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Thermally induced excited-state coherent raman spectra of solids
CHEMlCAL
Volume 82, number 3
15 September 1981
PHYSICS LETTERS
THERMALLY INDUCED EXCITED-STATE COHERENT RAMAN SPECTRA OF SOLIDS * J-R. ANDREWS Department
** and R-M. HOCHSTRASSER
of Chemistry.
University
of Pennsylvania.
Philadelphia,
PennsylvarGa 19104,
USA
Received 20 July 1981
_4 difference frequency resonance has been observed for the 747 cm-’ vibration in the first excited singlet state of pentacene in benzoic acid. The resonance is absent at low temperature (4.5 K) and its appearance is exponentially activated with an activation energy of 13 8 cm-‘. These observations are compared to theoretical expectations-
1. Introduction The coherent generation of light at os = 2ul - w2, with w1 < w2, when a medium is irradiated with light at two frequencies o1 and 02, is the coherent analogue of Stokes Raman spectroscopy (CSRS). We have shown in recent studies [l-4] that under resonant conditions, when wl, c+ and ws are close to molecular transition frequencies, ihe CSRS process can be used to study excited-state transitions that may not be accessible through the use of the more common coherent antiStokes spectroscopy (CARS). In the present paper we describe experiments that confirm some of the basic aspects of resonant CSRS, particularly in regard to its dependence on pure dephasing in condensed-phase systems. Our studies of condensed phases [24] are analogous to recent studies of collision-induced coherent light signals obtained from atomic vapors [5-7]_ The theoretical structure of the third-order susceptibility that describes these processes is well-known [8-121, though the recognition that the introduction of pure dephasing effects into the theory leads to new resonances appears to be traceable to Bloembergen et al. 183. The basic idea that emerges is that in the absence of pure dephasing such as with a perfect solid at absolute zero or an atomic beam, only spontaneous * This research was supported by NIH-grant GM12592.
The instrumentation was obtained in part from the Regional Laser Laboratories at the University of Pennsylvania_
**
National Eye Institute Post-Doctoral Fellow.
decay processes occur so that definite relationships exist amongst the damping parameters for certain molecular transitions_ In such circumstances the resonant thirdorder susceptibility, consisting of 48 terms, does not in actuality manifest the resonances of each term. The cancellation of resonances arising from the collection of terms does not occur when there are pure dephasing contributions to the resonance widths [S] . Thus as the temperature is raised in the solid, or as collisions are allowed to occur in the gas [5-71, there arise new resonant terms in the susceptrbrlity. For the case of CSRS one of these terms involve excited-state vibrational transitions, so that we have the opportunity to study vibrational spectra, dephasing and relaxation effects in electronically excited states. Such processes cannot be directly studied by single-frequency optical hole burning or conventional photonecho methods which always involve the electronic dephasing. Other multiple-frequency spectroscopic techniques can be used to study inter-excited-state dynamics [13,14]. The system studied is pentacene in a benzoic acid host lattice_ The resonant CARS and CSRS spectra of this system at l-6 K [l] indicated that ground- and excited-state Raman transitions could be obtained in a single experiment. On-resonance pumping gives rise to resonances that are a superposition of excited-state Raman and optical resonances. Since the usual way to obtain Raman spectra of excited states is to populate them and subsequently take their spectra, it seemed important to develop further the coherent method which does not depend on excited-state populations_ The present experiments are designed to study the 381
CHEMICAL
Volume 82, number 3
15 September 1981
PHYSICS LETTERS
effect of detuning from electronic transitions and to measure the temperature effect on that part of the resonant CSRS that is expected to be modified by the introduction of pure dephasmg. This allows us to confirm the basic theoretical model [8.4], and also to generate new information on the mechanism of dephasing of transItIons in molecular sobds [IS] _
2 Theory The system pentacene m benzoic acid is chosen so that its response to two laser fields IS expected to conform to that of a four-level system. The field frequencIes are cd1 and ~2, chosen with 02 - ~1 m the range 750 cm-l _near to the pentacene vibrations w, = 755 (ground St&e) and 0,’ = 747 cm-l (excited state)_ The laser al is fixed dt various detunings cl below the O-O transition at 17003 cm-l _The CSRS susceptlblhty for these four ievels 0, O’, u, u’ neglecting inhomogeneous broadenmg sho\%sresonances in A = wz - w1 of the form [4]:
mechanism is introduced, the factors I’1 and r2 behave very differently. The r: or I’;# are small and only slowly varying functions of Tin the temperature range examined here [3,16], whereas IYOIuJrVeO, I”,,~ and r’,,a0are all quite sensitive to temperature and in several observed cases have similar exponentiaily activated temperature dependences [IS]. Thus rl = P&u - r&y x 0 over the restricted temperature range examined here and rZ = I’&. + I’&,*_ Expression (1) mdicates that as d increases at low temperature (where r, = 0) the excited-state resonance at w,,~ = A should be absent, but a resonance at constant optical frequency o2 = wou~ should be present. As the temperature increases (r2 # 0) the difference frequency with width rUt should appear. The purpose of the present experiments is to study these two predicted effects. For the case of large detuning, o, % d > raO, the susceptibility has the simple form A(d.
