Picosecond vibrational cooling in mixed molecular crystals studied with a new coherent raman scattering technique

Picosecond vibrational cooling in mixed molecular crystals studied with a new coherent raman scattering technique

Volume 147, number 1 CHEMICAL PHYSICS LETTERS 27 May 1988 PICOSECOND VIBRATIONAL COOLING IN MIXED MOLECULAR CRYSTALS STUDIED WITH A NEW COHERENT RA...

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Volume 147, number 1

CHEMICAL PHYSICS LETTERS

27 May 1988

PICOSECOND VIBRATIONAL COOLING IN MIXED MOLECULAR CRYSTALS STUDIED WITH A NEW COHERENT RAMAN SCATTERING TECHNIQUE *

Ta-Chau CHANG and Dana D. DLOTT 1,2 School of Chemical Sciences, Universityof Illinois at Urbana Champaign, 505 S. Mathews Avenue, UrbanaIL 61801, UsA

Received 16 February 1988; in final form 25 March 1988

We demonstrate the pump-induced coherent Stokes Raman scattering (CSRS) technique by measuring vibrational cooling in low temperature crystals of pentacene in naphthalene following excitation of a vibration 747 cm-’ above the S, origin. Using picosecond photon echoes and a two-color pump-probe technique, we find that the initial state decays in 33 ps, and reappears at the origin 25 ps later. We show that pump-induced CSRS simultaneously measures the decay from the initial state and reappearance at the origin. This technique has many of the advantages of conventional coherent Raman (e.g. intense coherent signals), but is a direct measure of the populationdynamics in the initial and final states.

1. Introduction

When an excited vibration is prepared in a crystal of large molecules, it undergoes ultrafast radiationless relaxation caused by anharmonic coupling to other vibrations and lattice phonons. The disappearance of excitation energy from the initial state is called vibrational relaxation (VR) [ 11. Recently Hill et al. [ 2,3] have discussed the process of vibrational cooling (VC). The VC process is a measure of the repopulation of the vibrationless ground state, and in many systems, VC consists of several sequential and parallel VR processes. Consequently VC may occur on a time scale which is considerably slower than VR. Some dynamical processes, for example the broadening of a vibrational transition by lifetime effects, depend only on the VR rate, and are unaffected by any subsequent VR processes [4]. Others, such as solid state extimer formation, or exciton hopping in the strong exciton-phonon coupling limit, are instead dependent on the total rate of energy dissipation, i.e. the VC process [ 2,3], and there is only an indirect dependence on VR. In this work, we introduce a new ultrafast technique, the pump-induced coherent Stokes Raman scattering (CSRS) method. This method produces intense coherent signals, but in contrast to photon echoes [ 51 and picosecond CARS [ 6 1, it is a direct measure of population relaxation dynamics, even when other dynamical processes exist to dephase the initially excited state. In addition, this new method can be used to simultuoneously measure the leaving rate out of the initial state, and the arrival rate in a specific lower energy mode. It is thus ideal for the study of VC processes, in that the relationship between the leaving rates and arrival rates are immediately discernible in the same experiment. In the pump-induced CSRS method, an initial SYvibration, denoted Iv’ ) (fig. la), is excited by an ultrashort laser pulse, w2, tuned to the So-& transition at delay time t=O. Probing of the subsequent VC processes is * Research supported entirely by the National Science Foundation, Division of Materials Research, Solid State Chemistry program through grant NSF DMR 84- 15070. I To whom correspondence should be addressed. 2 On leave until June 1,1988 at Department of Chemistry, Stanford University, Stanford, CA 94305, USA.

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0 009-2614/88/$ 03.50 0 Elsevier Science Publishers R.V. ( North-Holland Physics Publishing Division )

CHEMICAL PHYSICS LETTERS

Volume 147, number 1

owAYTME

-

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Fig. 1. Schematic of pump-induced CSRS experiment. (a) Energy level diagram. (b) Kinetic scheme for vibrational cooling. (c) Schematic of population transfer processes. (d) CSRS time dependence for the processes diagrammed in (c ) .

