Control of Nuclear Dynamics with Strong Ultrashort Laser Pulses - The

Article pubs.acs.org/JPCA

Control of Nuclear Dynamics with Strong Ultrashort Laser Pulses Dominik Geißler,*,† Philipp Marquetand,*,‡ Jesús González-Vázquez,§ Leticia González,‡ Tamás Rozgonyi,∥ and Thomas Weinacht† †

Department of Physics, Stony Brook University, Stony Brook, New York 11794, United States Institute of Theoretical Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria § Instituto de Química Física Rocasolano, CSIC, C/Serrano 119, 28006 Madrid, Spain ∥ Institute of Materials and Environmental Chemistry, Research Centre for Natural Sciences, Hungarian Academy of Sciences, Pusztaszeri út 59-67, Budapest, HU-1025, Hungary ‡

ABSTRACT: We demonstrate how the evolution of a bound vibrational wave packet can be controlled by a strong field laser pulse. We consider two different control schemes within the same molecule (CH2BrI): reshaping of the wave packet via strong field population transfer (“hole burning”), and redirecting its trajectory by dressing the potential energy surface on which the wave packet evolves (“photon locking”). Our measurements are compared with calculations using wave packet propagation on ab initio potential energy surfaces. of CH2BrI, and a weak UV (260 nm) “probe” pulse. The results are compared with calculations which solved the time dependent Schrödinger equation using potentials calculated with ab initio methods. The discussion is organized into five sections. The following section introduces the basic scenario and discusses the dynamics without a control pulse. Sections 3 and 4 describe the theoretical simulations and experimental apparatus. Last but not least sections 5 and 6 discuss the results of the two control schemes in detail.

1. INTRODUCTION Intense ultrafast lasers not only provide the means to study electronic and nuclear dynamics of molecules but also allow for influencing their evolution. Several control schemes have been described and implemented.1−11 Adaptive approaches (often using a learning algorithm in combination with a pulse shaper) have been used to control molecular dynamics. Interpreting the mechanism underlying control in closed loop experiments is challenging although possible with the aid of ab initio electronic structure and quantum dynamics calculations.12−14 The complementary approach is to implement control with a particular mechanism in mind, based on a detailed understanding of the molecular potential energy surfaces involved. The work described in this manuscript belongs to the latter category and uses a strong IR pulse to change the evolution of a nuclear wave packet, whereas key parameters of the control pulse (timing, intensity and duration) are systematically varied. We describe two different schemes for control over the evolution of a vibrational wave packet. One scheme has been termed “photon locking” (or “optical paralysis”)15−21 and mixes (or dresses) two potential energy surfaces to lock a vibrational wave packet in position. The other scheme, termed “hole burning”, uses strong field population transfer to reshape a vibrational wave packet by population transfer in a spatially narrow window. Similar approaches, using position dependent ionization or strong field driven AC Stark shifts, have been used to create or reshape molecular wave packets in diatomic molecules.22−27 Other work using strong fields focused on using light-dressed states to control the branching ratio in dissociation.28−32 In this work we employ a three pulse sequence composed of a strong IR (780 nm) “pump” pulse, an intermediate IR “control” pulse (whose parameters are scanned) to influence the evolution of a nuclear wave packet on the lowest ionic state © 2012 American Chemical Society

2. BASIC SCENARIO The basic scenario is summarized in Figure 1a. Our discussion focuses on control of the motion of a nuclear wave packet on the lowest ionic surface (V1) of CH2BrI. This motion can be described to a large extent as a one-dimensional motion along the I−C−Br bending normal mode coordinate (u),33−35 as will be discussed in section 3. The IR pump pulse creates a nuclear wave packet at the position corresponding to the equilibrium position on the ground neutral state (from here on referred to as FCpump) via strong field ionization. (We note that ionization to excited ionic states also takes place for the pump pulse intensities used in our experiments.36) A subsequent UV probe pulse can transfer the wave packet on V1 at position FCprobe to a higher lying, dissociative state (labeled Vn in Figure 1), thus modulating the parent ion signal (which comes from molecules in V1). This can be observed directly and is shown in Figure 1b or its Fourier transform in panel c. The period of the modulations observed (both in CH2BrI+ and in CH2I+) with a Special Issue: Jörn Manz Festschrift Received: July 5, 2012 Revised: August 3, 2012 Published: August 6, 2012 11434

