Letter pubs.acs.org/JPCL
Transient Two-Dimensional Infrared Spectroscopy in a Vibrational Ladder Vincent Kemlin, Adeline Bonvalet, Louis Daniault, and Manuel Joffre* Laboratoire d’Optique et Biosciences, Ecole Polytechnique, CNRS, INSERM, Université Paris-Saclay, 91128 Palaiseau, France ABSTRACT: We report on transient 2D Fourier transform infrared spectroscopy (2DIR) after vibrational ladder climbing induced in the CO-moiety longitudinal stretch of carboxyhemoglobin. The population distribution, spreading up to seven vibrational levels, results in a nonequilibrium 2DIR spectrum evidencing a large number of peaks that can be easily attributed to individual transitions thanks to the anharmonicity of the vibrational potential. We discuss the physical origin of the observed peaks as well as the qualitative behavior of the subsequent dynamics governed by population relaxation in the vibrational ladder.
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combination with advanced mid-IR pulse-shaping technologies, optimal control has been successfully demonstrated, with, for example, the enforcement of an abrupt cutoff in the vibrational population above a specific level.14 Clearly, the high degree of control in the vibrational population that can now be achieved should make VLC an ideal playground for extending transient2DIR methods to highly excited vibrational systems. We report on the first observation of transient 2DIR spectroscopy on a vibrational system brought extremely far from equilibrium by VLC. In contrast with the recent studies mentioned above where VLC resulted from higher order effects in the 2DIR pulse sequence itself,15 here we clearly separate the VLC process, achieved by a downchirped mid-IR pulse playing the part of the actinic pulse, from the subsequent 2DIR measurement. It is thus straightforward to shape the VLC pulse independently from the 2DIR pulses, which must be transformlimited. Because of the large number of populated levels, the measured 2DIR spectra exhibit a large number of peaks resulting from new pathways made possible by the fact that the system is not at equilibrium. We discuss how 2DIR spectroscopy on a vibrational ladder provides new insight on vibrational relaxation processes by mapping these population transfers in the sign, amplitude, and dynamics of new cross peaks hidden to 1D experiments. Figure 1 shows the experimental setup. A 1 kHz amplified Ti:sapphire system (Libra-HE, Coherent) pumps a two-stage setup made of the double-pass parametric amplification of a near-infrared white-light continuum, followed by a differencefrequency generation stage mixing signal and idler. The mid-IR pulses thus generated are centered at 1900 cm−1 and have a
he availability of intense mid-infrared (mid-IR) femtosecond pulses has opened the way to a great variety of powerful experimental methods sensitive to the vibrational dynamics of a molecular system. Depending on the purpose of the experiment, which may be either to learn new information on the system or to actually control its vibrational state toward a specific target, these methods may be categorized into either vibrational spectroscopy or vibrational control. Emblematic illustrations of these two categories are, respectively, twodimensional infrared (2DIR) spectroscopy and vibrational ladder climbing (VLC). When implemented in time domain, 2DIR spectroscopy1−3 relies on a sequence of three pulses, each of which being associated with one of the field−matter interactions needed for inducing a third-order vibrational coherence in the system. Transient 2DIR spectroscopy4−10 consists of inserting an additional pulse, usually in the UV or visible spectral domain and often called the actinic pulse, either before the entire 2DIR pulse sequence or between the second and third 2DIR pulses. VLC consists of exciting high values of the vibrational quantum number n of a specific molecular vibration by use of an intense broadband mid-IR femtosecond pulse.11−15 Because of molecular anharmonicity, the transition frequency between higher excited states decreases so that best efficiencies are achieved when two conditions are met: The pulse spectral width must be broad enough for encompassing a large number of transitions, and the pulse must be downchirped so that different transition frequencies are sequentially addressed with the proper time ordering. VLC has been previously applied to various molecular systems, including large molecules such as hemoproteins,13 and has even been shown to trigger groundstate ligand photolysis in small molecules.12 VLC has also been recently observed in attenuated total reflectance 2DIR spectroscopy by taking advantage of the enhancement of the electromagnetic field near a metal surface.15 Furthermore, in © 2016 American Chemical Society
Received: July 13, 2016 Accepted: August 10, 2016 Published: August 10, 2016 3377
DOI: 10.1021/acs.jpclett.6b01535 J. Phys. Chem. Lett. 2016, 7, 3377−3382
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Figure 1. Pulses from a 4 mJ 1 kHz Ti:Sa amplifier seed an optical parametric amplifier (OPA) with subsequent difference frequency generation (DFG). Generated mid-IR pulses are split into four pulses: the probe, two 2D pumps, and the chirped pump for VLC. The four pulses are focused in the sample, and the transmitted probe is detected by chirped-pulse up-conversion (CPU).
