads to a blue-shifted antiStokes emission. This fourth emitted photon, spectrally shifted from the probe frequency by a rovibrational energy quantum, is the CARS signal (see Fig. 1(a)). We first present the theoretical background that applies to non-resonant Raman selective excitation and wavepacket shaping. This first part of the CARS process only involves the pump and Stokes photons. We then focus on the shaping of the probe photon which allows the suppression of the non-resonant background and a detection sensitive to the phase of the induced wavepacket. 2.1. Stimulated Raman selective excitation In stimulated Raman scattering, an electric field of complex spectral amplitude E(x) excites a Raman mode

T. Polack et al. / Chemical Physics 318 (2005) 163–169

through a second-order process. The excitation amplitude is given by summing all the different two-photon paths amplitudes leading to the X frequency Raman level: Z Z AðXÞ ¼ dx1 dx2 dðx1
x2
XÞEðx1 ÞEH ðx2 Þ.

In a temporal point of view, the second-order excitation leads to a mode driving force proportional to the field temporal intensity I(t) = |E(t)|2. Therefore, A(X) is equivalently given by the Fourier transform of I(t). Let us highlight the role of the field spectral phase /(x) (E(x) = |E(x)| ei/(x)) by rewriting Eq. (1) as Z 1

AðXÞ ¼ dx
EðxÞEH ðx
XÞ
eið/ðxÞ
/ðx
XÞÞ . ð2Þ
1

For a given Raman level frequency X and a spectral amplitude |E(x)|, the excitation amplitude A(X) is maximized when /(x)
/(x
X) is a constant function of x. In other words, an X-periodic spectral phase function leaves A(X) unchanged compared to its maximum value obtained for a Fourier-transform limited pulse. For such a phase function, all the two-photon paths leading to the X energy level possess the same phase and interfere constructively. This constructive interference also automatically occurs for the Raman levels which frequency is an integer multiple of X. For other levels, the interference is generally not constructive. Their precise population further depends on the details of the periodic phase function such as its modulation amplitude or its harmonics that can be tuned to enhance spectral selectivity. This optimal population of the Raman levels can also be understood in a time-domain picture. To an X-periodic modulation of the spectral phase corresponds a sequence of Fourier-transform limited pulses separated by s = 1/X, as shown in Fig. 2. Each sub-pulse of the sequence exerts a force on all the Raman modes lying within its spectral bandwidth. However, due to the coherent nature of the excitation, only the modes having the same temporal phase at each pulse arrival are maximally populated after the entire interaction. The frequencies of theses modes are X and its harmonics, as given by the Fourier-transform of the pulse-sequence intensity. Because an optimal population requires the mode to be in-phase with the pulse sequence intensity, optimally excited modes must also be in-phase at the time of excitation. For two Raman levels having frequencies X1 and X2, such an optimal population is achieved with an X0-periodic phase function such that, within the spectral width of these levels, X1 and X2 are both harmonics of X0. If one takes into account the limited bandwidth of the spectrum and considers high frequency modes excited by the spectral wings of the pulse, one can, however, apply a phase-shift between different modes with a nearly opti-

a

b

c

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1

0

I 0 740 1 Intensity [arb. units]

ð1Þ

165

0

840

750

755

750

755

φ

–π

d

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0 t [fs]

1000

Fig. 2. Schematic drawing of the pulse-shaping configuration. (a) xpolarized spectral intensity of the excitation pulse (black line). The spectrum is blocked at high frequencies where the CARS signal appears. The applied X-periodic spectral phase function (gray line) induces a train of pulses separated by a time-delay s = 1/X: see panel (d) for the corresponding temporal intensity (solid black line). (b) and (c) y-polarized probes spectral intensities and phases (black and gray lines). These spectral phase functions reduce the temporal overlap between the probe and the excitation pulse. Panel (d) shows their temporal intensity profile (dashed black and solid gray lines for probes (b) and (c), respectively). Both probes barely overlap with the excitation pulse at t = 0. Probe (c) furthermore reduces the overlap with the less energetic replica.