dx.doi.org/10.1021/jp306686n | J. Phys. Chem. A 2012, 116, 11434−11440

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Figure 1. (a) Basic scheme used in the experiments. A strong IR pump pulse (780 nm) creates a wave packet on the lowest ionic surface V1 of CH2 BrI, which primarily evolves along the I−C−Br bending coordinate. The UV probe pulse (260 nm) can transfer population from V1 within a narrow Franck−Condon window (referred to as FCprobe in the article) to a higher lying dissociative state (Vn), leading to parent ion fragmentation into CH2I+. If the pump−probe time delay is varied, this can be observed as a near-sinusoidal modulation of the parent and CH2I+ fragmentation ion signal, as shown in panel (b). Modulations in the I+ yield that are comparable to the CH2I+ modulations, are also observed, although not shown here. Panel c shows the Fourier transform of the pump probe signal, which has only one dominant peak for a period of about 346 ± 30 fs (highlighted in red). The amplitude and phase of this frequency component is a direct measure of the amplitude and phase (position) of the V1 wave packet, respectively. A second IR pulse (the control pulse, which arrives in between the pump and probe) can distort the V1 potential by coupling it to neighboring ionic states V3/4 and change the wave packet evolution. This can be reflected as a change of amplitude and phase of the pump probe signal.

UV probe pulse, 346 ± 30 fs, agrees well with the calculated period of motion in the V1 potential, 350 fs (section 3), and the period observed with an IR probe 351 ± 11 fs in previous publications.33−35 An IR probe photon provides sufficient energy to the molecule (starting from V1) to dissociate into CH2Br+ and I, but the UV probe leaves the molecule with sufficient energy to produce CH2I+ and Br.37 The phase of the modulations (the phase of the peak in the Fourier transform shown in Figure 1c) is roughly zero, indicating that FCprobe is close to FCpump. We note that there is sufficient energy with a UV probe to also produce I+ (presumably from further fragmentation of CH2I+), and we observe modulations in the I+ yield that are comparable to those in the CH2I+ yield. The modulations in the fragment yields sit on top of a significant background that results from the pump pulse populating excited states of the molecular cation; see ref 38 for a representative time-of-flight mass spectrum. Figure 2 shows the two control mechanisms discussed in this article. State V1 has two closely spaced IR resonances with ionic states V3 and V4, which facilitate control over the wave packet dynamics on V1, and which for the sake of simplicity will be treated as a single broad resonance at “FCcontrol” in this article. Similarly, V3 and V4 will be jointly referred to as V3/4. Section 3 will justify this simplification. The control is most pronounced when the wave packet is in proximity of FCcontrol during the control pulse. This happens twice per round trip of the wave packet with qualitatively different results: In the case where the wave packet is moving from the outer (FCpump, u = 0.85 a.u.) to the inner turning point (u = −0.5 a.u.) we observe photon locking. This is illustrated in Figure 2a and will be discussed in section 5. The IR control pulse dresses V1 and V3/4, such that a “wall” is temporarily introduced on the dressed potential (labeled as V+), which stops and reflects the wave packet. In contrast, when the wave packet is moving from the inner

Figure 2. Two control scenarios discussed in this article. Panel a illustrates the photon locking control scheme: The control pulse dresses the potentials V1 (dashed orange line) and V3/4 (dashed violet line, shifted by one IR photon in energy), such that the wave packet encounters a “wall” on the light-dressed V+ (solid green line). This can hold/reflect the wave packet. Panels b and c illustrate the hole burning control scheme: Depending on the arrival time of the control pulse, parts of the wave packet are removed to V3/4. The control pulse “burns” a spatial hole into the V1 wave packet and changes the center of gravity and momentum distribution. Panel b refers to a control pulse delay shortly before 610 fs (t1), whereas panel c to a delay shortly after 610 fs (t2). This can be observed as shift in magnitude of parent ion modulation depth and phase.

turning point to the outer turning point we observe hole burning, as illustrated in panels b and c. If the control pulse arrives when the front of the wave packet is at FCcontrol, then a hole is burnt into the front of the wave packet, shifting the center of gravity backward (panel b). In contrast, if the control 11435