Figure 2. (a) Pump−probe pulse sequence and (d) four-pulse sequence used for 2DIR measurement following VLC. (b,c) Differential pump−probe spectra obtained for T0 = 18 (b) and 23 ps (c). Blue dots are experimental data points, whereas the black dashed line is a sixth-order polynomial background and the red line is a multigaussian fit, with 8.5 cm−1 fwhm. (e,f) Transient 2DIR spectra obtained for T0 = 18 (e) and 23 ps (f), with a waiting time T = 1 ps.
spectral width of 150 cm−1 fwhm. The mid-IR pulses are then split into four pulses, the first one of energy equal to 16 μJ being dedicated to VLC, whereas the three others, each of 0.15 μJ energy, are used for recording the 2DIR spectra. VLC is achieved here using a mid-IR pulse down-chirped by linear dispersion in a 6.3 cm thick CaF2 crystal and focused to a spot size close to 150 μm. The associated second-order spectral phase is −44 000 fs2, resulting in a fwhm duration of ∼1.2 ps. The measurement of the 2DIR spectra is achieved using the pump−probe geometry.16 As shown in Figure 1, the corresponding pump beam consists of two collinear pulses, hereafter referred to as the 2D pump pulses to distinguish them from the main chirped pump pulse. They are separated by a delay τ interferometrically controlled through the simultaneous acquisition of the linear autocorrelation function and of the interference signal generated by a copropagating HeNe beam, allowing rapid-scanning acquisition of the 2DIR spectra. The transmitted probe mid-IR spectrum is recorded on a CCD camera using CPU,17,18 which allows an infrared spectral resolution better than 1 cm−1.19,20 Detrimental spectral interferences resulting from scattering of the pump pulses are
suppressed using two mirrors mounted on oscillating piezoelectric actuators.21 Preparation of the carboxyhemoglobin (HbCO) sample (heme concentration 10 mM) has been described elsewhere.22 Note that switching from a pump−probe to a transient 2DIR setup, respectively, associated with the pulse sequences schematized in Figure 2a,d, is easily achieved by merely unblocking the 2D-pump beam of the experimental setup shown in Figure 1. Figure 2b,c displays the 1D differential pump−probe spectra measured for two different delays between the centers of the chirped-pump and probe pulses, namely, T0 = 18 and 23 ps. As already reported,13 these spectra exhibit a sequence of equally spaced peaks owing to the constant anharmonicity, Δ = −25 cm−1, of the vibrational ladder. Indeed, assuming a slightly anharmonic oscillator, the transition frequency ωn+1,n between level n and level n + 1 can be approximated with the law ωn + 1, n = ω1,0 + nΔ
(1)
where ω1,0 ≈ 1950 cm−1 corresponds to the fundamental transition frequency. This relation allows a straightforward 3378
DOI: 10.1021/acs.jpclett.6b01535 J. Phys. Chem. Lett. 2016, 7, 3377−3382
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The Journal of Physical Chemistry Letters attribution of the peaks observed in Figure 2b,c, from n = 0 to 6 for wavenumbers decreasing from 1950 down to 1800 cm−1. The bleach at 1950 cm−1 (positive peak) corresponds to a decrease in the CO-stretch absorption consecutive to pump excitation of the fundamental level. The six other peaks at frequencies ωn+1,n result from the competition between absorption from level n and stimulated emission from level n + 1. The negative peaks observed in most cases thus indicate a net absorption due to a population usually greater for lower levels, at least for the two pump−probe delays shown in Figure 2, where a significant amount of vibrational relaxation has taken place after VLC. Furthermore, the peak distribution clearly shifts to the right when the pump probe delay varies from 18 to 23 ps, reflecting additional population relaxation. Figure 2e,f displays 2DIR spectra measured after vibrational climbing for T = 1 ps and T0 = 18 and 23 ps. The nonequilibrium “initial” states in these two figures are different and result from free relaxation in the ladder over the time T0 elapsed after VLC. Adjusting T0 and T independently is a key feature of the pulse sequence used in our experimental approach as it allows a high degree of control over the nonequilibrium population