One- and two-photon spectroscopy on single molecules of diphenyloctatetraene

16 May 1997

CHEMICAL PHYSICS LETTERS ELSEVIER

Chemical Physics Letters 270 (1997) 16-22

One- and two-photon spectroscopy on single molecules of diphenyloctatetraene Daniel Walser, Taras Plakhotnik, Alois Renn, Urs P. Wild Physical Chemistry Laboratory, Swiss Federal Institute of Technology, ETH Zentrum, CH-8092 Zurich, Switzerland

Received 20 January 1997; in final form 18 March 1997

Abstract We report investigations on one- and two-photon excitation of single molecules of diphenyloctatetraene in n-tetradecane at cryogenic temperatures. Saturation intensities, count rates and linewidths of single molecules are compared with corresponding ensemble values obtained from statistical fine structure investigations. The single-molecule linewidths under one-photon excitation are generally two to three times narrower than in two-photon excitation spectra. This effect is discussed with respect to saturated spectral diffusion induced by the high power IR light necessary for efficient two-photon absorption.

1. Introduction Optical spectroscopy on single guest molecules in solids at low temperatures is a sensitive method which has developed quickly in the last few years [1]. Using the single-molecule technique, basic photophysics can be studied on single quantum systems, spectroscopic characterizations are obtained at high precision, and information can be revealed that is not accessible in experiments where ensembles of molecules are probed. Recently, two-photon excitation from the 1 ~Ag ground (S 0) to the 2 lAg lowest excited singlet (S~) state of single 1,8-diphenyl-l,3,5,7-octatetraene (DPOT) molecules trapped in an n-tetradecane Shpol'skii matrix at cryogenic temperatures was achieved [2]. Excited molecules were observed through weak S~ ~ S o one-photon emission resulting from a symmetry breaking induced by the crystal

field o r / a n d vibronic coupling between S t and nearby ~B, states [3]. Two Shpol'skii sites with different symmetry breaking were observed [4]. The fluorescence emission from the site at Aso.~S, = 442.1 nm was very weak, revealing almost undisturbed symmetry of the corresponding DPOT molecules. This site could only be observed under TPE. In a site of broken symmetry, with Aso ~ s, = 444.0 nm, the fluorescence was much stronger and the inhomogeneous spectra showed identical lineshapes and positions for both one-photon excitation (OPE) and two-photon excitation (TPE). Three different types of DPOT molecules in tetradecane can be distinguished in the site with As0~ s, = 444.0 nm [5]. ' T y p e 1' molecules can be detected by OPE, whereas TPE is impossible or very inefficient. ' T y p e 2' molecules can be detected upon simultaneous absorption o f two photons, while OPE is very inefficient. ' T y p e 3' molecules can be de-

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D. Walser et a l . / Chemical Physics Letters 270 (1997) 16-22

tected in both one- and two-photon excitation spectra. This classification is of phenomenological nature, and there is not yet a microscopic model to describe it. The number of one-photon excited molecules, which may belong to 'type 1' or 'type 3', is generally two to three times the number of twophoton excited molecules, being of 'type 2' or 'type 3'. The presence of spectral dynamics makes a reliable identification of 'type 3' molecules difficult, and has prevented their detailed study until now. In a specific example [5], one tenth of the one-photon excited molecules and correspondingly one third of the ones detected under TPE were of 'type 3'. In this paper, the OPE and TPE single molecule spectra in the site with As0,_,s, = 444.0 nm are further characterized by studying their power dependences. Single molecule data are compared with corresponding ensemble values.

17

characterized by well separated Lorentzian peaks is observed. Near the inhomogeneous line center, where N H > l, a high-resolution scan shows reproducible fluctuations called statistical fine structure [6,7]. The relative rms-amplitude of these fluctuations is approximately equal to (NH)-l/Z ( N H >> 1). The statistical fine structure allows for the determination of the spectral number density and the 'average' homogeneous linewidth of an ensemble of molecules. Investigations of the fine structure can be regarded as a complementary method to spectral hole burning, when high-resolution spectroscopic data of an ensemble are required. In contrast to hole burning, the fine structure signal results from the excitation of photostable molecules. This technique was used for comparison of the OPE and TPE processes on ensembles.