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assumption is supported by the fact that the oscillation period of the experimental CH2I+ signal is the same as that of the calculated bending mode frequency in V1. The location of FCprobe is determined as u = 0.76 au from a comparison of the experimental offset of the CH2I+ signal with respect to the pump−probe delay and the time-dependent position expectation value of a wave packet moving on V1. The borders of the probe window were defined as u = 0.56 au and u = 0.96 au to match approximately the width of the moving wave packet. Quantum dynamics calculations were performed using the above-mentioned five ionic states (V1, ..., V5) and the neutral ground state. As the ionic states are doublets, two degenerate potential curves represent each ionic state, which are nonetheless termed V1, ..., V5, respectively. Consequently, 11 potentials (5 × 2 ionic potentials + the neutral singlet ground state) are coupled in our simulations. The coupling is achieved by ab initio TDMs and SOCs among the five ionic states (V1, ..., V5) and an ad hoc constant TDM between the neutral ground state and V1. The electric field of the pump and the control pulses were included explicitly in the TDSE. The TDSE is solved on a grid of 128 points with the help of the splitoperator method41 and the fast Fourier technique. A time discretization of 0.01 fs and a spatial discretization of 0.025 au is employed. The grid size was checked for convergence. A detailed description of how the TDSE is solved may be found in ref 33. The strong-field ionization process is modeled using two laser fields instead of the true strong IR pump pulse. These two laser fields are chosen to capture two important aspects of the experimental strong field ionization pulse: (1) Excitation of population from the neutral to the ionic ground state and (2) inducing a Stark shift of the ionic levels during the interaction. The Stark shift is induced by a strong (I0 = 53 × 1012 W cm−2) field with the experimental wavelength of 780 nm, whereas population transfer is caused by the second, short (fwhm = 20 fs) and weak (I0 = 0.53 × 1012 W cm−2) XUV pulse (with hν = 9.25 eV) tuned to be resonant between V0 and the AC-Stark shifted V1. For the simulation of the photon-locking scenario the control pulse intensity is scanned between 0 and 4 GV/m, while its pulse duration is varied by adding second-order phase (starting with 47 fs transform-limited pulse duration). Its position in time is fixed at the same time delay as the pump pulse. For the hole-burning scenario, the control pulse intensity is fixed at 4 GV/m, with a duration of 40 fs, but its time delay is scanned between 0 and 900 fs. In all simulations the molecule is oriented with respect to the electric field polarization so that the control pulse has the strongest interaction with the molecule and no averaging over orientation or laser intensity distribution was taken into consideration. For both control scenarios, the simulations yield the V1 population in the FC window of the probe pulse, Y(t,α). Here t is the time delay between pump and probe pulses and α is a generalized variable summarizing the relevant control pulse parameters: time delay relative to the pump, intensity, and second-order phase. Because Y(t,α) should correspond to the modulations in the parent/fragment ion pump probe signal shown above, one can extract a theoretical prediction for the amplitude A and phase ϕ versus control pulse α. In the context of simulation results, as presented in Figures 3 and 6, we define (with C as the appropriate normalization constant):

pulse arrives when the back of the wave packet is at FCcontrol, then the center of gravity shifts forward (panel c). This is discussed in more detail in section 6. By using control and probe pulses at different frequencies, which couple to different states from V1, the actions of the probe and control can be clearly separated, which simplifies the interpretation. To characterize the wave packet on V1 (modified by the action of the control pulse), we Fourier transformed the pump probe signal. Because the modulations in CH2BrI+, CH2I+, and I+ reflect the same wave packet motion, it is sufficient to study the Fourier transform of any of them. We focused on the parent ion signal, because it has the most favorable signal-to-noise ratio. The amplitude of the Fourier transform at the V1 frequency (corresponding to a period of 351 fs) provides a measure of the amplitude of the wave packet on V1. The phase is proportional to the displacement of the wave packet on V1.

3. CALCULATIONS The picture outlined in the previous section is supported by quantum dynamics calculations on potential energy curves computed previously with ab initio methods. The calculations are restricted to one degree of freedom (the I−C−Br bending coordinate, u). This simplification can be justified by the good agreement of our model with experimental measurements, as demonstrated in previous publications.33−35 The minimum energy geometries of the ground electronic states of the neutral and that of the ionized CH2IBr molecule differ mainly in the I− C−Br bending angle: the angle is smaller for the ion than for the neutral. The ionization into the ground electronic state of the cation therefore induces a wave packet (with a mean vibrational quantum number of 7 and a spread (-full with half max-) of about 5 quantum numbers33), whose motion we simulated by numerically solving the time-dependent Schrödinger equation (TDSE) in one dimension (1D) along the bending normal mode, u, of the cation. The normal mode coordinates were determined by density functional theory,39 and the potential energy curves (PEC), transition dipole moments (TDM), and spin−orbit couplings (SOC) were determined by the state averaged complete active space selfconsistent field (SA-CASSCF) method.40 For details see ref 33. The ground state minimum for the neutral molecule along the coordinate u defines the location of the Franck−Condon region for the pump excitation FCpump, which is located at u = 0.85 au. The lowest two potentials of the ion (V1 and V2) are bound for vertical excitation at FCpump, whereas the rest of the potentials (V3, V4, and V5) computed and involved in the simulation are (either directly or indirectly) dissociative along the C−I bond. The two close lying excited state potentials, V3 and V4, come into resonance with V1 at roughly the same bending angle for the photon energy of the IR control field, which justifies their combination into V3/4 as mentioned above. Accordingly, we will use FCcontrol for the location (at u = 0.34 au), where resonance between V1 and V3/4 is obtained with the IR control pulse. Nevertheless V3 and V4 and their resonances with V1 are treated as separate in the simulations described below. Potentials beyond V5 were not computed and are not involved in the simulations. Consequently, Vn, from which C− Br dissociation occurs, and which gives rise to the experimental signal is only schematically depicted in Figure 1a, but it is not included explicitly in our calculations. The population arriving in Vn is assumed to be proportional to the population in a Franck−Condon window around FC probe in V 1 . This

