Excited-State Molecular Vibration Observed for a Probe Pulse Preceding the Pump Pulse
by Real-Time Optical Spectroscopy
Takayoshi Kobayashi,1,2,3,4,*Juan Du,1,2Wei Feng,5and Katsumi Yoshino6
1Department of Applied Physics and Chemistry and Institute for Laser Science, the University of Electro-communications, 1-5-1 Chofugaoka, Chofu, Tokyo, 182-8585, Japan
2JST, ICORP, Ultrashort Pulse Laser Project, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan 3Department of Electrophysics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsin-Chu 3005, Taiwan
4Institute of Laser Engineering, Osaka University, 2-6 Yamada-Oka, Suita, Osaka 565-0971, Japan 5School of Materials Science and Engineering, Tianjin University, Tianjin 300072, P.R.China 6Shimane Institute for Industrial Technology, 1 Hokuryo-cho, Matsue, Shimane 690-0816, Japan
(Received 19 December 2007; published 18 July 2008)
It is shown experimentally that the absorbance change observed in the ‘‘negative’’ time range, where probe pulse precedes pump pulse in real-time vibrational spectroscopy is induced only by the excited-state wave-packet motion as theoretically expected. Coherent molecular vibration of a polymer in the excited state was observed in the real-time trace without the effect of wave-packet motion in the ground state, which usually makes it difficult to ascribe the signal either to the ground state or to the excited state. DOI:10.1103/PhysRevLett.101.037402 PACS numbers: 78.47.p, 42.65.k, 78.47.J, 78.40.Me
In pump-probe spectroscopy, the pump pulse perturbs the absorption spectrum of the medium, which is subse-quently probed after a set time delay. This method assumes implicitly that the weak probe pulse does not induce any substantial excitation of the sample [1]. However, in the femtosecond regime difference absorption spectra cannot be directly interpreted as a change of the absorption spec-trum because of coherence effects. These effects fall into two categories: one is ‘‘coherent coupling’’ due to the induced grating formed by temporally coincident pump and the probe in the sample [1–4], and the other is the ‘‘perturbed free polarization decay’’ generated by the probe and perturbed by a pump. In the present Letter, the coherent molecular vibration in the excited state in the ‘‘negative time’’ region, where the probe pulse pre-cedes the pump, was observed and compared with the ‘‘positive time’’ data in the short ‘‘positive’’ delay time range after excitation.
Sample films of conjugated polymer, poly{[3-hex-ylthiophene-2,5-diyl] - [p-dimethylaminobenzylidenequi-noidmethene]} (PHTDMABQ) were investigated at room temperature (298 1 K) [5,6]. Using the 6.3 fs pulse, the pump induced absorbance change (A) was measured at 128 different wavelengths from 515 to 716 nm [7,8].
Figures1and2show the traces of real-time molecular vibration probed at four different wavelengths from 200 fs to 1800 fs and near zero delay time, respectively. The negative time traces have periodic structures similar with positive delay traces as indicated by the delay-time figures attached to the peaks or valleys.
In the previous reports, the experimental results ob-served in the negative delay-time region were discussed in terms of perturbed free induction decay and coherent coupling [1–4,9–12]. The difference absorption spectrum was calculated for a two-level system and applied to
mo-lecular systems [13,14]. In the following we modified their treatment for the vibronic system, assuming only one mode is coupled to the excitation to the exciton state, but it can easily be extended to a multimode system.
In the rotating reference frame, the time evolution of the elements of the density matrix for two-electronic state system, which interacts with pump (Eput) and probe (Eprt) fields is described in Ref. [4] by
_bar; t i 1 T2 bar; t i @Vbar; tN; (1) _ N N N0 T1 2i @Vba r; tbar; t Vbar; t bar; t : (2)
The interaction potential Vbar; t is given by [4]
Vbar; t Eput expikpur Eprt expikprr ; (3) where is the transition dipole moment, T1and T2are the longitudinal and transverse electronic relaxation time, re-spectively, between state 1 and state 2; N bbr; t
aar; t is the population difference, and N0 bbr; t aar; t 0is the equilibrium population differ-ence without the field; !ba !1 is the detuning between the pump-field frequency !1 and the transition frequency !ba.
Molecules composed of N atoms can have complicated vibronic absorption spectra due to the large number (3N 6) of vibrational modes and strong vibronic coupling. Because of the vibronic coupling, the signal described by Eq. (3) in Ref. [4] for the two-electronic state must be modified. In the following discussion, the system is con-sidered to be composed of two electronic states, both PRL 101, 037402 (2008) P H Y S I C A L R E V I E W L E T T E R S 18 JULY 2008week ending
coupled to the same vibrational mode with same frequency
!, which is not thermally excited.
