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Synthetic Metals
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Ultrafast real-time vibronic coupling dynamics of a breather soliton in
trans-polyacetylene with a few-optical-cycle-pulse laser
夽
Takayoshi Kobayashi
a,b,c,d, Takahiro Teramoto
a,b,∗, Valerii M. Kobryanskii
e, Takashi Taneichi
a,baDepartment of Applied Physics and Chemistry and Institute for Laser Science, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan bInternational Cooperative Research Project (ICORP), Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
cDepartment of Electrophysics, National Chiao Tung University, Hsinchu 30010, Taiwan dInstitute of Laser Engineering, Osaka University, 2-6 Yamada-oka, Suita, Osaka 565-0871, Japan eInstitute of Chemical Physics, Russian Academy of Science, Kosygin Street 4, Moscow 117977, Russia
a r t i c l e i n f o
Article history:
Received 28 November 2008 Received in revised form 22 April 2009 Accepted 12 May 2009
Available online 11 June 2009
Keywords:
Ultrafast spectroscopy Coherent vibration Nuclear wave packets Polymers
a b s t r a c t
The dynamics preceding the spatial separation of a charged soliton pair after photoexcitation in trans-polyacetylene was successfully investigated by using ultrafast spectroscopy with a 6.2 fs pulse laser. It was directly verified that after photoexcitation, the electron–hole pair relaxes with a breather mode (i.e. multi-quanta vibronic states), as theory predicts, with an electron–hole pair lifetime of 33–50 fs. By applying spectrogram analysis to the time trace of the absorbance change, the ultrafast amplitude and frequency modulations of C C and C C stretching modes, induced by breathers and lasting no longer than 100 fs, can be observed simultaneously for the first time. The frequency shifts of both modes were in good agreement with a simulation based on the Su–Schrieffer–Heeger model. It was found that the intensities of transition dipoles changed due to breathers, whereas transition energies were dominantly modulated by C C stretching modes as recent theoretical work predicted.
© 2009 Elsevier B.V. All rights reserved.
1. Introduction
Recently, rapid growth in research into applications of conju-gated polymers to optoelectronic devices has been well recognized, the interest being aroused because of high conductivity and light-emitting efficiency associated with these devices. Realistic design of novel plastic materials, with enhanced functionalities for such devices, requires deep insight into their electronic structure, charge and energy transport, and photoexcitation dynamics.
The simplest conjugated polymer is trans-polyacetylene (t-PA). For modelling purposes, it is considered to be an infinitely long polyene. It is also well known that it has a doubly degenerate ground state and nonlinear photo-generated excitations called solitons, which arise because of the degeneracy and strong electron–phonon coupling[1–12]. The soliton dynamics after photoexcitation have been thoroughly investigated both experimentally[1,2,6–8,12]and theoretically[9–11], motivated by the high conductivity based on the soliton dynamics in the polymer chain.
The soliton dynamics in t-PA has been successfully inter-preted about three decades ago by the Su–Schrieffer–Heeger (SSH)
夽 This paper is a proceeding of the 18th Iketani Conference.
∗ Corresponding author at: Department of Applied Physics and Chemistry and Institute for Laser Science, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan. Tel.: +81 42 443 5846; fax: +81 42 443 5826.
E-mail address:[email protected](T. Teramoto).
model [3] followed by several attempts to improve this model [10,11]. Recently, with the aid of progress in computational tech-nology, quantum chemical approaches such as time dependent Hartree–Fock calculations have also been implemented[13,14]. All theoretical models have predicted that a breather soliton is cre-ated due to the excess energy of photoexcitation and modulates the frequencies of stretching modes of C C and C C bonds. This mod-ulation is considered to last until a photo-generated electron–hole pair relaxes to an unbound charged soliton–antisoliton pair [2,3,9–12].