A(α) = max t ∈ (t0 , t0+ 351) Y (t ,α) − min t ∈ (t0 , t0+ 351) Y (t ,α) 11436


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electrostatic lens (similar to the one described in ref 44) maps the momentum of the fragments at interaction point onto position at the detector. The detector is position sensitive and is composed of two microchannel plates (MCPs) and a phosphor screen. The ion signal is digitalized either by using a camera (for momentum resolved measurements) or by reading the electron current off the phosphor screen after a highpass filter and a fast A/D board (yielding time-of-flight resolution). The MCPs can be gated, which allows us to single out a particular ion species in momentum imaging mode. The data presented in this article only used the time-of-flight capability of the setup, although the momentum resolution was utilized to exclude systematic errors (section 6).

tYc(t ,α) dt

0

The time interval (t0,t0+351) fs is chosen such that it covers one complete round trip of the wave packet on V1 (starting from FCpump) but has no overlap with the control pulse. In addition to the detailed quantum dynamics calculations, we also carry out a simplified calculation to test our interpretation of the hole burning control mechanism. This simulation only includes V1 explicitly. The interaction with the control pulse is implemented by removing all population from V1 at FCcontrol in the window 0.325 ± 0.225 au at the arrival time of the control pulse. The resulting “cut wave packet” is then propagated on V1 and A, and ϕ is calculated as for the quantum dynamics calculations above.

5. CONTROL BY PHOTON-LOCKING In this section we discuss the influence of the control pulse on the wave packet when moving from the outer to the inner turning point on V1. This scenario is a form of photon-locking, as illustrated in Figure 2a. While the control pulse is interacting with the molecule, the V1 wave packet propagates on the dressed state potential V+, which changes its character from that of bare V1 to bare V3/4 at FCcontrol.33 As pointed out before, this effectively adds a “wall” at FCcontrol that can block or reflect the wave packet from propagating from FCpump. Experimentally, the control pulse is superimposed with the IR pump pulse and stretched out in time by adding second-order phase. Its pulse energy and duration are varied with our pulse shaper, between 0 and 19.6 μJ and 75 and 240 fs (fwhm), respectively. As discussed below, this range for the control pulse parameters is selected such that there is no ionization due to the control pulse alone. For a sufficiently high control pulse field strength, the “wall” is high enough to trap the population between FCcontrol and FCpump in the dressed state V+. In this case the wave packet will not cross FCcontrol but will rather be reflected back toward the outer turning point of the dressed potential, or simply held in the dressed potential near FCpump. Thus there is negligible population transfer to V3/4 induced by the control pulse; this is confirmed by both the measurements and calculations. The distinction between reflection and holding of the wave packet is subtle given the fact that for a strongly dressed potential, the displacement between the minimum on dressed V1 and FCpump can be smaller than the width of the wave packet (which is about 0.35 au, at creation). As the control pulse is turning off, the minimum of V+ approaches the intersection of V1 and (V4 − hν), lowering the total energy of the wave packet (the energy is transferred to the control field). Once the field is sufficiently low, the wave packet can leak through the wall and cross FCcontrol. The decreased energy of the wave packet means that it does not reach FCprobe completely on subsequent round trips. Thus, one expects a decrease in the modulation depth in the parent ion signal due to the influence of the control pulse. In contrast, if the locked wave packet were released suddenly (completely nonadiabatically), then rather than a decrease in V1 wave packet amplitude, one would expect a delay of the wave packet proportional to the duration of the control pulse, which would manifest itself as a phase shift in the pump probe signal. To observe a phase shift in the pump probe signal as a function of control pulse duration, one would require a rapid turn off of the control pulse, and that all molecules experience the same control pulse intensity. However, angle averaging of the control pulse polarization relative to the V1 − V3/4 transition dipole moment (TDM) results in many molecules not experiencing