mal population efficiency. For instance, applying a pphase step at the central frequency of the pulse leads to a corresponding p phase difference between low frequency modes – that have a frequency significantly smaller than the pulse bandwidth – and high frequency modes. Since high frequency modes are only populated by photons pairs originating from the pulse spectral wings, such a phase jump at the center of the pulse has no influence on their population. As for low frequency modes, the destructive contribution of the photon pairs originating from the pulse spectral center is small compared to other photon-pairs contributions and only have a reduced influence on their total population. On the contrary, the population of modes having a frequency close to the pulse bandwidth is strongly reduced. Similarly, we consider a series of p phase shifts applied with a crenel-like phase function: /ðxÞ ¼ p2 sign ðcosð2p Xx0 ÞÞ, where ‘‘sign’’ stands for the sign function. Due to the X0-periodicity of the phase function, modes that are harmonics of X0 are optimally excited. Besides, since frequencies separated by X0/2 have a constant p phase difference, the modes having frequencies X0/ 2 + NX0, where N is an integer, are excited with an opposite phase with respect to the harmonics of X0. The population of the X0/4 + NX0/2 frequency modes, however, is completely cancelled. Using such a crenel-like phase function or a simple p-phase step allows to achieve both amplitude control and phase control [19].

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2.2. Probing the induced excitation The induced vibrational coherence is monitored by the anti-Stokes Raman scattering of a probe field. This anti-Stokes emission is blue-shifted with respect to the probe. It is accounted for, in the case of a single Raman mode having a frequency XR and a spectral width C, by the following resonant contribution to the third-order polarization [16]: Z Ej ðx
XÞ ð3Þ P i ðxÞ ¼ vijkl dX Akl ðXÞ ð3Þ XR
X þ iC R with Akl ðXÞ ¼ dx Ek ðxÞEH l ðx
XÞ. In the femtosecond regime, without further precaution, non-resonant contributions typically an order of magnitude higher than the resonant emission smear the CARS signal. Therefore, elimination of this non-resonant background is a prerequisite to femtosecond CARS. Rejection of the non-resonant background is obtained from a combination of spectral and polarization shaping [16]. The shaped pulse has two orthogonal polarization components: the x-polarized component is assigned to the stimulated Raman excitation and uses the large bandwidth of the incoming femtosecond pulse; the y-component supplies the probe pulse. Because the spectral width of the probe pulse sets the spectral resolution of the measured CARS emission spectrum, this probe only uses a narrow portion of the incoming pulse spectrum. Only the y-component of the emission is retained and measured. Consequently, in an isotropic sample, the measured signal can only depend on the non-zero ð3Þ ð3Þ ð3Þ vð3Þ yyxx ; vyxyx ; vyxxy or vyyyy tensor elements of the thirdorder susceptibility. Due to the small spectral extent of ð3Þ the y-polarized field shape, the vyyyy contribution – either resonant or not – does not affect your signal. Indeed, such an emission does not spectrally spread away from the probe central frequency by more than the y-field spectral extent. It therefore does not reach our detection spectral range lying at higher frequencies. The first two photons, involved in a instantaneous process have to be simultaneous. Therefore, by shaping the probe such as the x- and y-polarization do not temporally overlap, both the resonant and the non-resonant ð3Þ vð3Þ yxyx and vyxxy contributions can be ruled out. Similarly, since the non-resonant background involves three simulð3Þ taneous photons, its contribution to the vyyxx emission is also suppressed. Thus, the shaping of the y-polarized probe leads to a spectrum only sensitive to the CARS resonant contribution to the third-order susceptibility vð3Þ yyxx tensor element. Note that the shaping of the probe allows to fulfill very stringent conditions. First, the probe should not temporally overlap with the x-polarized excitation field. Second, it has to probe the excitation within a 1/C duration – the dephasing time of the vibrational coherence – after the excitation pulse. And third, to retain a