By utilizing an ultrashort pulse laser with 6.2 fs width, that is shorter than the C C stretching vibration period and broad-band multi-channel lock-in detector, detailed ultrafast dynamics revealing the very early-stage dynamics of soliton formation has been studied. In this paper, we present observations of the modu-lated wave packet real-time dynamics due to the electron–phonon coupling of the breather soliton in t-PA and analysed by ultrafast multi-channel pump–probe spectroscopy, finding that the results are in good agreement with recent theoretical predictions[9–14].
2. Experimental aspects
2.1. Sample
Trans-polyacetylene films were fabricated by polymerizing
acetylene with a new rhenium catalyst in a highly viscous solution 0379-6779/$ – see front matter © 2009 Elsevier B.V. All rights reserved.
of polyvinyl butyral (PVB)[15]. This synthetic method can provide soluble compositions containing nanoparticles of polyacetylene in PVB solution. These nanoparticles with diameters of 15–30 nm con-tain only a negligibly low concentration of conformational and chemical defects in contrast to those obtained by conventional methods of polyacetylene synthesis[16]. They are extremely sta-ble even under atmospheric conditions and exhibit a number of unique optical properties such as large Raman cross-section, ther-mochromism, and a transparent band in the optical spectrum in the near-infrared field[16].
2.2. Ultrafast spectroscopy
Both pump and probe pulses were derived from a non-collinear optical parametric amplifier (NOPA) system developed in our group[17,18]. The pump source of this system is a regen-erative amplifier (Spectra-Physics, Spitfire). The visible NOPA pulse was 6.2 fs in duration and covered a photon energy range of 1.69–2.37 eV, with constant spectral phase throughout the whole laser spectrum. Pump–probe signals were detected with a 128-channel lock-in amplifier. Real-time vibrational spec-tra were measured at delay times between pump (40 nJ) and probe pulses (2 nJ) from −100 fs to 1100 fs with 1-fs incre-ments.
3. Results and discussion
3.1. Primary energy relaxation process
Fig. 1displays the stationary absorption spectrum of t-PA show-ing a strong absorption in the visible region due to interband intrachain dipole allowed → * transitions. The peak wavelength (photon energy) of 630 nm (1.97 eV) in the spectra corresponds to the1B
ustate[19]. The laser spectrum is also shown inFig. 1.
The overlap of the spectra of laser and sample absorption is very good.
Using the femtosecond laser and multi-channel detection sys-tem described in Section2, the time-resolved spectra of a t-PA sample film were measured. The results of the pump–probe exper-iment are shown inFig. 2(a).Fig. 2depicts the three-dimensional display of real-time difference absorption spectrum, A(, t), of over the spectral range from 528 nm (2.35 eV) to 730 nm (1.70 eV) extending from the delay time of−100 fs to 1100 fs. The
modula-Fig. 1. Laser spectrum (solid line) and stationary absorption (dotted line) spectrum
of t-PA.
tions of A(ω, t) due to molecular vibrations can be seen clearly in Fig. 2(b) which is a expanded view ofFig. 2(a) in the time range from 0 fs to 300 fs.Fig. 2(c) show the real-time traces of A(t) at the pho-ton energies of 1.86 eV, 1.96 eV, and 2.12 eV, andFig. 2(c) depicts the difference absorption spectrum, A(ω), at the delay times of 40 fs, 60 fs, and 120 fs.
The three-dimensional difference absorption spectra A(ω, t) were decomposed into phenomenological components of three dif-ference spectra A1(ω), A2(ω), and A3(ω) with a set of three
corresponding decay time constants, 1, 2, and 3, by a global
fitting method as given by the following equation: A(ω, t) = A1(ω) exp
−t 1 + A2(ω) exp −t 2 + A3(ω) exp −t 3 (1)The decay times of the signal were determined by the singular value decomposition method to be 1= 66± 20 fs, 2= 565± 50 fs,
and 3 2 ps, by fitting Eq.(1)to the absorption spectra over the
whole probe photon energy region. The shortest time constant, 1,
is the lifetime of the electron–hole pair, which is in good agree-ment with values found in the literature[8,13,14]. The medium length decay time 2 corresponds to the lifetime of a charged
soliton–antisoliton pair to geminate recombination[8]. The abso-lute value of the longest time constant 3 cannot be determined,
Fig. 2. Three-dimensional real-time absorbance change spectrum of t-PA: (a) three-dimensional display of A(ω, t) of t-PA over the spectral range from 528 nm (2.35 eV) to
730 nm (1.70 eV) extending from delay time of−100 fs to 1100 fs; (b) expanded view of (a) in the time range of 0–300 fs. (c) The upper three show the real-time traces of A at photon energy 1.86 eV, 1.96 eV, and 2.12 eV, respectively. The lower three show the photon energy dependencies of A at delay time 40 fs, 60 fs, and 120 fs, respectively.