4. EXPERIMENTAL SETUP AND DATA ACQUISITION The laser system has been described in detail in prior publications.42 We use a Kerr-lens mode-locked titanium sapphire oscillator in combination with a chirped pulse multipass amplifier. This source provides a 1 kHz train of 30 fs pulses, with a central wavelength of 780 nm, and a pulse energy of 1 mJ. The main beam is split into two arms with a 60:40 ratio. One arm contains a frequency tripling setup, providing 1.6 μJ UV (260 nm) pulses with a pulse duration of ∼50 fs. The length of this UV arm can be varied with a delay stage. The second arm is equipped with an acousto-optic modulator (AOM) based pulse shaper,43 which can produce pulses with up to 300 μJ pulses. The UV and shaped IR beams are collinearly combined using a dichroic beam splitter and focused into a molecular beam in the vacuum chamber. The pulse shaper is used to create a pulse sequence of one strong, unshaped IR pulse used as a “pump” and a weaker shaped IR pulse, referred to as “control”. The pump pulse ionizes the molecules and launches a vibrational wave packet on the ground ionic state. The control pulse modifies the wave packet on the ground ionic state surface, which is then probed by the UV pulse referred to as the “probe”. The probe time delay is scanned between −100 and +2500 fs relative to the pump pulse. The probe pulse intensity is fixed at about 4.5 × 1012 W cm−2. It promotes a portion of the wave packet evolving on the ground ionic state to a higher lying dissociative state of the ion (Vn), allowing us to follow the wave packet evolution by monitoring the parent and fragment molecule ion yields. In the photon-locking control scheme the peak intensity of the pump was about 5.1 × 1013 W cm−2. The control pulse was centered at the same time delay as the pump pulse, but its pulse duration was varied between a minimum duration of about 50 fs and a maximum of 240 fs by applying second-order spectral phase (i.e., a linear chirp). The intensity was scanned from 0 to a maximum peak intensity (for an unshaped control pulse) of 1.7 × 1013 W cm−2. In the hole-burning scheme the control pulse was unshaped (with a duration of about 50 fs), but its time delay (relative to the pump) and intensity were varied. Its intensity was fixed at 1.7 × 1013 W cm−2, while the pump had an intensity of about 5.1 × 1013 W cm−2. The laser pulses interact with the target molecule CH2BrI in a molecular beam chamber with a background pressure of about 10−6 Pa. With the introduction of the sample, the total pressure rises to about 6 × 10−4 Pa. All results presented in this paper are based on measuring the ion yield after the sample interacts with the sequence of laser pulses. The vacuum chamber is equipped with a velocity map imaging spectrometer. An 11437



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the full effect of the control field. Thus, molecules whose TDM is not aligned with the control pulse polarization do not see the full height of the wall, leading to the wave packet in many molecules to escape “over” the wall and smear out the expected phase delay. As a result, we do not observe a significant phase shift in the pump probe signal proportional to the control pulse duration. In fact, although we do measure a small phase shift in the pump probe signal with the control pulse, the sign and size of the phase advance are consistent with a minor systematic error, rather than with photon locking. The modulation depth in the pump probe signal from calculations is shown in Figure 3. As expected on the basis of

Figure 4. Measured decrease in modulation amplitude as a function of control pulse field strength relative to unperturbed pump probe signal. Results are shown for different control pulse durations. For control pulse durations less than 100 fs, no decrease in modulation amplitude is observed. Note that the x axis shows the peak field strength corresponding to an unshaped (transform limited) pulse. The peak field strengths for the chirped pulses are therefore less by the square root of the ratio of the unshaped to the chirped pulse duration. This choice of showing the peak field strength for an unshaped pulse rather than for the chirped pulses is made to allow for comparison of pulses with the same energy. The choice of using peak field strength rather than pulse energy is made to facilitate comparison between experiment and theory.

and phase of the parent ion pump probe signal are used to characterize the V1 wave packet. The effect on the modulations is captured in Figure 5.

Figure 3. Results from numerical integration of TDSE. The main prediction of the photon-locking effect is a decrease of the modulation depth of the parent ion yield, with increasing time duration and intensity of the control pulse. The x-axis refers to the field strength of the control pulse alone. Its pulse duration is varied by adding second order phase. The modulation depth is normalized to the unperturbed case. The increase in modulation depth with field strength for the shortest control pulse duration is an artifact of the simple model used to describe the ionization process.

the discussion above, the calculations predict a decrease in modulation depth with increasing intensity and time duration of the control pulse. The experimental result is shown in Figure 4. One can see that there is qualitative agreement between the calculations and experimental data. The quantitative disagreement is due to the angle averaging present in the experimental measurements, but not included in the calculations.