A>
1 o,-Adir,
i-
irZ/ci A - a,,
_ ir,,
1
-i-‘(‘1
where A and B are slowly varymg (“non-resonant”) functions of A.
2 (3-I
A>
3. Experimental
c.J~’ ir2(wv
+ (A-
- A + il?,)
---~ilTup)(A f d - wu - So*,)
1 (1) ’
where I?, = To*, - Foot - rU; Z’7 = I”nVo+ I’,, 0 - r,t and raa = $ (I?& + rp)+ r$ wtth r, and rp being spontaneous decay constants, and K’& the pure dephasing (I?+ 1s just l/T2 for the transition (Y* @)_ The second term in brackets in expression (1) describes a pure dephasing-induced resonance for the output frequency ws matching WOKS.The third term gives rise to a pure dephasing-induced resonance as in the second term but in addition shows a resonance when the difference between two input Iaser frequencies o2 - u1 matches an excited-state Raman transition wUp. The levels involved in these pure dephasing-induced resonances are aU unpopulated ~II the absence of the laser fields. For a stable ground state ro = 0 so both rr and I’, are zero in the absence of pure dephasing. As the temperature is increased or some other pure dephasing 382
A crystal of pentacene in benzoic acid (~3 X 10” M/M) was mounted in an exchange gas helium dewar and cooled with liquid helium. One YAG-laser-pumped dye laser was tuned to the region of the O-O band of pentacene (17003 cm-l) with &ton Red dye. A second dye laser was tuned to the region of the 747 cm-1 excited-state vibration using coumarin 540A. Both lasers were linearly polarized along the CIcrystallographic axis. The u2 laser was scanned and the w3 signal frequency detected by a photomultiplier tube after filtering with a double monochromator synchronously scanned by computer with the dye laser. Signals were amplified with a boxcar integrator and plotted on a stripchart recorder. The dynamic range of the measurements was greater than three orders of magnitude when neutral density filters were used to attenuate the strongest signals. Detuning from the O-O band was calculated from the fluorescence excitation measured O-O position and the dye-laser setting. This was in agreement with that expected from the position of the A = 755 cm-l ground-state vibration to +1 cm-l. Tempera-
Volume 82, number 3
CHEMICAL PHYSICS LETTERS
tures were controlled by a Wheatstone bridge-lock-in amplifier system and were set to better than It0.I K.
4. Results The effect of detuning is shown in fig. 1. With no detuning
there appear two comparably 761 I
755 I
intense lines
747 L
45K
d=OOcm-’
15 September 1981
at A = 755 and 747 cm-l corresponding to the groundand excited-state modes. The spectrum also contains a line at 761 cm --I which is actually a doublet corresponding to another ground- and excited-state pair. At 4.5 K (fig. 1) the detuning todower wavenumber results in a shift of the peak initially at 747 cm-l to higher wavenumber (w2 - wl)_ These results are consistent with eq. (l), so that we can be certain that the 747 cm-f peak at 4.5 R arises from the energy denominator (0,’ + d - A - iI?,& At 4.5 IS the O-O optical linewidth is comparable with the laser bandwidth while run0 is ~0.2 cm-l. Fig. 2 shows the CSRS spectrum at d = 16.8 cm-l for three temperatures. At T = 4.5 K the region around 747 cm-l (displayed on an expanded intensity scale) shows no trace of the excitedstate resonance_ As the temperature is raised the A
d=168cm-
. 761
755
747
13K
I
f
1
760 A$
750
740
(cm-t)
Fig, 1. The CSRS spectra as a function of deiuning tc lower wavenumber, d,from the O-O transition of pentacene in benzoic acid (17003cm-r) at 4.5K_ Tire right solid lines are theoretical shmdatious using expression (1). Note that the resonance at A = 747 cm-r ford = 0 moves to center frequencies of A = 751.5 cm-’ for d = 4.5 cm-’ and A = 763.8ford = 16.8 cm-l as predicted by theory. The topmost scale shows several of the resonance frequencies for d = 0 cm-‘.