3. Results and discussion 2. Experimental

3.1. Single molecule spectra The experimental setup has been described in detail [4]. The sample is immersed in a superfluid He bath at 1.8 K. The purely electronic S O~ S L zero° phonon line of DPOT at 444 nm is selectively excited either by one or two photons using a single mode Ti'sapphire laser (CR 899-29) emitting at 888 nm and an external cavity (LAS, Wavetrain) for second harmonic generation. The two laser beams are focused to the same spot of about 2 Ixm diameter with a microscope objective integrated into the sample holder. The fluorescence emitted by DPOT is collected by the same objective and recorded as a function of the laser frequency. In the following, the molecular frequency scale, being twice the laser frequency, is used. An aperture is placed in the conjugate focal plane of the objective outside the cryostat, and only light emitted from the same sample volume V of about 10 i~m 3 independent of the excitation process is collected. The 2 Ixm diameter of V is given by the aperture's projection inside the sample. Moreover, this aperture is indispensable for background reduction in OPE experiments. When a high-resolution spectrum is recorded in the wings of the inhomogeneous band, where the number of molecules per homogeneous linewidth, Nrt, is low (Nrt < 1), a single molecule spectrum

OPE single molecule spectra were investigated in different samples - an example is shown in Fig. 1. Usually, the single molecule lines were not stable, and spectral dynamics such as discrete frequency jumps were generally present - a phenomenon which

250

E "

200 4

g

2

3

3

o c o

10o

Relative frequency [MHz|

Fig. l. One-photon excitation spectrum of four DPOT single molecules in the tetradecane matrix. The excitation wavelength was at 444.175 nm (laser at 888.35 nrn), the power was 3.2 W f c m z. The mirror symmetry, produced by the triangular laser frequency scan, shows the reproducibility of the spectrum.

18

D. Walser et al. / Chemical Physics Letters 270 (1997) 16-22 2000

A

o

o

~15oo

i

lOOO

=- 500

50

B 40

o

"Nr

E &:

!

30

o

o o

2O o

lO o

5

10

15

20

Excitation intensity I [ W / c m 2]

Fig. 2. Power dependence of the line intensity (A) and the linewidth (B) for molecule 1 in Fig. 1. The solid lines are simultaneous least squares fits with the equations R(1)= R~/(1 + I s / I ) (A) and -FOPE(I)= F O P E ~ (B), resulting in the values I s = 3.0 W / c m 2, R~ = 1900 cps and Fo°PE = 16 MHz for the measured saturation intensity, high power count rate and low-power limit of the homogeneous linewidth, respectively. The relative errors of 4-43% for I s, + 18% for R~, and +68% for F °PE were estimated as the range in which the error function was doubled from its minimum value under variation of the corresponding fit parameter. The first two points of the linewidth data (filled circles in B) were excluded from the fit. Considering the large scatter of the data points in (B), reflected by the large error interval for F °PE, we e s t i m a t e F00PE is in the range 15-25 MHz.

has also been observed on other Shpol'skii systems (e.g. [8-10]). A few molecules were stable enough to be investigated over a longer period of time, and for one of them (molecule 1 in Fig. 1), the dependence of the line intensity and width on excitation power is plotted in Fig. 2. The measured saturation intensity I s = 3 W / c m 2 for this molecule. The value of R~ = 1900 cps for the observed high power count rate is about twice the corresponding value for two-photon excited molecules [2], taking into account the 50% reduction of the total collection efficiency by the notch filter which was used to suppress the excita-