with a delayed, but simultaneous pair of pulses at w2 and wl, where o1 is tuned to the Sz +Sy transition. This probe pulse pair stimulates coherent Stokes Raman scattering (CSRS) from a coherent superposition of the Sp (denoted (0’ > ) and S; states (fig. 1a) at frequency 20, - u)~. The intensity of this CSRS signal will be shown to be proportional to the square of the population difference between Sy and Sp. Thus when S; is excited (fig. lc), the pump-induced CSRS signal rises to a maximum, decays to a minimum when VR out of S; equalizes the populations of SYand Sy, and rises to a plateau as excitations accumulate at the Sy origin (figs. lc and Id). Vibrational dephasing processes affect only the overall intensity of the pumpinduced CSRS emission; the time dependence is determined only by population redistribution processes. We demonstrate this new technique on the mixed crystal system pentacene in naphthalene (PTC/N) . The VC process in this system is initiated by excitation of the pentacene S; mode 747 cm- ’ above the Sy origin, and culminates in repopulation of Sy. The PTC/N system was chosen because it has been previously characterized by many optical coherence techniques (see, e.g. refs. [ 5,7] ). In particular, Hesselink and Wiersma (hereafter HW) [ 5 1, have recently reviewed measurements of VR in this system. However, to our knowledge, there has yet been no direct time-resolved measurements of VC. In the VC model of Hill and Dlott [ 21, processes which populate the Sy state after S; excitation may be “direct” or “indirect”. In the direct case, the rate of excitation arrival in Sy is identical to the rate of decay from S;; in the indirect case, the rate of arrival is slower that the decay rate because the excitation spends time in the “bath” consisting of other molecular vibrations or phonons, before repopulating the origin. In order to distinguish between the direct and indirect model, and to verify our theoretical treatment of the pump-induced CSRS method, we used photon echoes to remeasure the VR decay out of the Sy 747 cm-’ mode, and then measured the subsequent arrival of excitation at S? via a two-color pump-probe absorption saturation method. Our photon echo results are in exact agreement with HW [ 5 1. We find that the 33 ps lifetime of this mode is somewhat faster than the rate of repopulation of the S’: state, which occurs in -60 ps. Thus the VC process is indirect, inasmuch as the vibrational excitation spends roughly 25 ps in the bath states before repopulating the ground S? state. The pump-induced CSRS method is then used on this system, and it is shown to give results exactly consistent with the other two measurements except that the deexcitation and repopulation processes are simultaneously measured in the same experiment. accomplished

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2. Theory of pump-inducedCSR!3 The theory of resonance-enhanced CSRS is well known [ 7-9 1. For our purpose, we treat the pentacene molecule as a four-level system [ $10 1, weakly coupled to a bath. The four levels, diagrammed in fig. la, are the ground state IO), a vibrational mode of the electronic ground state 1ZJ), an electronic excited state origin IO’) , and a vibrational mode of the excited state 1u’ ) . If or = o 0,0 and w~=w~,~, then resonant population transfer to the excited states is facile. The intensity of the CSRS probe is dependent on the third-order non-linear susceptibility, xt3’ (us), where w,=201, -w2. If the diagonal elements of the density matrix are denoted pO,po,, pv and pur, then the largest terms of xc3) (w,) are [ 7-91

f3’(o)=C

x

(

1t

PO

[ (~o+A-~~,~)(~,~o G Wi)$- w, + ir,,

-w2+i~U~o)(wo~o-w,+i~o~o) ~2(w”o+~-~“o)

+( o&-WI

t ir,,) (W”!O, Sd-ir,,!)

P”, (O,!O!tA-ir",~)(o,, -o2+ir”‘o)(o,~“-co,

x

(

1+

ir, wlJIU-o,+iro,,

r, doto tr,,-r,,,,

tir,,)

ir,(o,,~+d-ir,,~) + (0,0tLl-ir,,)(o,~“-c0~

r,

)

tirot,)

)I’

doto+r,, -rbtoT, r, =r,,,+r,,,-rot,, r, =r,!,-r,, -r,,

,

(1)

where C= -~~o,~~,o~~v,~t,v(6N-‘~3)-‘, with pz being the vibronic transition moment between levels i and j associated with a photon of type CL The damping parameters r are defined in the usual way as r,j= f (& trj) t r;, with r; being the “pure” dephasing. r,, r,, r, and r, give rise to the dephasing-induced coherent emission (DICE), which has been observed for the 747 cm-’ mode of pentacene in benzoic acid [ 111 and naphthalene [ 71 matrices by inducing the DICE effect with increasing temperature. It has also been observed in the gas phase, and referred to as pressure-induced extra resonances in four-wave mixing (PIER-4) [ 12 1. For simplicity, we take r, =r, =r, =r, = 0 because pure dephasing is negligible at low temperature [ 5 I. The wI and w2 pulses are tuned to the wo,Oand w,,~ transitions, respectively, but the wI pulse is off-resonance to the o),,Utransition. Thus 1woTv-co, I = I co,,, - co1I = d= cove- o,,~, x= ro8, x r,,,, and eq. ( 1) can be simplified as

x(3)= (c/6) ( -poirv~orofo +potir~~o~rofo -P,iru,fru,)

.