I
760 AC
1
750
I
740
(cm-‘)
Fig. 2. The CSRS spectrum as a function of temperatureat d = 16.8 cm-r. The portion of the spectrum near A = 747 cm-l is shown on an expanded vertical scaIe. Note that the band at A = 747 cm-” grows relative to the peak at A = 7.55 cm-l -
383
= 747 cm-l
transition
state resonance
1S September 1981
CHEMICAL PHYSICS LETTERS
Volume 82, number 3
grows relative to the ground-
consistent
with expectatrons
(3) one finds I?(T) = r , + 26Ru2. The positlve sign is taken because 26R fi is greater than rut over the whole range of the experiment, and because the vibrational dephasing is slow (see below)_ Note that for 26 R 1/z< rue we should chose the negative sign to allow I’(T) to go smoothly to zero as R1j3 + lYup/26_ We know from independent CSRS experiments carried out with narrow laser sources [2,15] that rV = rVe = 0.22 + 0.02 cm-l over the temperature range 1.6-25 K. Thus in this range the pure dephasing of the Raman transitions stays less than -0.02 cm-l, and the 0.22 cm-l corresponds to population relaxation_ Thus I’(T) should be given accurately by (rofo + Go) at all the temperatures used here. Fig. 3 shows a plot of T(T) calculated from experimental data versus T. The solid line is the calculated best fit to expression (3) where r2 has the form relation
based
on expression (1). It should be noted that incoherent fluorescence 1s the major source of background signal in fig 2. The ratio of the peak Intensities at A = 747 and 4 = 754 cm-l were measured at 10 temperatures between 4.5 and 25 K. The pure dephasmg-induced resonance at ws = wonU might also be observable_ Since the damping parameter for ttis resonance, rorU, is increasing in approximately the same way as r? ds a function of temperature, the two effects should cancel one another to a large extent. Tlus is apparently the case since no evidence for the resonance has been obtained. It is important in experiments of this type to understand the effects of introducmg populations into excited states by the incident fields. Expressions (1) and (2) are expected to provide a complete description of the system under the condition that the ground state alone is populated. A population in the 0’ level would result in a CSRS signal at the excited-state frequency_ This signal would be expected even at the lowest temperature_ We have found the ratio of 747 to 75.5 cm-l resonance peaks to be independent of laser power in the range reported_
r2 = rbpo+ rLto=(9.7cm-l)
exp(-13.8
cm-l/kT)
. (4)
The observed exponential growth with an activation parameter of 13.8 cm-l is consistent with the electronic dephasing being brought about by a particular phonon of benzoic acid. Phonon transltlon near this I
I
c I-
/
5. Discussion In the present experiments the ratio R of the CSRS intensity for the 747 and 755 cm-l transitions is quite accurately represented by the followmg expression, obtained from eq. (2)R=
(pr,*
- r#
+ a?
(cd- a)) + [I?**0 + (d/ti)r”. = [r,
-
r,+f/s
d*
-
+ I-+“]2
(3)
03”
-
where p = (c1 - 6)/6 and Q!= (l/~)(r,,,I’,~, + rUr2 + r,I’,*), with 6 = wU - wUI_ At 0 K when we expect rZ = 0 the value of R is finite because of contributions to the signal at 4 = 0,~ which do not show a resonance pezk. Expressions (1) and (3) show minima for R at an httermediate temperature which is a manifestation of interference between the ground-state vibrational resonance wing and the dephasing-induced resonance_ As r2 grows larger, a peak develops at A = GJ,‘. From 384
c
20
10
T (K) Fig. 3. The growth of pure dephasing, rz(T), as a function of temperature. R is the experimentaNy measured quantity and is the ratio of the resonance height at A = 747 and A = 754 cm-’ _ The solid Iine is a least-squares fit to an Arrhenius activation eq. (4). The point x represents twice the observed pure-dephasing contribution to the 0 + v’ transition and is an independent estimate of Q(T).