6. CONTROL BY HOLE-BURNING This section discusses the influence of the control pulse on the wave packet when going from the inner to the outer turning point on V1. Experimentally, control time delays in the interval (560, 660) fs (this corresponds to a ± 50 fs window around the fourth passage of the V1 wave packet through FCcontrol at 610 fs) have been studied. The probe pulse delay was scanned between 1100 and 2200 fs. As pointed out in section 2, the V1 wave packet motion is periodic (as reflected in the period pump probe signal in Figure 1b) and shows little dephasing within the first few picoseconds. Thus qualitatively similar results are achieved when using an IR control pulse delay corresponding to the second/fourth/etc. passage through FCcontrol, i.e., from inner to outer turning point. From the experimental point of view this is convenient, because one can choose time delays for the pulses long enough to avoid systematic effects due to optical interference. As described in section 2, the amplitude

Figure 5. Summary of the measured effect of the IR control pulse on the V1 wave packet motion versus IR control pulse timing. It shows the amplitude and phase advancement (difference in phase of the pump probe signal for the evolution with and without the control pulse) of the V1 wave packet modulations after the control pulse versus control pulse timing. The amplitude is normalized to 1 at its maximum.

The decrease in amplitude reflects the passage of the V1 wave packet through FCcontrol. because the control pulse is “strong” (i.e., pulse area larger than π), it can effectively transfer a significant fraction of the wave packet on V1 to V3/4, leading to a reshaping of the remaining wave function on V1. The difference in phase, of up to 0.15 rad, can be interpreted as hole-burning: The control pulse removes a portion of the wave packet, which shifts the center of gravity of the wave packet and 11438



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responsible for the phase advances and delays seen in the full calculations and measurements.

introduces additional momentum components. Excitation when the wave packet is centered at FCcontrol leads to the greatest decrease in the amplitude of modulation, but not much phase advance or delay. In contrast, excitation when the front/back of the wave packet is at FCcontrol can result in a phase delay/ advance of the wave packet because the portion remaining on V1 has its center of gravity behind/ahead with respect to the original undisturbed wave packet. To verify this interpretation, two different sets of simulations have been performed (as described in section 3) to calculate the change in amplitude and phase induced by the control pulse. The first is based on solving the TDSE including the interaction with the control pulse field (solid lines of Figure 6),

7. SYSTEMATIC EXPERIMENTAL ERROR CHECKS Several experimental checks have been performed to give upper bounds on systematic effects that also affect the depth of modulation in the photon locking measurements. We consider two additional effects that could show a similar signal: (1) ionization due to the control pulse, and (2) population transfer to V3/4 via the control pulse. The modulation depth of the pump probe signal is found to increase monotonically with increasing pump intensity. Thus we can rule out the first possibility in the case of the photon locking control, as it actually would lead to an increase of the amplitude of modulation, whereas we observe a decrease in the amplitude with increasing control pulse field strength (Figure 4). In the case of the hole burning experiment, we performed measurements at several control field strengths. We find that if the control pulse intensity is too high, there is some ionization due to the control pulse, which can be identified by phase shifts in the pump probe signal, which are qualitatively different from the calculations and the results for lower control pulse intensities. Thus, we show results for a control field strength where we do not have any ionization due to the control pulse. With regard to (2), we consider possible population transfer by the tail of the control pulse to V3/4 at around FCcontrol. This would decrease the overall V1 population (instead of locking it). The population loss to V3/4 with a chirped IR pulse can be measured directly (which is described in ref 34 in detail) and is found to be roughly constant for pulse parameters with an energy above 9 μJ and a pulse duration longer than 127 fs (covering most of the range shown in Figure 4). Thus we conclude that the change in depth of modulation of the ion yield with increasing control pulse amplitude is due to the effect of the “wall” in the dressed state PES rather than population transfer. In addition to these checks, we also performed measurements for parallel and perpendicular polarizations of the control pulse relative to the probe pulse. Though earlier measurements indicated that the ionization to V1 is not very sensitive to the alignment of the molecule relative to the pump pulse polarization vector,33 our current measurements show similar control for both parallel and perpendicular polarizations, indicating that the TDMs for the control transition (V1 to V3,4) and the probe transition (V1 to Vn) are not parallel. This means that molecules that interact to the probe pulse and are promoted to Vn see a reduced control pulse field strength (given by the projection of the control pulse polarization vector onto the V1 to V3,4 TDM). Therefore there is some averaging over control pulse field strengths in our experimental measurements. This leads to differences in the degree of control in comparing experiment with theory.