(2)

In the pump-induced CSRS experiment, I v’ ) is excited by an intense pulse at r= 0, and the subsequent population flow from 1Y’ ) tolO’), and then ultimately to 10) (fig. lc) is probed by a pair of weak w1 and o2 pulses. The intensity of the stimulated CSRS signal as a function of the delay time is 10)~

IX(~) iz= ~c/~i~~~~~~~i~,,~~~~

-po47~/~,,r~o,

+p,wi~dz,i2.

(3)

In the experimental conditions used in this work, the CSRS pulse pair was attenuated sufficiently that population transfer induced by the probing process was negligible. We also neglect the relaxation from the IO’> state to the 10) state because this is typically two or more orders of magnitude slower than the relaxation from I v’ ) to 10’) . In this case eq. (3 ) can be rewritten as 20

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~(~)~(C/~~“,~)2~Po~(~)l~o,-P,(~)/~~~o12 *

27 May 1988

(4)

Eq. (4) shows that the time-dependent intensity of the CSRS probe is proportional to the square ofthe pop ufution difference between ( u’ ) and IO’) . Thus with this technique one measures the decay of population from I v’ ) and the arrival of population into IO’ ) in a single experiment. Fig. 1 presents a more intuitive model of the pump-induced CSRS experiment. In fig. lc, the population of the various levels is expressed by the open circles, while in fig. Id, the expected picosecond CSRS intensity is shown. In region I, which occurs at negative values of 7, the delay time (time before excitation at r=O), all the population is in the IO) state, the population difference pUJ-pot = 0, and thus there is no observed emission at 0,. In region II, the initial cr)~pump excites Iv’ ) . Now the population difference between I v’ ) and IO’ ) is large, and the CSRS signal rises abruptly. In region III, the excitation decays out of Iv’}. The population difference and the CSRS signal then decrease. In region IV, the populations of I v’ > and IO’ ) are nearly equal (exactly equal when rut0 =roto) and the CSRS signal drops to zero. In region V, all excitations have accumulated in I0’ ) and the CSRS signal rises to a plateau in region V. This plateau will eventually decay to zero with the IO’) lifetime. The ratio of the CSRS signal in region V to the peak at region II is equal to the ratio (r,.o/ro.o)2. In the PTC/N system, the rdamping constants are expected to be the inhomogeneous linewidths, so the signal intensity in this plateau is determined by the relative optical dephasing rates of these two transitions. Fig. Id shows that the various regions of the pump-induced CSRS signal contain different information. Region III gives the decay out of I v’ ), and legion V gives the buildup of accumulated population in IO’ ) , the ratio of damping parameters, and at long times the IO’) lifetime.

3. Vibrational cooling and pump-inducedCSRS In this section we consider different models for the VC process and their relationship to the pump-induced CSRS experiment. The kinetic scheme we employ is shown in fig. 1b. After the excitation of I v’ ) , it may relax directly to IO’> with rate constant k,, or it may relax indirectly via intermediate “bath” states (broken line). For simplicity we consider only one intermediate state I I), although the extension of this problem to large or infinite numbers of intermediates can be performed in a straightforward manner using the VC expressions derived by Hill and Dlott [ 21. In this case I u’ ) relaxes to II) with rate constant kb, and then I I) continues to relax to IO’) with rate constant kc. Finally, I0’ ) relaxes to states in the ground electronic manifold with rate constant kf. We first consider the case where VC is a direct process, which corresponds to k,,= kc= Q Assuming that ,QK k,, and that the experiment is performed over a time range such that hr -ZZ1, we find that

The minimum of I( T) occurs when td = ( 1/k,) In [ (T,,+rvo) /I’,,], where td is the time delay of the dip denoted by region IV in fig. Id. Some sample calculations with eq. (5) are shown in fig. 2a, where the pump induced CSRS signal is plotted for k,= (1, 0.5, 0.25) X 10” s-‘, and ro,o/rv.o= 1. As the value of k, is systematically decreased, the dip in the signal moves progressively to longer values of time. With one intermediate state I I), assuming that k,= 0 and kb and kc $0, and neglecting kf as before, we find

(6) Figs. 2b and 2c show the effect on the pump-induced CSRS signal of varying the rate constants kb and kc, with k,=O and ro.o/I’,.O= 1. In fig. 2b, kb is held constant while k, is varied. As k, decreases, the fall from the 21