Volume
82, number
frequency
also
CHEMICAL
3
occur
in the phonon-sideband
PHYSICS
spectra
of pentacene in benzoic acid. This situation is similar to that reported for pentacene in naphthalene as a result of photon-echo measurements [ 15]_ The present experiments have confirmed the occurrence of phonon-induced excited-state Raman transitions in molecular solids. The experiments can be utilized in the study of pure-dephasing contributions to the electronic and Raman linewidths. It is possible to carry out the experiment in a variety of ways leading to different simplifications of eq. (1). Measurements of the intensity I of the resonance at A = oU’ relative to a constant internal standard, such as a host crystal CSRS transition, yields for large d I=C(D-Er’)2)
(2
where C, D and E are determinable numbers. The introduction of population into the zero-point level of the excited state gives rise to an additional contribution to the third-order susceptrbility. This term is not considered here because the observed effects were shown to depend on the ground-state population_ The coherence introduced between the levels 0’ and u’ by the two laser fields must also be accompanied by increases in their populations. However, in the perturbation expansion of the density operator these population changes are not described until higher orders than third. It is easy to see that coherence between any two levels of a system described by a statistical density operator cannot exist unless both levels have population_ This can be deduced from the inequality tr p2 < 1, leading to 1~0 l2 < piipii for any pair of levels i and j. Thus we see the simple physical picture for the occurrence of our signal is that temperature-induced fluctuations of the energy levels allow the coherent process to occur. The concomitant occurrence of fluorescence as well as spontaneous Raman scattering is well known [ 173 _ The actual populations in these upper levels can only be calculated from terms fourth-order or higher in the molecule-field interactions.
LETTERS
1.5 September
1981
Acknowledgement We like to thank Dr. H.P. Trommsdorff for invaluable help with the lmear spectroscopy of this system, Mr. M.E. Huster for assistance wrth the cryogenics and Mr. ES. Hilfer for assistance with the computer graphics.
References 111 P L. DeCola, J-R. Andrews, R M Hochstrasser
and H P Trommsdorff, J. Chem. Phys. 73 (1980) 4695. I21 J-R. Andrews and R.M. Hochstrasser, Bull_ Am. Phys. Sot. 26 (1981) 13. [31 J.R. Andrews and R M. Hochstrasser, Bull. Am Phys. Sot. 26 (1981) 278. [41 J.R Andrews, R.M. Hochstrasser and H P. Trommsdorff, Chem. Phys., to be published. Opt Letters 151 A-R. Bogdan, Y Prior and N. Bloembegen, 6 (1981) 82. 161 Y. Prior. A.R. Bogdan, hl. Dagenais md N. Bloembergen, Phys. Rev. Letters 46 (1981) 111 Phys. Rev. 171 A. Bogdan, M. Downer and N. Bloembergen, A, submitted for publication. PI N Bloembergen, H. Lotem and R.T. Lynch Jr., Indian J. Pure Appl. Chem. 16 (1978) 151. 191 S-A-J. Druet, B.A. Attal, T.C. Gustafson and J.P. Tar-an, Phys. Rev. A18 (1978) 1529. 1101 T K. Yee and T.K. Gustafson, Phys. Rev. A18 (1978) 1597. 1111 S.A J. Druet, J.P E Taran and Ch. J. Bordd, J Phys. (Paris) 40 (1979) 819. WI J.-L. Oudar and Y.R. Shen, Phys. Rev. A22 (1980) 1141. 1131 H-R. Schlossberg and A. Java, Phys Rev. 150 (1966) 267. [ 141 T.W. Mossberg, E. Whittaker, R. Kachn and S.R. Hartman, Phys. Rev_ A22 (1980) 1962. 1151 W-H. Hesselink and D.A. Wiersma, J. Chem. Phys. 73 (1980) 648. [16] J-R. Andrews and R.hl. Hochstrasser, Chem. Phys Letters, submitted for publication_ [17] R-hi. Hochstrasser and C. Nyi, J. Chem. Phys 70 (1979) 1112.