Figure 6. Solid lines: results from numerical integration of the TDSE. The blue line and the green line show the amplitude and phase advancement respectively as a function of control pulse delay. The minimum at 610 fs is due to the control pulse transferring population to the dissociative V4 and thus reducing the amplitude of the V1 wave packet. The model also predicts a change in the arrival time of the residual V1 population. This is captured in the green line (phase). Dashed lines: results of the simplified simulations that propagate the perforated wave packet. The blue line (amplitude) shows the total wave packet amplitude at FCprobe on V1 as a function of the control pulse delay.

and the second is a simplified calculation described below (dashed lines). The TDSE calculations including the interaction with the field demonstrate qualitative agreement with experiment. They reproduce the loss of V1 population when the wave packet passes through FCcontrol at 610 fs. The simulations predict a larger phase delay/advancement (0.3−0.6 rad) than observed in experiment. The difference between theory and experiment in the magnitude of the phase and amplitude changes is due to the experimental orientation averaging, which means that many molecules see a reduced control pulse Rabi frequency along the V1 − V3/4 TDM. To test whether hole-burning indeed captures the essence of the control mechanism, we also carried out a calculation where we cut out a narrow portion of V1 wave packet around FCcontrol at the arrival of the control pulse and then propagated the perforated wave packet from FCcontrol to FCprobe, without taking further interaction into account. These simplified calculations (without explicit treatment of the control pulse field) shown in the dashed lines in Figure 6 agree with the earlier simulations both qualitatively and quantitatively. This indicates that spatially selective population transfer (hole burning) is

8. CONCLUSION In conclusion, we have demonstrated two different mechanisms for controlling wave packet evolution in a small polyatomic molecule. Both “hole burning” and “photon locking” were demonstrated and the results were shown to be in qualitative agreement with solutions of the TDSE. In the case of photon locking, the strong field of the control laser pulse distorts the potential energy surface on which the wave packet evolves. This surface can be distorted such that the wave packet is held, or 11439



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“locked” in position for the duration of the control pulse. To our knowledge, this is the first experimental demonstration of “photon locking” for a vibrational wave function. In the case of hole burning, the strong field control pulse transfers a portion of the vibrational wave function to an excited state surface, shifting the center of gravity of the remaining wave packet. Both approaches require strong field (nonperturbative) interactions with the control pulse.

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(23) Goll, E.; Wunner, G.; Saenz, A. Phys. Rev. Lett. 2006, 97, 103003. (24) Goto, H.; Katsuki, H.; Ibrahim, H.; Chiba, H.; Ohmori, K. Nat. Phys. 2011, 7, 383−385. (25) Bryan, W. A.; Calvert, C. R.; King, R. B.; Nemeth, G. R. A. J.; Alexander, J. D.; Greenwood, J. B.; Froud, C. A.; Turcu, I. C. E.; Springate, E.; Newell, W. R.; Williams, I. D. Phys. Rev. A 2011, 83, 021406. (26) Niikura, H.; Villeneuve, D. M.; Corkum, P. B. Phys. Rev. Lett. 2004, 92, 133002. (27) Niikura, H.; Villeneuve, D.; Corkum, P. Phys. Rev. A 2006, 73, 021402. (28) Sussman, B.; Ivanov, M.; Stolow, A. Phys. Rev. A 2005, 71, 051401. (29) Marquetand, P.; Richter, M.; González-Vázquez, J.; Sola, I.; González, L. Faraday Discuss. 2011, 153, 261−273. (30) Bajo, J. J.; González-Vázquez, J.; Sola, I. R.; Santamaria, J.; Richter, M.; Marquetand, P.; González, L. J. Phys. Chem. A 2012, 116, 2800−2807. (31) Kinzel, D.; Marquetand, P.; González, L. J. Phys. Chem. A 2012, 116, 2743−2749. (32) Richter, M.; Marquetand, P.; González-Vázquez, J.; Sola, I.; González, L. J. Chem. Theory Comput. 2011, 7, 1253−1258. (33) González-Vázquez, J.; González, L.; Nichols, S. R.; Weinacht, T. C.; Rozgonyi, T. Phys. Chem. Chem. Phys. 2010, 12, 14203−14216. (34) Geißler, D.; Rozgonyi, T.; González-Vázquez, J.; González, L.; Marquetand, P.; Weinacht, T. C. Phys. Rev. A 2011, 84, 053422. (35) Nichols, S. R.; Weinacht, T. C.; Rozgonyi, T.; Pearson, B. J. Phys. Rev. A 2009, 79, 043407. (36) Geißler, D.; Rozgonyi, T.; González-Vázquez, J.; González, L.; Nichols, S.; Weinacht, T. Phys. Rev. A 2010, 82. (37) Lago, A. F.; Kercher, J. P.; Bödi, A.; Sztáray, B.; Miller, B.; Wurzelmann, D.; Baer, T. J. Phys. Chem. A 2005, 109, 1802−1809. (38) Langhojer, F.; Cardoza, D.; Baertschy, M.; Weinacht, T. J. Chem. Phys. 2005, 122, 014102. (39) Koch, W.; Holthausen, M. A Chemist’s Guide to Density Functional Theory; Wiley-VCH: New York, 2001. (40) Roos, B. O.; Taylor, P. R.; Siegbahn, P. E. M. Chem. Phys. 1980, 48, 157−173. (41) Feit, M.; Fleck, J.; Steiger, A. J. Comput. Phys. 1982, 47, 412− 433. (42) Langhojer, F.; Cardoza, D.; Baertschy, M.; Weinacht, T. J. Chem. Phys. 2005, 122, 014102. (43) Dugan, M. A.; Tull, J. X.; Warren, W. S. J. Opt. Soc. Am. B 1997, 14, 2348−2358. (44) Eppink, A. T. J. B.; Parker, D. H. Rev. Sci. Instrum. 1997, 68, 3477−3484.