spectrally structured emission, it has to be spectrally narrow. If one desires a spectral resolution on the order of C, the natural frequency resolution to resolve the vibrational spectrum, such criteria cannot be simply fulfilled with a delayed Fourier-transform limited probe. We now focus on the probe shaping that allows to temporally separate the x-excitation from the y-probe. Applying a spectral p-phase step at the center of the ypolarized probe leads to a probe temporal intensity that vanishes at t = 0 and results in a minimal overlap with the x-polarized pulse, as shown on Fig. 2(b) and (d) [16]. This is, however, not sufficient when the pump pulse is shaped into a pulse sequence which is not concentrated at t = 0. Then, a longer probe-free timewindow is required. This is obtained by ensuring that not only the probe intensity, but also its first derivative vanishes at t = 0. Indeed, the enhanced shaping of the probe shown in Fig. 2(c) and (d) leads to a much smaller overlap between the pump pulse-train (as used in the following experiments) and the probe. This reduction of the non-resonant background, however, comes at the cost of some distortion of the lineshape in the measured CARS spectrum. Note that using more complex pulse shapes, higher order time derivatives of the probe intensity at t = 0 can be eliminated, resulting in an increased probe-free time window. In practice, due to the birefringence of the collecting optics, a small part of the non-resonant background, ð3Þ due to a vxxxx process, arise in the y-polarization [16]. As a result, this spectrally large background and the resð3Þ onant vyyxx emission, which have the same order of magnitude, interfere. One can, however, differentiate between these two contributions by their dependance on the probe field. Applying a p phase-shift to the ypolarized probe field with respect to the x-polarized excitation inverts the sign of the interference cross-term between these two emissions. Consequently, recording two spectra with different values of the probe field overall phase (0 or p) leads to a differential spectra which eliminates the background and only retains the spectrally narrow interference term. Because non-resonant and resonant signal are in quadrature [13], such a procedure requires the excitation and probe relative phase to be set to ±p/2 to lead to a maximal interference.

3. Experimental results 3.1. Set-up The femtosecond pulse are delivered by a Ti:Sapphire oscillator (Femtolaser) and has a bandwidth of approximately 95 nm. It is sent through a programmable 4-f pulse-shaper with two liquid crystal spatial light modulator arrays (CRI, SLM256) which allows shaping in polarization and phase (see Fig. 1(b)). The two light

T. Polack et al. / Chemical Physics 318 (2005) 163–169

3.2. Experiments Experiments are performed in liquid toluene where several Raman levels are under the control of the excitation pulse. Their vibrational frequencies are r = 788, 1001, 1028 and 1210 cm
1. The y-polarized probe corresponds to 4 pixels of the pulse shaper and leads to a 45 cm
1 bandwidth pulse (shown in Fig. 2). Such a bandwidth does not allow to distinguish between the 1028 and 1001 cm
1 levels. Using p-phase steps (shown in Fig. 2(c)), the probe is shaped to minimize its temporal overlap with the excitation pulse. A periodic phase function /x(x) = a cos (s(x
x0)), where x0 is the pulse center frequency, is applied to the x-polarized component of the pulse. X = 1/s, the spectral periodicity of the phase function, is varied to selectively excite different Raman levels. The value of a is fixed at 1.2, half the first zero of the J0 Bessel function. When s is larger than the pulse duration, this value of a leads to the population cancellation of levels having frequencies X þ N X, where N is an integer. Consequently, it maxi2 mizes the population contrast between excited and non-excited levels. The measured CARS emission is shown on Fig. 3(c). The 788, 1001 and 1210 cm
1 Raman levels appear as spectral lines at 712, 701 and 693 nm due to a probe centered on 752 nm. Rejection of the non-resonant background is ensured by the probe phase-shaping and the differential procedure described above. The asymmetric shape of the lines is due to the spectral phase profile of the probe. The different spectra displayed on Fig. 3 correspond to particular values of the phase function periodicity X which optimize the population of the Ra-

1

Intensity [arb. units]

modulators perpendicular neutral axes are oriented at 45 with respect to the incoming pulse polarization; their retardance and difference retardance applied at each frequency pixel sets the phase and polarization of the shaped pulse. The spectral resolution of the pulse-shaper, set by the spot size at the Fourier plane is 0.3 nm (5 cm
1) and each pixel covers about 11 cm
1. The high frequency part of the pulse spectrum is blocked at 750 nm. The pulse is focused down in liquid toluene using a NA = 0.2 objective. Dispersion induced by the optics is corrected for, at the focus, by the optimization of the spectrally integrated third-order signal. After collection of the signal, a Glan polarizer only retains the y-polarization of the emission. The low frequency part of the outcoming field is blocked by a short pass filter at 725 nm (Omega optical). Since the high frequency part of the excitation pulse is blocked, the measured signal is only sensitive to non-linear contributions. The non-linear emission is spectrally resolved (0.5 nm resolution) by a computer-controlled spectrograph.