The macroscopic polarization P3prt in a molecular vibronic system propagating in the probe direction is given by P3pr N0F2t fEprtF1t EputPput E putPput EputF1t EprtPput EputF1t E putPprt Eprtg; (4) where F1t F2t 0; t 0 (5) F1t 2i @ expt=T1 expi!t ; t 0 (6) F2t i
@ expt=T2el expit expt=T2vib
expi!t ; t 0 (7)
arctan! !e !Tvib ; (8)
Pxt F2t Ext x pu; pr: (9) Here Tvibis the vibrational period, and Tel
2 and T2vibare the electronic and vibrational dephasing times, respectively, and !eis the frequency corresponding to the 0-0 transition energy from the ground state to the electronic excited state. The symbol denotes convolution.
The absorbance difference A! is then given by
A! Im f 2! epr! F EprtNpu2t EputF1t EprtP put EputF1t E putPprt : (10)
Here Npu2t is the population change induced by the pump field, which is modified phenomenologically correspond-ing to those in [4] and is given by
Npu2t F1t EputPput c:c: ; (11)
f2! F F2t is the Fourier transform (FT) of F2t. The first (population) term in Eq. (10) appears only after the onset of pump [Eqs. (6) and (7)], contributing to the positive time region. The second (pump polarization cou-pling) term [Eq. (10)] is due to the coherent coupling between pump-field induced polarization and probe field appearing only when the probe and pump overlap.
The third (perturbed free polarization decay) term rep-resents the case when the probe pulse comes earlier than the pump pulse, and there is no temporal overlap between them. The probe pulse generates electronic coherence in the sample with the duration of the electronic dephasing time. Then the intense pump field forms a grating [EputPprt term in Eq. (10)], which interacts with an-other pump field to be diffracted into the probe direction, satisfying the causality. In the present case, vibronic cou-pling expected to be strong in the conjugated electron system is the origin of the electronic spectrum of the ground state. Therefore the polarization generated by the
-200 0 200 400 600 800 1000 1200 1400 1600 1800 -0.012 -0.008 -0.004 0.000 2.08eV 595nm A Delay time (fs) (a) -200 0 200 400 600 800 1000 1200 1400 1600 1800 -0.015 -0.010 -0.005 0.000 500 550 600 650 700 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Absorbance Normailized intensity Wavelength (nm) (b) 2.01eV 618nm A Delay time (fs) -200 0 200 400 600 800 1000 1200 1400 1600 1800 -0.010 -0.005 0.000 0.005 (c) 1.98eV 625nm A Delay time (fs) -200 0 200 400 600 800 1000 1200 1400 1600 1800 -0.008 -0.004 0.000 0.004 (d) 1.92eV 645nm A Delay time (fs)
FIG. 1. The vibrational real-time spectra of difference absorption in the whole pump-probe delay time range from 200 fs to 1800 fs at four typical probe photon energies of 2.08, 2.01, 1.98, and 1.92 eV. The dotted lines show zero absorbance change (A). The inset in (a) is the molecular structure of PHTDMABQ, and that in (b) is sample stationary absorption spectrum (dotted line) and laser spectrum (solid line).
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probe pulse preceding to the pump pulse is not pure electronic transition but a vibronic transition. This is the origin of the observed signal of vibrational oscillation. Therefore, the induced polarization by the probe pulse Pprt is the vibronic polarization associated with the tran-sition between the ground vibrational level in the ground electronic state and the vibronically excited state. The wave-packet formation in the ground state requires the two fields of the pump pulse. Therefore, the third-term signal increases with delay time with the time constant of
T2el, and disappears quickly at t 0 [4]. The ‘‘negative time’’ data provide the electronic dephasing time Tel
2 12 1 fs, which limits the precision of the vibrational frequency together with the vibrational dephasing time by the Fourier transformation.
Following the above discussion, let us discuss the ex-perimental results of real-time spectra in both negative and positive time ranges.
Figures 3(a)–3(c) were calculated for different probe delay-time range at the probe wavelength of 618 nm. It is noticeable that the spectral shapes of the positive probe time ranges are substantially different from those of the negative time range even at the same probe wavelength. The FT power spectrum obtained for 200 to 1800 fs has peaks at 1111, 1184, 1343, 1461, 1514, and 1591 cm1, which are high enough for the vibrational levels not to be populated at room temperature. In Figs. 3(b) and 3(c), there is almost no contribution of the most and the second most intense peaks at 1343 and 1111 cm1, respectively. Instead, there are two peaks at 1290 24 and 1530
23 cm1for 0 to 200 fs region, and 1245 19 and 1514 23 cm1 for 200 to 0 fs range, respectively. The posi-tions of the two corresponding peaks are close to each other for both peaks. Therefore the frequencies observed in Fig. 3(b) are attributed to the excited state. The fre-quency difference may be due to the small contribution of the ground-state modes existing only in the positive time range.