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CAL,CULATED

CHEMICAL PHYSICS LETTERS

PUMP-INDUCED

27 May 1988

CSRS

Fig. 2. Sample calculations for pump-induced CSRS. (a) Direct repopulation ofthe ground state with k,=k,=O, and rea/rv,e= 1. As k. is decreased from 10” s-‘, the minimum is moved to longer time. (b) Indirect repopulation with k,=O, kb= 10” s-‘, and k, is varied. (c) Indirect repopulation with k,=O, k= 10” s-l, and kb is varied. The position of the minimum is mostly dependent on the value of kb.

peak is unaffected, while the rise to the plateau is slowed. In fig. 2c, kc is held constant while k,, is decreased. Decreasing kb slows the fall from the peak and moves the dip to longer time while hardly affecting the rise to the plateau. The position of the dip at t,, is mostly dependent on the value of kb, because when ro,o/Z’,, = 1, td occurs when the 1v’ ) and ]0’ ) populations are equal.

4. Experimentalresults

Three types of measurements were performed on pentacene in naphthalene crystals ( x lo-’ M/M) immersed in superfluid He at 1.7 K: the two-pulse photon echo, an absorption recovery experiment which probes arrival of excitation at the Sp origin, and pump-induced CSRS. AI1the experiments were performed with a dual dye laser system described previously [ 131, In every case we were very careful to attenuate each pulse to ensure that high laser power effects other than those desired were eliminated. In fig. 3a, we show the photon echo data (solid line) taken on the 747 cm-’ ST mode using the standard non-collinear geometry [ 5 1. The decay of the echo signal I(r) ccexp ( - 2r/ r, ) at this temperature [ 5 1. The instrument response function (broken line in fig. 3a) was experimentally determined from the photon echo of cresyl violet in methanol at 300 K. This response was convolved with exponential decay functions and the best fit (open circles) was obtained with T, = 33 ? 4 ps, in quantitative agreement with HW [ 51. In fig. 3b, we show the results of a two-color absorption recovery experiment where an intense pulse pumps the S: 747 cm-’ state, and a weaker pulse detects the transient absorbance change of the $+S? transition. We plot the time-dependent change in optical density of the probed transition (noisy line), which is proportional to the (normalized) accumulated population of Sp. The apparatus response in this case should be the integral of the cross correlation function of the two dye lasers. This function (broken line) was measured with a KDP sum crystal and numerically integrated. For a first guess, we tried to fit the data to a simple exponential growth function, and achieved best fit with t,z60 ps. This demonstrated that recovery of the origin is significantly slower than decay from 747 cm-‘, so we assumed that the intermediate, 1I), was populated, fixed k,=1/(33 ps), and fit the data with k,=1/(25?5 ps) (solid line). We thus find that VC out of the 747 cm- l mode is an indirect process, commencing with a 33 ps decay from the initial state into the bath, followed by appearance at the Si origin after a delay of ~25 PS. 22

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CHEMICAL PHYSICS LETTERS

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-100

0

DELAY TM

100

200

tpsl

Fig. 3. (a) Photon echo data (solid line) on S; state 747 cm-’ above the S, origin. The broken line is the apparatus response, and the open circles are obtained by convolving apparatus response with a 33 ps lifetime. (b) Origin absorption recovery after 747 cm-’ excitation (noisy line). The apparatus response (broken line) is convolved with the indirect repopulation model, with !+,= l/(33 ps), and /c, is varied for best fit with k,= l/(25? 5 ps) (solid line).

-200

-100

0

loo

200

300

DELAYlMIueI

Fig. 4. Pump-induced CSRS data (solid line) on excited state 747 cm-’ vibration and origin. The data are fit with eq. (6) (broken line), using kb= l/(33 ps) from the photon echo data in fig. 3a and k,= I /(25 ps) from the data in fig. 3b.

In fig. 4 we show the results of the pump-induced CSRS experiment performed on the 747 cm- ’ and origin levels. In accordance with the predictions of fig. 2, the data show an initial rise to a maximum, a fall to the “dip” at td= 33 ps, and other rise to a plateau at a level of 0.58 of the maximum. A small amount of CSRS occurring before T= 0 was subtracted from the plot. On the time scale of this experiment the S! lifetime of 19 ns [ 41 is unimportant. The plateau value gives the ratio ro,O/r,,o = 1.3 &.0.05, in quantitative agreement with HW, who report the ratio of inhomogeneous linewidths is ro,o/r,.o = 1.0/0.8 [ 141. We simulated the pump-induced CSRS data in fig. 4 using eq. (6) with /cband k, determined from the data fig. 3 (broken line). The fit is adequate, considering that no adjustable parameters were used. The difference between our simulation and the calculated curve is presumably due to our neglect of the finite duration laser pulses.