167

a

0 1 b

0 1 c

0 685

695

705

715

λ [nm] Fig. 3. Resonant CARS spectra of toluene. The spectral lines at 712, 701 and 693 nm corresponds to the 788, 1001 and 1210 cm
1 frequency modes. A mode at 1028 cm
1 is not resolved and merge with the 1001 cm
1 mode the 45 cm
1 spectral width of the probe. The dashed line indicates a magnification (·10) of the spectra. Depending on the pulse train delay s, Raman modes at frequencies 788, 1001 and 1210 cm
1 are either excited or not (see Fig. 4). For s = 64 and 85 fs ((a) and (b)), the excitation of the 788 and 1001 cm
1 modes are, respectively, suppressed. For s = 168 fs (c), all modes are excited.

man levels. The corresponding values of s = 1/X are highlighted by dashed-dotted lines in Fig. 4. The population of the three different Raman modes are controlled by changing the phase modulation periodicity X. The modes populations are obtained by integrating the Raman spectra around each emission frequency and are displayed as a function of the pulse sequence delay s = 1/X in Fig. 4. Because each level is maximally populated when s is a multiple of the level vibrational period, the population of each mode oscillates along s, with a 1/cr period. The value of s can be chosen so as to selectively excite particular modes. When s is on the order of the transform-limited pulse duration (15 fs), the population cancellation is not complete. This behavior is due to a non-negligible overlap between sub-pulses which modifies the pulse-sequence properties. In particular, the chosen value of a does not lead anymore to a population cancellation. The small decrease of the population level for large values of s is due to the diffraction in the pulse-shaper Fourier plane induced by a steep phase function. Monitoring the relative phase of the wavepacket excited modes is achieved by shaping the probe pulse. The excitation pulse corresponds to a pulse sequence

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T. Polack et al. / Chemical Physics 318 (2005) 163–169

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0 1

0 695 50

100

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715

Fig. 5. Control of the CARS emission spectrum. The excitation is a pulse sequence with delay s0 = 129 fs (see Fig. 4). (a) The emission from the 1001 cm
1 mode appears around 712 nm when probed with a single probe-band at 764 nm. (b) Using a probe with the same spectral width and phase, but now centered at 752 nm, the CARS emission is spectrally shifted: the 1001 cm
1 mode now appears at 701 nm and the 788 cm
1 mode, which is not seen in panel (a), appears at 712 nm. The probe at 764 nm, more energetic, leads to a stronger emission. (c) and (d) Using these two probe-bands simultaneously, the CARS emissions from the 788 and 1001 cm
1 modes interfere at 712 nm. The interference depends on the relative phase of the two probes; (c) it is constructive when the probes are in-phase; (d) it becomes destructive when the probe-bands are p phase-shifted.

Compared to a sinusoidal phase function, a crenel-like modulation of the phase induces a longer pulsesequence. Therefore, due to residual overlapping between the probe and the excitation sequence, a background not present in Fig. 5 appears. Using the same excitation pulse with p phase-shifted probe-bands, a constructive interference is retrieved between the two CARS emissions (see Fig. 6(b)).