only a lower limit being obtained. However, this time constant is considered to be associated with the thermalization of the system, which does not necessarily have to be described with a single expo-nential decay constant, but can have complicated decay dynamics including diffusion process. The dynamics then cannot be described by the rate equation, but by a diffusion equation considered to take place in the time range of 5–10 ps.
3.2. Electronic phase relaxation time between S0and S1states
To begin, a brief theoretical background is described so as to discuss the determination of the electronic phase relaxation time.
In the rotating reference frame, the time evolution of the ele-ments of the density matrix is described as two-electronic state system. The density matrix is corresponding two of the eigen states relevant to the optical transition resonant to the laser field. The electronic states in trans-polyacetylene is strongly coupled to the vibration. The eigen states between which transition is taking place are vibronic eigen states of the Hamiltonian considered to be solved without factorisation into vibrational and electronic eigen-state wave functions.
The two-electronic state system interacting with pump (Epu(t))and probe (Epr(t)) fields is described by
˙ba(r, t) = −
i˝ + 1 T2 ba(r, t) + i ¯hVba(r, t)N (2) ˙bb(r, t) − ˙aa(r, t) = −N − N0 T1 + 2i ¯h[Vba∗(r, t)ba(r, t) − Vba(r, t)∗ba(r, t)] (3)The interaction potential Vba(r, t) is given by
Vba(r, t) = −[Epu(t) exp(ikpur) + Epr(t) exp(ikprr)] (4)
where is the transition dipole moment, T1 and T2are the
lon-gitudinal and transverse electronic relaxation time, respectively, between states 1 and 2; N = bb(r, t) − aa(r, t) is the population
difference, and N0= (bb(r, t) − aa(r, t))0is the equilibrium
pop-ulation difference without the field; ˝ = ωba− ω1 is the detuning
between the pump field frequency ω1and the transition frequency
ωba.
The time envelope function of the macroscopic polarization P(3)
pr(t) in a molecular vibronic system propagating in the probe
direction is given by the following[20]: P(3) pr = [bb(r, t) − aa(r, t)]0
+∞ −∞ dt3A2(t3) Epr(t − t3) +∞ −∞ dt2A1(t2) Epu(t − t3− t2) +∞ −∞ dt1A2(t1)E∗pu(t − t3− t2− t1) −E∗ pu(t − t3− t2) +∞ −∞ dt1A2(t1)Epu(t − t3− t2− t1) +Epu(t − t3) +∞ −∞ dt2A1(t2) Epr(t − t3− t2) +∞ −∞ dt1A2(t1)E∗pu(t − t3− t2− t1) −Epu(t − t3) +∞ −∞ dt2A1(t2) E∗pu(t − t3− t2) +∞ −∞ dt1A2(t1)Epr(t − t3− t2− t1) + Epr(t − t3) (5) Here, the initial condition is given by A1(t) = A2(t) = 0 (t < 0)A1(t) = 2i ¯h exp
−t Tel 1 × exp(−i(ωvt + tan−1((ω − ωe+ ω)Tvib))) (t > 0) (6) A2(t) = i ¯hexp
−t Tel 2
exp(−i˝t) exp
−t T2vib × exp(−i(ωt + tan−1((ω − ω e+ ω)Tvib))) (t > 0) (7)
Here Tvibis the vibrational period, T2eland T2vibare the electronic and
vibrational dephasing times, respectively, and ωeis the frequency
corresponding to the 0–0 transition energy from the ground state to the electronic excited state.