distribution. Note that T0 is chosen much longer than the homogeneous dephasing time in this system (2.3 ps according to previous 2DIR measurements22), so that all coherence terms induced during the VLC excitation have relaxed, allowing to assume a fully incoherent population distribution. The measured 2DIR spectra exhibit far more peaks than the usual equilibrium 2DIR spectra, obviously as a consequence of the greater number of levels populated by VLC. These peaks are clearly arranged on a square grid corresponding to different vibrational transitions for the 2D pump and probe pulses. In each 2DIR spectrum, the first line, associated with a 2D pump transition from n = 0 to 1 (at 1950 cm−1), exhibits two peaks of opposite signs. As shown, for example, in the outlined area labeled (0) in Figure 2e, there is one peak on the diagonal and one peak left of the diagonal, as in an equilibrium 2DIR spectrum. In contrast, the other lines in the 2DIR spectra exhibit most often a three-peak structure, with one peak to the left and one peak to the right of the diagonal peak (see, e.g., outlined area labeled (2) in Figure 2e,f). To get a better understanding of the multipeak structure observed in Figure 2e,f, we start by drawing in Figure 3a−d the rephasing Feynman diagrams1,3 starting from a population in level n, assuming a coupling to level n+1 through dipolar interaction with the 2D-pump laser field at frequency ωn+1,n. The first three diagrams, corresponding to stimulated emission (a), bleaching (b), and excited-state absorption (c) are already found in equilibrium 2DIR spectroscopy. However, the fourth diagram (d) can only occur for n ≥ 1 because the final induced coherence |n⟩⟨n − 1| cannot exist when n = 0. Another difference with equilibrium spectra is that level n + 1 will be also populated by VLC so that we must consider additional diagrams starting from |n + 1⟩⟨n + 1| instead of |n⟩⟨n|. These diagrams, shown in Figure 3e−h, are associated with the same ωn+1,n 2D pump frequency as long as we simply move the first arrow from the bra side to the ket side. This change results in a contribution of opposite sign as compared with the first four diagrams, yielding a total contribution to the third-order response function proportional to the population difference (ρn,n − ρn+1,n+1). The overall effect of the 2D pump is thus proportional to the population difference, as a result of the competition between absorption and stimulated emission. Finally, taking into account the nonrephasing Feynman
Figure 3. (a−d) Rephasing double-sided Feynman diagrams starting from |n⟩⟨n| and corresponding to induced stimulated emission (a), bleaching resulting from initial state depletion (b), excited-state absorption (c), and decrease of stimulated emission (d). (e−h) Similar diagrams obtained when starting from |n + 1⟩⟨n + 1|. (i) Typical population distribution in the vibrational ladder. The vertical arrows highlight in a different way the process associated with diagram (d), where the 2D pump depletes level n = 2, resulting in a decrease in stimulated emission experienced by the probe at frequency ω2,1.
diagrams, we obtain a total of 16 quantum pathways instead of only 6 in case of equilibrium 2DIR spectroscopy. Figure 3i shows a typical population distribution after VLC and population relaxation that corresponds to the experimental situation shown in Figure 2b,e and that strongly deviates from a time-independent equilibrium distribution. Let us now give an interpretation of the peaks observed in the 2DIR spectra, in terms of both Feynman diagrams and pump−probe measurement spectrally resolved along the 2D pump and probe axes. The ωn+1,n frequency component of the 2D pump promotes population from level n to n + 1, as shown by the arrow drawn in Figure 3i for n = 2, thus inducing stimulated emission (diagram (a)) and bleaching (diagram (b)) for a probe 3379
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Figure 4. Full sequence of raw 2DIR spectra after VLC in HbCO measured for T0 = 18 ps and waiting times T = 1, 2, 3, 4, 5, and 10 ps. As compared with Figure 2, the colorscale has been expanded to better visualize the signal at larger waiting times. Saturated values are shown in white.