Intensity [arb. units]

with delay s0 = 129 fs which selectively excites the 788 and 1001 cm
1 modes (see Fig. 4). Using a probe centered at 752 nm, these modes, respectively, appear at 712 and 701 nm. A probe centered at 764 nm downshifts the CARS spectrum: the 1001 cm
1 mode appears at 712 nm (see Fig. 5(a) and (b)). Because the frequency difference between the probe-bands at 752 and 764 nm corresponds to the vibrational frequency difference between the 788 and 1001 cm
1 modes, the emission from the two different modes appear in both probe cases at the same wavelength. If the two probe-bands are now used simultaneously, the spectrum at 712 nm, where the two emissions overlap, results from a coherent superposition of the two CARS signals (see Fig. 5(c)). Therefore, it is sensitive to the relative phase of the two modes. Additionally, it depends on the relative phase of the two probe-bands, as shown in Fig. 5(d) by shifting this phase by p. The resulting destructive interference is not complete due to differences in strength and width of the two levels. Finally, with this phase-sensitive probe configuration, we measure a wavepacket phase controlled by the excitation pulse. The excitation pulse is spectrally modulated by a crenel-like phase function of height p and periodicity X0 = 2/s0. As in the case of the previously used sinusoidal phase modulation, the pulse selectively excites the 788 and 1001 cm
1 modes. Moreover, it induces a p phase-shift between the 788 (3X0/2) and 1001 cm
1 (2X0) modes. As a consequence of the modes opposite phases, the CARS emissions interference at 712 nm is destructive, as shown in Fig. 6(a).

705

λ [nm]

Pulse train delay [fs] Fig. 4. Modes population as a function of the pulse train delay s. For each mode (panels (a), (b) and (c) correspond to the r = 788, 1001 (1028) and 1210 cm
1 frequency modes), the CARS spectrum is integrated over the probe bandwidth to yield the shown mode population. The oscillation of the mode population occurs with a 1/cr period along the pulse train delay, therefore allowing a selective excitation. The dash-dotted lines indicate the spectral cuts shown in Fig. 3. The dotted line indicates the period s0 = 129 fs corresponding to the experiment shown on Fig. 5.

715 695

1 a

0 695

b

705

715 695

705

715

λ [nm] Fig. 6. Phase wavepacket control. Modes at 788 and 1001 cm
1 are controlled in amplitude and phase. A crenel-like phase function is applied to the x-polarized excitation pulse (see text). The resulting excitation pulse efficiently populates the two modes and shifts their phase by p. As in Fig. 5(c) and (d), the spectrum at 712 nm is a coherent superposition of the 788 and 1001 cm
1 anti-Stokes emissions sensitive to the modes relative phase: (a) for in-phase probe-bands, the p shift between the 788 and 1001 cm
1 modes leads to a destructive interference; (b) for p phase-shifted probe-bands, the modes still have an opposite phase but their CARS emissions constructively interfere.

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4. Conclusion

References

Single-pulse CARS originated as a method to perform coherent Raman spectroscopy using a single, fixed frequency laser source. The broad bandwidth of the Raman excitation pulse enables, however, not only to perform spectroscopy but also to exert control over the vibrational wavepacket while monitoring its dynamics in a phase-sensitive manner – a significant departure from the capabilities of standard two-color coherent Raman spectroscopy systems. One of the ultimate goals of coherent control is the mastering of chemical reactions. Driving a molecular system on its electronic ground-state is an interesting path to reach such a goal. Indeed, since it does not rely on electronic transitions, it therefore allows to ignore the coupling between the electronic and the nuclear degrees of freedom. Controlling a vibrational wavepacket in amplitude and phase is a first step towards such a control which, at higher pulse energies, involves the exploration of the system anharmonicities. Optical techniques that require selection of a specific non-linear process and phase-sensitivity, such as multidimensional spectroscopy, generally rely on the phase-locking of multiple pulses, resulting in complicated optical setups to ensure interferometric stability. Shaping of a single femtosecond pulse automatically generates phase-locked femtosecond pulse sequences, as has been recently demonstrated for the case of two-photon absorption spectroscopy in an atomic gas [30]. At appropriate pulse energies, the generated pulse sequences used in the above experiments are sufficient for performing phase-sensitive two-dimensional vibrational spectroscopy. Overall, we have shown how a single ultrafast excitation pulse can be tailored to produce a complex pump-probe sequence, from which the properties of the measured system can be easily extracted. With slight variations, this principle can be applied not only to ground-state dynamics but also to probe excited state dynamics via either direct or multiphotonic absorption.

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Acknowledgements Financial support by the Israel Science Foundation and by the Horowitz Foundation is gratefully acknowledged.