AUTHOR INFORMATION

Corresponding Author

*E-mail: D.G., [email protected]; P.M., philipp. [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge support from the National Science Foundation under award number 0854922, from a joint project funded by the Deutsche Forschungsgemeinschaft and the Hungarian Academy of Sciences (No. 436 UNG 113/188/0-1) and the European COST Action CM0702. J.G.-V. also acknowledges support from a Juan de la Cierva contract.

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REFERENCES

(1) Shapiro, M.; Brumer, P. Rep. Prog. Phys. 2003, 66, 859−942. (2) Engel, V.; Meier, C.; Tannor, D. J. In Advances in Chemical Physics; Rice, S. A., Ed.; Advances in Chemistry and Physics; John Wiley & Sons Inc.: 605 3rd Ave, New York, NY 10016 USA, 2009; Vol. 141, pp 29−101. (3) Bergmann, K.; Theuer, H.; Shore, B. W. Rev. Mod. Phys. 1998, 70, 1003−1025. (4) Stuart, A. R.; Meishan, Z. Optical Control of Molecular Dynamics; Wiley-Interscience: New York, 2000. (5) Dantus, M. Annu. Rev. Phys. Chem. 2001, 52, 639. (6) Shapiro, M.; Brumer, P. Principles of the Quantum Control of Molecular Processes; Wiley-Interscience: New York, 2003. (7) Hertel, I. V.; Radloff, W. Rep. Prog. Phys. 2006, 69, 1897. (8) Nürnberger, P.; Vogt, G.; Brixner, T.; Gerber, G. Phys. Chem. Chem. Phys. 2007, 9, 2470−2497. (9) Worth, G. A.; Sanz, C. S. Phys. Chem. Chem. Phys. 2010, 12, 15570−15579. (10) Brif, C.; Chakrabarti, R.; Rabitz, H. New J. Phys. 2010, 12, 075008. (11) Sussman, B. J. Am. J. Phys. 2011, 79, 477−484. (12) Daniel, C.; Full, J.; González, L.; Lupulescu, C.; Manz, J.; Merli, A.; Vajda, Š.; Wöste, L. Science 2003, 299, 536−539. (13) White, J. L.; Carroll, E. C.; Spears, K. G.; Sension, R. J. Isr. J. Chem. 2012, 52, 397−406. (14) Cardoza, D.; Baertschy, M.; Weinacht, T. Chem. Phys. Lett. 2005, 411, 311−315. (15) Sleva, E. T.; Xavier, I. M., J.; Zewail, A. H. J. Opt. Soc. Am. B 1986, 3, 483−487. (16) Bartana, A.; Kosloff, R.; Tannor, D. J. Chem. Phys. 1997, 106, 1435−1448. (17) Malinovsky, V.; Meier, C.; Tannor, D. Chem. Phys. 1997, 221, 67−76. (18) Bayer, T.; Wollenhaupt, M.; Sarpe-Tudoran, C.; Baumert, T. Phys. Rev. Lett. 2009, 102, 023004. (19) Tannor, D. J. Introduction to Quantum Mechanics - A timedependent perspective; University Science Books: Mill Valley, CA, 2007. (20) González-Vázquez, J.; González, L.; Sola, I. R.; Santamaria, J. J. Chem. Phys. 2009, 131, 104302. (21) Sola, I. R.; Chang, B. Y.; Rabitz, H. J. Chem. Phys. 2003, 119, 10653−10657. (22) Fang, L.; Gibson, G. N. Phys. Rev. Lett. 2008, 100, 103003. 11440


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