385
Volume 82, number 3
15 September 1981
PHYSICS LETTERS
THERMALLY INDUCED EXCITED-STATE COHERENT RAMAN SPECTRA OF SOLIDS * J-R. ANDREWS Department
** and R-M. HOCHSTRASSER
of Chemistry.
University
of Pennsylvania.
Philadelphia,
PennsylvarGa 19104,
USA
Received 20 July 1981
_4 difference frequency resonance has been observed for the 747 cm-’ vibration in the first excited singlet state of pentacene in benzoic acid. The resonance is absent at low temperature (4.5 K) and its appearance is exponentially activated with an activation energy of 13 8 cm-‘. These observations are compared to theoretical expectations-
1. Introduction The coherent generation of light at os = 2ul - w2, with w1 < w2, when a medium is irradiated with light at two frequencies o1 and 02, is the coherent analogue of Stokes Raman spectroscopy (CSRS). We have shown in recent studies [l-4] that under resonant conditions, when wl, c+ and ws are close to molecular transition frequencies, ihe CSRS process can be used to study excited-state transitions that may not be accessible through the use of the more common coherent antiStokes spectroscopy (CARS). In the present paper we describe experiments that confirm some of the basic aspects of resonant CSRS, particularly in regard to its dependence on pure dephasing in condensed-phase systems. Our studies of condensed phases [24] are analogous to recent studies of collision-induced coherent light signals obtained from atomic vapors [5-7]_ The theoretical structure of the third-order susceptibility that describes these processes is well-known [8-121, though the recognition that the introduction of pure dephasing effects into the theory leads to new resonances appears to be traceable to Bloembergen et al. 183. The basic idea that emerges is that in the absence of pure dephasing such as with a perfect solid at absolute zero or an atomic beam, only spontaneous * This research was supported by NIH-grant GM12592.
The instrumentation was obtained in part from the Regional Laser Laboratories at the University of Pennsylvania_
**
National Eye Institute Post-Doctoral Fellow.
decay processes occur so that definite relationships exist amongst the damping parameters for certain molecular transitions_ In such circumstances the resonant thirdorder susceptibility, consisting of 48 terms, does not in actuality manifest the resonances of each term. The cancellation of resonances arising from the collection of terms does not occur when there are pure dephasing contributions to the resonance widths [S] . Thus as the temperature is raised in the solid, or as collisions are allowed to occur in the gas [5-71, there arise new resonant terms in the susceptrbrlity. For the case of CSRS one of these terms involve excited-state vibrational transitions, so that we have the opportunity to study vibrational spectra, dephasing and relaxation effects in electronically excited states. Such processes cannot be directly studied by single-frequency optical hole burning or conventional photonecho methods which always involve the electronic dephasing. Other multiple-frequency spectroscopic techniques can be used to study inter-excited-state dynamics [13,14]. The system studied is pentacene in a benzoic acid host lattice_ The resonant CARS and CSRS spectra of this system at l-6 K [l] indicated that ground- and excited-state Raman transitions could be obtained in a single experiment. On-resonance pumping gives rise to resonances that are a superposition of excited-state Raman and optical resonances. Since the usual way to obtain Raman spectra of excited states is to populate them and subsequently take their spectra, it seemed important to develop further the coherent method which does not depend on excited-state populations_ The present experiments are designed to study the 381
CHEMICAL
Volume 82, number 3
15 September 1981
PHYSICS LETTERS
effect of detuning from electronic transitions and to measure the temperature effect on that part of the resonant CSRS that is expected to be modified by the introduction of pure dephasmg. This allows us to confirm the basic theoretical model [8.4], and also to generate new information on the mechanism of dephasing of transItIons in molecular sobds [IS] _
2 Theory The system pentacene m benzoic acid is chosen so that its response to two laser fields IS expected to conform to that of a four-level system. The field frequencIes are cd1 and ~2, chosen with 02 - ~1 m the range 750 cm-l _near to the pentacene vibrations w, = 755 (ground St&e) and 0,’ = 747 cm-l (excited state)_ The laser al is fixed dt various detunings cl below the O-O transition at 17003 cm-l _The CSRS susceptlblhty for these four ievels 0, O’, u, u’ neglecting inhomogeneous broadenmg sho\%sresonances in A = wz - w1 of the form [4]:
mechanism is introduced, the factors I’1 and r2 behave very differently. The r: or I’;# are small and only slowly varying functions of Tin the temperature range examined here [3,16], whereas IYOIuJrVeO, I”,,~ and r’,,a0are all quite sensitive to temperature and in several observed cases have similar exponentiaily activated temperature dependences [IS]. Thus rl = P&u - r&y x 0 over the restricted temperature range examined here and rZ = I’&. + I’&,*_ Expression (1) mdicates that as d increases at low temperature (where r, = 0) the excited-state resonance at w,,~ = A should be absent, but a resonance at constant optical frequency o2 = wou~ should be present. As the temperature increases (r2 # 0) the difference frequency with width rUt should appear. The purpose of the present experiments is to study these two predicted effects. For the case of large detuning, o, % d > raO, the susceptibility has the simple form A(d.