effects of very different nature. The first effect is related to excessive energy in the 2D pump pulses, so that higher-order terms come into play. Indeed, after the expected n → n + 1 transition induced by the 2D pump, two additional interactions with the 2D pump field can transfer some population from level n + 1 to level n + 2, or from level n to level n − 1, so that new peaks will appear at probe frequencies ωn+3,n+2 and ωn−1,n−2. Such a peak is indeed observed, for example, to the left of the area labeled (2) in Figure 2e,f, at a probe wavenumber of 1850 cm−1. We note that this VLC-like process triggered by the 2D pump pulse itself has been recently observed in a quite different experimental context.15 Because the amplitude of this higher order peak is known to be quadratic with respect to 2D-pump pulse energy,15 whereas the 2DIR signal is linear, the simplest method to reduce this effect would be to reduce the 2D-pump pulse energy. However, this approach turns out to be quite challenging as the resulting decrease in 2DIR signal would make it more difficult to detect against the background resulting from scattering by the chirped pulse, whose energy is already two orders of magnitude greater than that of the 2DIR pulses. Thus, the current level of signal-to-noise ratio in our experiment did not allow us to choose a better compromise between pulse energy and signal level, where such peaks could be entirely eliminated. Furthermore, getting rid of these peaks is made more difficult left of the diagonal due to the fact that the transition strength increases with vibrational quantum number. Indeed, for a harmonic oscillator the dipole associated with a transition from level m to level m + 1 reads μm + 1, m = m + 1 μ1,0 . Combining the higher-order interaction with the 2D pump and the interaction with the probe at appropriate frequencies, we thus obtain scaling factors respectively proportional to (n + 2)(n + 3) and n(n − 1) for the two probe frequencies discussed above (ωn+3,n+2 and ωn−1,n−2). Considering the case n = 2, this means that this higher-order contribution will yield a peak at a probe frequency of 1850 cm−1 with an amplitude ten times greater than for the peak at 1950 cm−1. We conclude that although this higherorder effect explains the peaks observed further left of the diagonal, it will play only a minor role in the peaks observed
frequency identical to that of the 2D pump. The associated decrease in probe absorption explains the series of positive (blue) peaks observed on the diagonal in Figure 2e,f. As in equilibrium 2DIR spectroscopy, the excited-state absorption from level n + 1 to level n + 2 (diagram (c)) explains the negative (red) peak observed left of the diagonal. Additionally, the fourth diagram (d) results in a decrease in the stimulated emission experienced by the probe at frequency ω n,n−1 (corresponding to the transition indicated by the dashed-line arrow in Figure 3i). This new process explains the negative (red) peak observed right of the diagonal. Unlike equilibrium 2DIR spectra, nonequilibrium 2DIR spectra thus exhibit a three-peak structure, observed, for example, in the outlined areas labeled (2) in Figure 2e,f. In the above discussion we assumed that the 2D pump transfers population from the lower level to the upper level, which is only true when the lower level is more populated than the upper level. As already mentioned, the net effect of the 2D pump is actually proportional to the population difference (ρn,n − ρn+1,n+1). This is illustrated in the experimental case associated with Figure 2b,e, where the populations in levels n = 1 and n = 2 happen to be nearly identical, so that the associated pump−probe peak vanishes (see Figure 2b for a probe wavenumber of 1925 cm−1) as well as the 2DIR response (area labeled (1) in Figure 2e). Actually, although the cross peaks cannot be observed because of the noise, a barely visible diagonal peak of negative sign can be observed on the diagonal, indicating a very small population inversion between levels 1 and 2 in this particular case. Note that the population