Eq.(5)is the result of the perturbation of optical fields up to the third-order nonlinear susceptibility, and not the perturbation of vibration to the electronic transition due to the vibronic cou-pling. The vibronic coupling is fully taken into account in ab(r, t)
which is not the pure electronic polarization or electronic polar-ization with perturbative vibrational levels included in the direct product of the linear combination of the electronic wave functions coupled through the perturbative coupling up to some lower order vibronic coupling. Instead it is the vibronic polarization, where all orders of perturbation and fully taken into account.
The difference spectrum of the probe transmittance is found to have three distinct polarization components as described in Eq.(5). The difference spectrum corresponding to the first term is propor-tional to the level population changes induced by the pump pulse, which is detected when the probe pulse arrives. This level popu-lation term gives a signal due to incoherent process of popupopu-lation transfer from the ground state to the electronic excited state being coupled through dipole allowed electronic transition. In this inco-herent term, coinco-herent effects do not play an important role. This same term appears only after the onset of the pump pulse, as seen from Eqs.(6) and (7), which contribute only to the positive time region. The change in the transition probability due to the time-dependent Franck–Condon factor (Franck–Condon mechanism) or to the non-Condon effect (non-Condon mechanism) is associated with the motion of the wave packet[20–23]. Therefore, it is the only term which persists when the probe follows the pump and decays exponentially with time constant T1el.
The second term in Eq.(5)is proportional to the pump-induced polarization present when the probe pulse arrives at the same time as the pump pulse. The probe field interacts with this pump polar-ization to create a grating due to spatial modulation of the level populations. The pump field then interacts with the grating to cre-ate a polarization component spatially coherent with the probe field[20,24–26]. This term is called the “pump polarization cou-pling” term. It is effective only when the pump pulse overlaps the probe pulse in time, since it requires the presence of the pump field both before and after the arrival of the probe pulse.
The third term occurs because the presence of the pump field modifies the otherwise free decay of the probe-induced polariza-tion. This term is called the “perturbed free induction decay” term. It persists when the probe precedes the pump, grows exponentially with time constant T2eland becomes zero quickly at t = 0. Therefore
relax-Fig. 3. A(t) in negative-time region of t-PA at 1.88 eV: (a) the results are experiment
(solid line) and fitted (dashed line) and (b) the difference between experimental and fitted data, associated with molecular vibrations. (c) FFT power spectrum of (b).
ation time. It can also be used to study vibrational phase relaxation in the electronic excited state(s)[27]. In the case t-PA studied in this paper, electron–hole pairs have very short lifetimes in form-ing excited states, and hence the vibrations in the excited state are difficult to detect.
As discussed above, in the time range when the probe pulse precedes the pump pulse, the probe delay time dependence of the signal provides information about the electronic polarization induced by the probe pulse. This time range is called the “negative-time” range in this paper. In this range, the pump pulse in the negative-time, by the electronic coherence grating and created by the probe light, induced coherent electronic polarization and pump field. Therefore, the signal lasts as long as the electronic coherence is maintained. The phase relaxation time of the relevant electronic states can be obtained from the delay time dependence in the nega-tive time. From the spectral overlap relation between the absorption and laser in the present experiment, it is seen, as will be described below, that the relevant electronic states are the ground state and the excited state corresponding to the electron–hole pair.
The rate of dephasing (1/Tele
2 ) obtained from the plot comprises
three components given below, 1 Tele 2 = 1 2Tele 1 + 1 Tele 2 + 1 T2∗ele (8) Here Tele
1 is the population decay time, and T ele
2 and T2∗eleare
respectively the pure electronic dephasing time and the electronic phase relaxation time due to inhomogeneous broadening. In order to discuss the pure phase relaxation time constant Tele
2 , we must
know more about T2∗ ele. Here, for simplicity, we assume T ele 2 = ∞.
Since the value of T2∗eleis very short, it can safely be considered that
T2∗ele T2ele, and the assumption is considered to be well-satisfied.