The instantaneous frequency of molecular vibration ob-served from 125 fs was analyzed by calculating a spectro-gram, as shown in Fig.4, at 2.01 eV (618 nm) by using a Blackman window of 240 fs FWHM (full width at half maximum). The dynamics of the amplitudes of 1290 and 1350 cm1 modes integrated with a 20 cm1 width were studied. The decay time constant of the former is about 160 fs, and the growth and the decay times of the latter were about 100 and 450 fs, respectively. This frequency shift could be explained in terms of the change in the electronic state associated with the geometrical relaxation from the free exciton to the exciton polaron [15]. The former decay time constant of 160 fs is overestimated because of the Blackman window of FWHM of 240 fs.
From the previous work on polydiacetylene [16], it is expected for the free exciton to decay into the nonthermal exciton polaron (self-trapped exciton) with vibrational mode of 1350 cm1 with 1 80 20 fs. The decay time is consistent with the growth time of about 100 fs of 1350 cm1component. This is also close to the formation time of exciton polaron of &100 fs in several polydi-acetylenes [16,17]. The mode frequencies of 1290 and
-100 -80 -60 -40 -20 0 20 40 60 80 100 -0.01 0.00 -87.0 -67.6 -45.4 -19.2 -6.2 12.8 33.0 55.4 76.8 -76.2 -54.0 -29.4 -12.4 5.2 20.8 44.2 66.2 86.8 -5.2 -20.8 -44.2 -66.2 -86.8 -12.8 -33.0 -55.4 -76.8 b ∆ A Delay time (fs) -100 -80 -60 -40 -20 0 20 40 60 80 100 -0.010 -0.005 0.000 -12.2 -31.0 -43.4 -55.0 -59.4 -78.0 -4.8 -21.8 -45.6 -57.8 -68.0 -81.4 -90.4 -91.2-79.6 -59.4 -41.2-34.0 -8.6 12.2 31.0 55.0 59.4 78.0 43.4 -86.8 -65.2-54.0 -38.0 -19.4 4.8 21.8 45.6 57.8 68.0 81.4 90.4 ∆ A Delay time (fs) a -100 -80 -60 -40 -20 0 20 40 60 80 100 -0.010 -0.005 0.000 0.005 -5.2 -20.8 -46.0 -67.6 -89.2 -12.0 -33.6 -57.6 -78.8 -91.2 -69.0-59.4 -38.8 -17.8-8.6 12.0 33.6 57.6 78.8 -77.6 -53.2 -36.6 -12.6 5.2 20 8 46.0 67.6 89.2 ∆ A Delay time (fs) c -100 -80 -60 -40 -20 0 20 40 60 80 100 0.00 0.01 -96.6-91.4 -69.0-59.4 -49.6 -29.2 -2.6 16.6 39.0 62.8 84.4 -87.4 -64.4 -53.8 -38.6 -17.2 5.8 29.2 49.2 59.8 70.4 95.6 -5.8 -29.2 -49.2 -59.8 -70.4 -95.6 -16.6 -39.0 -62.8 -84.4 ∆ A Delay time (fs) d
FIG. 2. The expanded real-time traces of corresponding near zero-delay time (in both negative and positive probe delay times) in Fig.1. The solid lines show the original graphs. The dotted curves were obtained by inverting the real-time traces in the positive time region to the negative time with respect to the origin of the graph at point [t 0, At 0] [except the curve in graph (a), which was obtained by mirror imaging at t 0].
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1350 cm1are then considered to be C-C bond stretching in the free exciton and the exciton polaron, respectively. As shown in Fig.4, the frequency of the C-C stretching mode coupled to the exciton polaron is elevated to 1350 cm1 from that of free exciton (1290 cm1). The increase of coupled mode frequency by about 60 cm1is due to the enhancement of the bond order by about 4.5% in the C-C bond in the polymer chain after geometrical relaxation from the ‘‘benzenoidlike’’ configuration to the ‘‘quinoid-like’’ one by -electron delocalization associated with the formation of the exciton polaron. The coherent molecular vibration after the geometrical relaxation is considered to be a kind of reaction induced coherence [18,19].
In conclusion, it was shown that the real-time trace in negative time provided information about polarization
modulated by molecular vibration in the excited state. The coherent molecular vibration was experimentally observed in the negative time range of the real-time trace of a poly-mer in the excited-state without the effect of wave-packet motion in the ground state. This ‘‘negative’’ time measure-ment is a powerful method for studying the excited-state dynamics using molecular structure information.
The authors would like to acknowledge Dr. Zhuan Wang for her help in the analysis and valuable discussion. This work was partly supported by the grant from the Ministry of Education (MOE) in Taiwan under the ATU Program at National Chiao Tung University.
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FIG. 3. The FT power spectra of real-time vibrational spec-trum at 2.01 eV (618 nm).
FIG. 4. The contour map of the two-dimension Fourier power spectra of vibrational components obtained by spectrogram calculation at 2.01 eV (618 nm). The solid line denotes the instantaneous Fourier power peak at each delay time.
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