is greater in level n = 0 than in n = 1, as schematized in Figure 3i and as evidenced by the positive diagonal peak observed at 1950 cm−1 in Figure 2e−f. The positive peak observed in the pump−probe spectra shown in Figure 2b,c only results from the fact that these are dif ference spectra, so that even though the transmission is greater than at equilibrium (hence the positive peak), we still have a net absorption from the ground state. A more careful examination of the spectra shown in Figure 2e,f reveals that other peaks of smaller amplitude can also be observed further left or right of the three-peak structure centered on the diagonal. We attribute this observation to two 3380
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is already observed at T = 2 ps for n ≥ 4, at T = 3 ps for n = 3, and for T ≥ 5 ps for n = 2. Another consequence of the greater decay rate for upper levels is that the relaxation of the population initially excited in level n + 1 will eventually catch up with the relaxation of the depletion initially excited in level n, so that the signal will vanish for greater values of the waiting times, as observed for the lower part of the 2DIR spectrum recorded for T = 10 ps. Although our model successfully explains the qualitative behavior observed in Figure 4, we were not able to extract the quantitative vibrational lifetimes by monitoring the dynamics of the first cross peak left of the diagonal. Indeed, because of the detrimental excitation of level n + 2 by the higher-order effect mentioned above, the additional relaxation channel from level n + 2 to level n + 1 leads to a nonexponential dynamics that precludes an accurate determination of the lifetime. Furthermore, although in the absence of VLC we measure Γ−1 1→0 = 22 ± 1 ps, in good agreement with values previously reported in this system,13,24 this lifetime is reduced to only 12 ± 1 ps when the chirped pump is unblocked. The lifetimes of upper levels estimated from our transient 2DIR spectra, although in good agreement with the expected 1/(n+1) law,23 are also observed to be two times shorter than previously reported values.13 Further work is currently under progress to clarify this unexpected behavior, which is clearly related to the high excitation condition associated with the chirped pump. To summarize, we have demonstrated transient 2DIR spectroscopy in carboxyhemoglobin brought strongly out of equilibrium by VLC. At short waiting times, we observed a series of positive peaks on the diagonal with negative peaks on both sides of the diagonal, the right cross peak resulting from pathways associated with transitions to lower levels not present in equilibrium 2DIR spectroscopy. New interesting features in the dynamics of the diagonal and cross peaks as a function of the waiting time have been interpreted and discussed. In particular, the dynamics of the first peak left of the diagonal has been shown to potentially provide a direct measurement of vibrational lifetimes for all addressed vibrational levels. Furthermore, the observed change in sign of the peaks right of the diagonal is a direct evidence of vibrational relaxation subsequent to excitation of transitions specifically addressed in 2D-pump frequency space. Although this work was focused on the interpretation of the observed multipeak structure and on population relaxation, analyzing the spectral widths and shapes of individual peaks is ideally suited for investigating homogeneous and inhomogeneous dephasing of the different transitions, which should be of particular interest for the upper levels where shorter population lifetimes become comparable with dephasing times. Finally, we note that an interesting prospect would be to extend this work to monitoring coherence transfer during and after VLC, assuming that the experimental setup is adapted to collect radiation emitted in the appropriate phase-matching directions. We conclude that the combination of VLC and 2DIR spectroscopy provides a unique method for exploring new regions of the potential energy surface in highly excited vibrational systems.