From the analysis of the plot shown in Fig. 3(a), the electronic dephasing time was found to be Tele
2 = 32 ± 2 fs. Then, from the
shortest population decay time T1ele= 1= 66 ± 20 fs determined
in the previous section, the pure electronic dephasing time is deter-mined to be Tele
2 = 62 ± 19 fs. Therefore, it can be concluded that
51% of the phase decay is due to a pure dephasing process and 49% is due to population decay resulting from electronic relaxation asso-ciated with extremely fast dissociation of bound solitons to form pairs of spatially separated solitons.
Fig. 3(a) shows plots of the decay in the negative time, from which a 32 fs decay time constant was determined, and the fitted curve of the decay function. It also depicts the oscillating compo-nent and its Fourier power spectrum, which has peak frequency of 773 cm−1corresponding to the breather mode frequency. From the
Fig. 4. Two-dimensional display of FFT power spectra of t-PA.
width of the power spectrum of the mode, the dephasing time of the vibrational mode was estimated to be Tex.vib
2 = 37 ± 5 fs.
3.3. Molecular vibration spectra
Probe delay time (t) dependent change, ıA(ω, t) in A(ω, t), is due to molecular vibration.Fig. 4shows the two-dimensional (, t) display of the fast Fourier transform (FFT) power spectra of real-time traces of A(, t) probed at the 128 photon ener-gies used to obtainFig. 2. The peak positions of the FFT amplitude due to C C and C C stretching modes were 1089± 6 cm−1 and
1487± 10 cm−1, respectively. The FFT cosine phases of C C and C C
stretching modes are (0.9± 0.3) and (0.7 ± 0.4) radian, respec-tively, in a photon energy range indicating that these modes are created initially in the excited state. The FWHM of the peaks of each mode were 59± 2 cm−1 and 70± 3 cm−1, respectively,
cor-responding to the vibrational dephasing times of 570± 24 fs and 480± 14 fs, respectively. The dephasing times of both modes are close to the above mentioned recombination time (565± 50 fs) of a charged soliton pair. This indicates that the dephasing of vibrational modes is determined partly by the recombination of the soliton pair and partly by the pure dephasing with nearly equal contribution.
3.4. Modulated phonon dynamics induced by the breather soliton
The results of the spectrogram analysis [28–30]of the real-time trace at 1.71 eV are shown inFig. 5. The probe delay time dependent Fourier amplitude reveals the time evolution of C C and C C stretching modes with 1100± 8 cm−1and 1488± 8 cm−1,
respectively. In addition to the main skeleton oscillation, there exist four peaks at 305 cm−1, 757 cm−1, 1877 cm−1, and 2254 cm−1 with an uncertainty of±8 cm−1. The separation between the main
bands and corresponding sidebands is 770± 40 cm−1 in all four
cases. This frequency separation corresponds to a modulation period of 43± 3 fs, which is consistent with the theoretically pre-dicted (33–50 fs) for the breather period[9–11]and the previously observed (44± 3 fs)[2]. In the present work, these sidebands were observed over the whole photon energy range from 1.70 eV to 2.35 eV, which is considered to be the tail of the breather absorp-tion with a peak located around 1.03 eV. In all cases, the lifetime of the sideband amplitude is about 60 fs, which is within experi-mental errors in agreement with the electronic dephasing time of 61± 14 fs. The coincidence is explained in the following discussion. The profile of the spectrogram from 10 fs to 90 fs in incre-ments of 20 fs is plotted inFig. 6(a). The peak FFT amplitude of the C C stretching mode shifts from 1155 cm−1to 1095 cm−1with time evolution, while that of the C C stretching mode shifts from 1488.5 cm−1to 1503 cm−1. Our scenario of the primary processes
of photoexcitation follows the steps proposed in earlier theoretical work[31,32]. The electron–hole pair formed by the photoexcitation associated with a localized breather mode relaxes to a spatially sep-arated pair of charged solitons with a localized breather mode. The observed frequency shifts are interpreted as a consequence of the coupling of the breather with the charged solitons. In the following, the SSH Hamiltonian model[3,4]is used to describe above scenario. The model Hamiltonian is given as follows:
H = −