5. Conclusions We have shown that VC from the 747 cm-’ Sy mode of pentacene in naphthalene at low temperature is an indirect process in the sense that the rate of deexcitation of SYis about twice as fast as the rate of accumulation in S?. We have also shown that the new pump-induced CSRS technique permits simultaneous measurement of these two processes and the ratio of dephasing rates of these two states, which is in exact agreement with well-characterized methods which measure these rates individually. Our measurements rule out the possibility that VR in pentacene involves vibrational energy transfer to the host, as in that case VC would be a direct process. Instead, VR probably involves multiple steps down a vibrational ladder, each step no larger than 180 cm- ‘, the phonon cutoff in naphthalene [ 2,3 1, with the average step size being z 95 cm- ’ [ 2,3]. This cascade process terminates at the “two-phonon” barrier at x: 360 cm-‘, 23

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where excitations relax by emission of two host phonons and repopulate the origin [ 2,3,5]. Thus on average four VR steps are involved in VC. From our results, we can deduce that the VR to the 609 cm-’ state does not occur to a significant extent, as the lifetime of this state, T, = 59 k 3 ps [ 51 is too long to account for the x 25 ps delay between the initial VR and origin repopulation. This VR process would involve emission of = 138 cm-’ phonons, which do not exist in naphthalene, because they would lie in the gap between the highest libron and lowest vibration [ 11, Other levels located below 747 cm- ’ have lifetimes in the 2 to 20 ps range [ 51, suggesting that on average each excitation samples one long-lived, a20 ps, state and three short-lived states during VC.

References [ I ] S. Califano, V. Schettino and N. Neto, Lattice dynamics of molecular crystals (Springer, Berlin, 1981). [2] J.R. Hill and D.D. Dlott, J. Chem. Phys. ( 1988) to be published; to be published. [3] J.R. Hill, E.L. Chronister, T.-C. Chang, H. Kim, J.C. Postlewaite and D.D. Dlott, J. Chem. Phys. 88 (1988) 949,236l. [4] A. Laubereau and W. Kaiser, Rev. Mod. Phys. 50 ( 1978) 608. [ 51 W.H. Hesselink and D.A. Wiersma, in: Spectroscopy and excitation dynamics of condensed molecular systems, eds. V.M. Agranovich and R.M. Hochstrasser (North-Holland, Amsterdam, 1983). [ 61 B.H. Hesp and D.A. Wiersma, Chem. Phys. Letters 75 (1980) 423; K. Duppen, B.H. Hesp and D.A. Wiersma, Chem. Phys. Letters 79 ( 1981) 399; C.L. Schosser and D.D. Dlott, J. Chem. Phys. 80 ( 1984) 1384; S.P. Velsko and R.M. Hochstrasser, J. Chim. Phys. 82 (1985) 153; J. Phys. Chem. 89 ( 1985) 2240. [ 71 T.-C. Chang, C.K. Johnson and G.J. Small, J. Phys. Chem. 89 (1985) 2984. [ 81 J.R. Andrews and R.M. Hochstrasser, Chem. Phys. Letters 82 (1981) 381. [9] T.-C, Chang, Ph.D. Thesis, Iowa State University ( 1985). [ lo] N. Bloembergen, H. Lotem and R.T. Lynch, Indian J. Pure Appl. Phys. 16 ( 1978) 15 1. [ 111 R. Bozio, P.L. DeCola and R.M. Hochstrasser, in: Time-resolved vibrational spectroscopy, ed. G.H. Atkinson (Academic Press, New York, 1983). ‘[ 121A.R. Bogdan, Y. Prior and N. Bloembergen, Opt. Letters 6 ( 1981) 82; Y. Pribr, A.R. Bogdan, M. Dagenais and N. Bloembergen, Phys. Rev. Letters 46 ( 1981) 111. [ 131R.E. Cline Jr., E.L. Chronister, T.J. Kosic, C.L. Schosser and D.D. Dlott, in: Proceedings of the International Conference on Lasers ‘83, ed. R.C. Powell (STS Press, McLean, 1984) p. 697. [ 141W.H. Hesselink and D.A. Wiersma, Chem. Phys. Letters 65 (1979) 300.

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