A>
1 o,-Adir,
i-
irZ/ci A - a,,
_ ir,,
1
-i-‘(‘1
where A and B are slowly varymg (“non-resonant”) functions of A.
2 (3-I
A>
3. Experimental
c.J~’ ir2(wv
+ (A-
- A + il?,)
---~ilTup)(A f d - wu - So*,)
1 (1) ’
where I?, = To*, - Foot - rU; Z’7 = I”nVo+ I’,, 0 - r,t and raa = $ (I?& + rp)+ r$ wtth r, and rp being spontaneous decay constants, and K’& the pure dephasing (I?+ 1s just l/T2 for the transition (Y* @)_ The second term in brackets in expression (1) describes a pure dephasing-induced resonance for the output frequency ws matching WOKS.The third term gives rise to a pure dephasing-induced resonance as in the second term but in addition shows a resonance when the difference between two input Iaser frequencies o2 - u1 matches an excited-state Raman transition wUp. The levels involved in these pure dephasing-induced resonances are aU unpopulated ~II the absence of the laser fields. For a stable ground state ro = 0 so both rr and I’, are zero in the absence of pure dephasing. As the temperature is increased or some other pure dephasing 382
A crystal of pentacene in benzoic acid (~3 X 10” M/M) was mounted in an exchange gas helium dewar and cooled with liquid helium. One YAG-laser-pumped dye laser was tuned to the region of the O-O band of pentacene (17003 cm-l) with &ton Red dye. A second dye laser was tuned to the region of the 747 cm-1 excited-state vibration using coumarin 540A. Both lasers were linearly polarized along the CIcrystallographic axis. The u2 laser was scanned and the w3 signal frequency detected by a photomultiplier tube after filtering with a double monochromator synchronously scanned by computer with the dye laser. Signals were amplified with a boxcar integrator and plotted on a stripchart recorder. The dynamic range of the measurements was greater than three orders of magnitude when neutral density filters were used to attenuate the strongest signals. Detuning from the O-O band was calculated from the fluorescence excitation measured O-O position and the dye-laser setting. This was in agreement with that expected from the position of the A = 755 cm-l ground-state vibration to +1 cm-l. Tempera-
Volume 82, number 3
CHEMICAL PHYSICS LETTERS
tures were controlled by a Wheatstone bridge-lock-in amplifier system and were set to better than It0.I K.
4. Results The effect of detuning is shown in fig. 1. With no detuning
there appear two comparably 761 I
755 I
intense lines
747 L
45K
d=OOcm-’
15 September 1981
at A = 755 and 747 cm-l corresponding to the groundand excited-state modes. The spectrum also contains a line at 761 cm --I which is actually a doublet corresponding to another ground- and excited-state pair. At 4.5 K (fig. 1) the detuning todower wavenumber results in a shift of the peak initially at 747 cm-l to higher wavenumber (w2 - wl)_ These results are consistent with eq. (l), so that we can be certain that the 747 cm-f peak at 4.5 R arises from the energy denominator (0,’ + d - A - iI?,& At 4.5 IS the O-O optical linewidth is comparable with the laser bandwidth while run0 is ~0.2 cm-l. Fig. 2 shows the CSRS spectrum at d = 16.8 cm-l for three temperatures. At T = 4.5 K the region around 747 cm-l (displayed on an expanded intensity scale) shows no trace of the excitedstate resonance_ As the temperature is raised the A
d=168cm-
. 761
755
747
13K
I
f
1
760 A$
750
740
(cm-t)
Fig, 1. The CSRS spectra as a function of deiuning tc lower wavenumber, d,from the O-O transition of pentacene in benzoic acid (17003cm-r) at 4.5K_ Tire right solid lines are theoretical shmdatious using expression (1). Note that the resonance at A = 747 cm-r ford = 0 moves to center frequencies of A = 751.5 cm-’ for d = 4.5 cm-’ and A = 763.8ford = 16.8 cm-l as predicted by theory. The topmost scale shows several of the resonance frequencies for d = 0 cm-‘.