n,s [t0+ ˛(un− un+1)][cn+1,s† cn,s+ c†n,scn+1,s] +K2
n(un− un+1) 2 +M2
n ˙u2n (9)
where unis the displacement of nth CH group in the polymer chain,
t0is the band width, ˛ is the electron–phonon coupling, K is the
spring constant, and M is the mass of each CH group. c†n,sand cn,sare,
respectively, the creation and annihilation operators of a electron in the nth site with spin s. Based on this Hamiltonian, the classi-cal equations of motion for order parameters ¯n(t) ≡ (−1)nun/u0,
and velocities, ˙¯ncan be derived[10]. Here u0= 0.04 Å, assuming
that the change in bond length due to dimerization from the non-dimerized structure (that is, all bond orders are 1.5) is 0.08 Å[9]. Frequencies of the single and double bonds are determined
exper-Fig. 6. Time traces and photon energy dependence of FFT amplitudes of C C, C C stretching and breather modes: (a) the results of experiment (blue line) and calculated
(yellow line) time traces of FFT amplitude of C C and C C stretching modes, (b) the time trace of bond order, (c) the probe photon energy dependence of FFT amplitude of sidebands of the C C stretching mode (solid and dashed black lines correspond to the lower and higher sidebands, respectively) and 0th derivative ofA(ω, t) with respect to photon energy (red line) at 50 fs, and (d) the probe photon energy dependence of C C stretching mode (black line) and the 1st derivative ofA(ω, t) with respect to photon energy (red line) at 100 fs. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
imentally to be 1095 cm−1and 1503 cm−1, respectively. Calculated results and the observed data are shown inFig. 6(a), revealing that the peak of the single bond red-shifts, while the peak of the dou-ble bond blue-shifts. It is also shown that the initially localized excitation, with a peak having an order parameter of−2, results in the two peaks being closer to each other. The time trace of the bond order is estimated from both experimental and calculated data [33](Fig. 6(b)). The figure shows that the bond order of each bond exceeds 1 on the lower order side and is less than 2 on the higher side at the moment of electron–hole pair generation.
Recently, Tretiak et al. found that the breather and the C C stretching modes mainly modulate the intensities (transition dipoles and oscillator strength) and transition energies, respec-tively[13,14]. To verify these calculations, the 0th and 1st derivative of A with respect to photon energy were compared with the probe photon energy dependence of FFT amplitude of spectrogram anal-ysis (Fig. 6(c) and (d)). The 0th and 1st derivative of A correspond to the modulation of the transition intensity and that of the elec-tronic transition energy, respectively. These results are consistent with the prediction made by Tretiak and others[13,14].
4. Conclusions
In conclusion, the prediction of[9–11]that after photoexcita-tion, the electron–hole pair relaxes via a breather mode with an electron–hole pair lifetime of 33–50 fs, have been directly verified. The electronic dephasing time which was determined by the A in the negative-time range revealed that 51% is due to a pure electronic dephasing process and 49% is due to population decay resulting from electronic relaxation associated with extremely fast dissoci-ation of a bound soliton to a pair of spatially separated charged solitons. We could also determine the ultrafast phonon dynamics induced by the breather in t-PA, including amplitude modulation, frequency modulation and frequency shifts of C C and C C stretch-ing modes. Calculations with the SSH Hamiltonian reproduced the time trace of the bond order of the C C bonds in the polyacetylene. As also theoretically predicted, the breather and the C C stretching modes were found mainly to modulate the transition intensity and transition energy, respectively.
Acknowledgements
The authors wish to thank Dr. A.R. Bishop, Dr. S. Tretiak, and their group members for their fruitful comments. This work was partly supported by a grant from the Ministry of Education (MOE) in Taiwan under the ATU Program at National Chiao Tung University. A part of this work was performed under the joint research project of the Institute of Laser Engineering, Osaka University under Contract No. B1-27.
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