further right of the diagonal. These latter peaks can only be explained by invoking vibrational relaxation, which cannot be neglected even during a waiting time as short as 1 ps. This second effect clearly calls for further investigation of vibrational relaxation by varying the waiting time. Figure 4 shows a series of 2DIR spectra recorded for a waiting time T varying between 1 and 10 ps. The most striking feature in these spectra is undoubtedly the asymmetric dynamics of the cross peaks. At short waiting time (T = 1 ps), the two main cross peaks are negative, as already discussed. However, as the waiting time increases, the first peak left of the diagonal simply decays, without changing sign, whereas the first peak right of the diagonal decays, changes sign, and eventually vanishes as well. For example, for a waiting time T = 4 ps, all nonzero cross peaks just left of the diagonal are negative, whereas the cross peaks just right of the diagonal are now all positive. To gain a qualitative understanding of these features, let us consider a specific line of the 2DIR spectrum, corresponding to a 2D pump frequency ωn+1,n. Assuming as in the previous discussion that in our experimental conditions lower levels are initially more populated than upper levels, this specific 2D pump frequency will selectively transfer population from level n to level n + 1, thus increasing population in level n + 1 while depleting level n. Because population relaxation proceeds only downward, level n + 1 will remain the highest populated level, so that the signal measured at probe frequency ωn+2,n+1 will directly reflect the population in level n+1. This fact explains the qualitative behavior of the first cross peaks left of the diagonal in Figure 4, which were indeed observed to decay monotonously with respect to waiting time. Monitoring these peaks as a function of waiting time is thus expected to provide a direct measurement of the vibrational decay rate, Γn+1→n, from level n + 1 to level n. This quite remarkable result, illustrating the selective power of 2D spectroscopy, would, in principle, allow a parallel measurement of vibrational population lifetimes for all levels initially populated by VLC. Note that this method is reminiscent of the use of optimal control for enforcing an abrupt cutoff in the population distribution.14 In both cases, the level of interest is the highest populated level so that population transfer from higher levels is eliminated, hence enabling a straightforward measurement of the vibrational lifetime. Obviously, the dynamics of the others peaks in the 2DIR spectra will be less straightforward. Indeed, there will now be two terms in the rate equation, involving both the decay of the population due to relaxation to the lower level and also a population increase due to the relaxation of the upper level. In particular, the dynamics of the diagonal peak is expected to depart from a purely exponential behavior. Regarding the first cross peak right of the diagonal, we may expect that after a waiting time on the order of the vibrational relaxation time a significant fraction of the population excited in level n + 1 will have relaxed down to level n, whereas the depletion in level n will have relaxed down to level n − 1. Consequently, the population difference between levels n and n − 1, which was initially negative, turns positive, so that the first cross peak right of the diagonal (at probe frequency ωn,n−1), which was initially negative, becomes positive. This expected behavior is in perfect qualitative agreement with the experimental findings shown in Figure 4. Furthermore, the sign change is observed at earlier waiting times for upper levels than for lower levels, in agreement with the fact that the vibrational decay rate Γn+1,n is expected to be proportional to n+1.23 Indeed, the sign change
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AUTHOR INFORMATION
Corresponding Author
*E-mail: manuel.joff
[email protected]. Notes
The authors declare no competing financial interest. 3381
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(19) Lee, K. F.; Nuernberger, P.; Bonvalet, A.; Joffre, M. Removing Cross-Phase Modulation from Midinfrared Chirped-Pulse Upconversion Spectra. Opt. Express 2009, 17, 18738−18744. (20) Anna, J. M.; Nee, M. J.; Baiz, C. R.; McCanne, R.; Kubarych, K. J. Measuring Absorptive Two-Dimensional Infrared Spectra using Chirped-Pulse Upconversion Detection. J. Opt. Soc. Am. B 2010, 27, 382−393. (21) Helbing, J.; Hamm, P. Compact Implementation of Fourier Transform Two-Dimensional IR Spectroscopy without Phase Ambiguity. J. Opt. Soc. Am. B 2011, 28, 171−178. (22) Falvo, C.; Daniault, L.; Vieille, T.; Kemlin, V.; Lambry, J.-C.; Meier, C.; Vos, M. H.; Bonvalet, A.; Joffre, M. Ultrafast Dynamics of Carboxy-Hemoglobin: Two-Dimensional Infrared Spectroscopy Experiments and Simulations. J. Phys. Chem. Lett. 2015, 6, 2216−2222. (23) Fourkas, J. T.; Kawashima, H.; Nelson, K. A. Theory of Nonlinear Optical Experiments with Harmonic Oscillators. J. Chem. Phys. 1995, 103, 4393. (24) Lim, M.; Hamm, P.; Hochstrasser, R. M. Protein Fluctuations are Sensed by Stimulated Infrared Echoes of the Vibrations of Carbon Monoxide and Azide Probes. Proc. Natl. Acad. Sci. U. S. A. 1998, 95, 15315−15320.
ACKNOWLEDGMENTS We thank Cyril Falvo, Christoph Meier, Thibault Vieille, and Marten H. Vos for fruitful discussions and acknowledge financial support from Agence Nationale de la Recherche (ANR-2011-BS04-027).
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REFERENCES
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