I
760 AC
1
750
I
740
(cm-‘)
Fig. 2. The CSRS spectrum as a function of temperatureat d = 16.8 cm-r. The portion of the spectrum near A = 747 cm-l is shown on an expanded vertical scaIe. Note that the band at A = 747 cm-” grows relative to the peak at A = 7.55 cm-l -
383
= 747 cm-l
transition
state resonance
1S September 1981
CHEMICAL PHYSICS LETTERS
Volume 82, number 3
grows relative to the ground-
consistent
with expectatrons
(3) one finds I?(T) = r , + 26Ru2. The positlve sign is taken because 26R fi is greater than rut over the whole range of the experiment, and because the vibrational dephasing is slow (see below)_ Note that for 26 R 1/z< rue we should chose the negative sign to allow I’(T) to go smoothly to zero as R1j3 + lYup/26_ We know from independent CSRS experiments carried out with narrow laser sources [2,15] that rV = rVe = 0.22 + 0.02 cm-l over the temperature range 1.6-25 K. Thus in this range the pure dephasing of the Raman transitions stays less than -0.02 cm-l, and the 0.22 cm-l corresponds to population relaxation_ Thus I’(T) should be given accurately by (rofo + Go) at all the temperatures used here. Fig. 3 shows a plot of T(T) calculated from experimental data versus T. The solid line is the calculated best fit to expression (3) where r2 has the form relation
based
on expression (1). It should be noted that incoherent fluorescence 1s the major source of background signal in fig 2. The ratio of the peak Intensities at A = 747 and 4 = 754 cm-l were measured at 10 temperatures between 4.5 and 25 K. The pure dephasmg-induced resonance at ws = wonU might also be observable_ Since the damping parameter for ttis resonance, rorU, is increasing in approximately the same way as r? ds a function of temperature, the two effects should cancel one another to a large extent. Tlus is apparently the case since no evidence for the resonance has been obtained. It is important in experiments of this type to understand the effects of introducmg populations into excited states by the incident fields. Expressions (1) and (2) are expected to provide a complete description of the system under the condition that the ground state alone is populated. A population in the 0’ level would result in a CSRS signal at the excited-state frequency_ This signal would be expected even at the lowest temperature_ We have found the ratio of 747 to 75.5 cm-l resonance peaks to be independent of laser power in the range reported_
r2 = rbpo+ rLto=(9.7cm-l)
exp(-13.8
cm-l/kT)
. (4)
The observed exponential growth with an activation parameter of 13.8 cm-l is consistent with the electronic dephasing being brought about by a particular phonon of benzoic acid. Phonon transltlon near this I
I
c I-
/
5. Discussion In the present experiments the ratio R of the CSRS intensity for the 747 and 755 cm-l transitions is quite accurately represented by the followmg expression, obtained from eq. (2)R=
(pr,*
- r#
+ a?
(cd- a)) + [I?**0 + (d/ti)r”. = [r,
-
r,+f/s
d*
-
+ I-+“]2
(3)
03”
-
where p = (c1 - 6)/6 and Q!= (l/~)(r,,,I’,~, + rUr2 + r,I’,*), with 6 = wU - wUI_ At 0 K when we expect rZ = 0 the value of R is finite because of contributions to the signal at 4 = 0,~ which do not show a resonance pezk. Expressions (1) and (3) show minima for R at an httermediate temperature which is a manifestation of interference between the ground-state vibrational resonance wing and the dephasing-induced resonance_ As r2 grows larger, a peak develops at A = GJ,‘. From 384
c
20
10
T (K) Fig. 3. The growth of pure dephasing, rz(T), as a function of temperature. R is the experimentaNy measured quantity and is the ratio of the resonance height at A = 747 and A = 754 cm-’ _ The solid Iine is a least-squares fit to an Arrhenius activation eq. (4). The point x represents twice the observed pure-dephasing contribution to the 0 + v’ transition and is an independent estimate of Q(T).
Volume
82, number
frequency
also
CHEMICAL
3
occur
in the phonon-sideband
PHYSICS
spectra
of pentacene in benzoic acid. This situation is similar to that reported for pentacene in naphthalene as a result of photon-echo measurements [ 15]_ The present experiments have confirmed the occurrence of phonon-induced excited-state Raman transitions in molecular solids. The experiments can be utilized in the study of pure-dephasing contributions to the electronic and Raman linewidths. It is possible to carry out the experiment in a variety of ways leading to different simplifications of eq. (1). Measurements of the intensity I of the resonance at A = oU’ relative to a constant internal standard, such as a host crystal CSRS transition, yields for large d I=C(D-Er’)2)
(2
where C, D and E are determinable numbers. The introduction of population into the zero-point level of the excited state gives rise to an additional contribution to the third-order susceptrbility. This term is not considered here because the observed effects were shown to depend on the ground-state population_ The coherence introduced between the levels 0’ and u’ by the two laser fields must also be accompanied by increases in their populations. However, in the perturbation expansion of the density operator these population changes are not described until higher orders than third. It is easy to see that coherence between any two levels of a system described by a statistical density operator cannot exist unless both levels have population_ This can be deduced from the inequality tr p2 < 1, leading to 1~0 l2 < piipii for any pair of levels i and j. Thus we see the simple physical picture for the occurrence of our signal is that temperature-induced fluctuations of the energy levels allow the coherent process to occur. The concomitant occurrence of fluorescence as well as spontaneous Raman scattering is well known [ 173 _ The actual populations in these upper levels can only be calculated from terms fourth-order or higher in the molecule-field interactions.
LETTERS
1.5 September
1981
Acknowledgement We like to thank Dr. H.P. Trommsdorff for invaluable help with the lmear spectroscopy of this system, Mr. M.E. Huster for assistance wrth the cryogenics and Mr. ES. Hilfer for assistance with the computer graphics.
References 111 P L. DeCola, J-R. Andrews, R M Hochstrasser
and H P Trommsdorff, J. Chem. Phys. 73 (1980) 4695. I21 J-R. Andrews and R.M. Hochstrasser, Bull_ Am. Phys. Sot. 26 (1981) 13. [31 J.R. Andrews and R M. Hochstrasser, Bull. Am Phys. Sot. 26 (1981) 278. [41 J.R Andrews, R.M. Hochstrasser and H P. Trommsdorff, Chem. Phys., to be published. Opt Letters 151 A-R. Bogdan, Y Prior and N. Bloembegen, 6 (1981) 82. 161 Y. Prior. A.R. Bogdan, hl. Dagenais md N. Bloembergen, Phys. Rev. Letters 46 (1981) 111 Phys. Rev. 171 A. Bogdan, M. Downer and N. Bloembergen, A, submitted for publication. PI N Bloembergen, H. Lotem and R.T. Lynch Jr., Indian J. Pure Appl. Chem. 16 (1978) 151. 191 S-A-J. Druet, B.A. Attal, T.C. Gustafson and J.P. Tar-an, Phys. Rev. A18 (1978) 1529. 1101 T K. Yee and T.K. Gustafson, Phys. Rev. A18 (1978) 1597. 1111 S.A J. Druet, J.P E Taran and Ch. J. Bordd, J Phys. (Paris) 40 (1979) 819. WI J.-L. Oudar and Y.R. Shen, Phys. Rev. A22 (1980) 1141. 1131 H-R. Schlossberg and A. Java, Phys Rev. 150 (1966) 267. [ 141 T.W. Mossberg, E. Whittaker, R. Kachn and S.R. Hartman, Phys. Rev_ A22 (1980) 1962. 1151 W-H. Hesselink and D.A. Wiersma, J. Chem. Phys. 73 (1980) 648. [16] J-R. Andrews and R.hl. Hochstrasser, Chem. Phys Letters, submitted for publication_ [17] R-hi. Hochstrasser and C. Nyi, J. Chem. Phys 70 (1979) 1112.
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