tion light in OPE experiments. The one-photon peak absorption cross section was estimated to o"(i~ -- 2 × 10-12 cm 2 t, using the following photophysical parameters: fluorescence quantum yield -- 0.1 [12], Debye-Waller factor = 0.43 (determined from an excitation spectrum [4]), intensity ratio of the 0 - 0 line to the full luminescence 0.1 (determined from an emission spectrum [4]), with a Franck-Condon factor of CFc = 0.04 for the purely electronic transition. The angle between the wavevector of the laser field and the molecular emission dipole, which is parallel to the absorption dipole moment and to the long axis of the molecule [13,14], was estimated to A - - 3 0 ° 2 Including all losses, the solid angle of collection, and the orientation of the molecular dipole, the emission rate at high power and saturation intensity are estimated to Rein = 3 × 105 s - 1 and /sat = 0.7 W / c m 2, respectively [15]. Because of linewidth fluctuations within + 3 0 % from scan to scan with very little correlation to the laser power, the data in Fig. 2B allowed only for an estimate F °PE = 15-25 MHz of the homogeneous linewidth at low power. Taking into account 12 investigated molecules in different samples F ° P E = 2 0 - 4 0 MHz, a distribution with a maximum around 30 MHz. The narrowest observed linewidth was 16 MHz. This F0°PE is in reasonable agreement with the value of 26 M H z derived from the excited state lifetime measured in cyclohexane solution 3. The fluctuations in the measured linewidths reflect the presence of spectral dynamics on a scale shorter than the accumulation time of one scan, i.e. -'- 200 s. Similar distributions of linewidths in a Shpol'skii matrix were also observed in other systems [9,10]. The occurrence of narrower lines with respect to the lifetime limited value must be attributed to an increase of the lifetime in crystalline tetradecane. Remarkably, the scatter in the line intensity (Fig. 2A) is much smaller than in the linewidth (Fig. 2B). This may indicate the presence of light induced spectral jumps [8]. In this case, a molecule changes its transition frequency when the exciting laser is close to resonance. Thus, when accumulating - - 1 0 0 scans to record a single molecule line, the

i Equation (19) in Ref. [11]. 2 According to the method described in [15]. 3 Ti ~ 6 ns, Trad = 66 ns [12].

D. Walser et a l . / Chemical Physics Letters 270 (1997) 16-22

measured line intensity is close to its real maximum, whereas the linewidth strongly depends on the jump distance. The above F °pE is confirmed by spectral hole burning data. Spectral holes could be burnt under OPE, but not under TPE. The low-power hole width which is twice the molecular linewidth, was usually around 60 MHz, the narrowest hole had a width of 32 MHz; the saturated hole depth was about 50%. In the same sample, the single molecule linewidth under TPE was F TPE ~ 75 MHz, in agreement with [2]. The homogeneous linewidths probed by TPE were two to three TPE times broader than in OPE spectra. F TPE fluctuated within + 25% from scan to scan, and no power dependence was observed in the range 0.6-8 M W / c m 2 except for saturation broadening [2] for a few single molecules. Most likely, spectral diffusion processes are responsible for the linewidth increase in TPE spectra. Contrary to the spectral dynamics seen under OPE, these spectral dynamics may be enhanced by the IR light [16]. However, such an effect must be saturated in the investigated power range. IR-induced spectral diffusion was found to be a resonant process in spectral hole-burning systems [17,18]. Additional H 2 0 molecules embedded into a polymer hole-burning matrix could perform flips or reorientations when resonantly illuminated with IR radiation. Consequently, solvent shifts of adjacent dye molecules changed, and an overall broadening of the hole profile was observed in those experiments. Less than 10 excitations of a fundamental vibration per H 2 0 molecule were enough to fully saturate that broadening. In our experiment, strongly localized matrix excitations [16] occur due to IR absorption of the third harmonic of the antisymmetric [19] C - H vibration with an absorption cross section of t r - - 4 × 10 -24 cm 2 at 888 nm. Each tetradecane molecule is excited vibrationally at least 104 times during the recording time of one scan when the sample is irradiated with 10 M W / c m 2 at 888 nm. One DPOT molecule has at least four tetradecane neighbors, which may slightly change their relative orientations upon excitation. Thus, even if the flip rate and matrix-chromophore coupling are much lower in our system compared to the one in [17], saturated IR induced spectral diffusion is a reasonable explanation for the line broadening in TPE single molecule

19

spectra. Further studies on 'type 3' molecules and their comparison with 'type 2' molecules may shed some more light on the origin of this broadening.

3.2. Ensemble investigations using statistical fine structure

Using single-molecule spectroscopy, preferentially the strongest absorbers are detected, and consequently, a specific group of molecules is investigated. Their properties might differ from the ensemble properties. Therefore, the ensemble features of the one- and two-photon excited molecules were compared by studying the statistical fine structure at different excitation powers. Assuming the same saturation intensity l~ns, linewidth F~,s(l) and high power count rate R~ for all molecules, the autocorrelation function of the excitation spectrum is a Lorentzian with FWHM 2 × F~ns(1) at any excitation intensity I, and the power dependence of this width is the same as for a single-molecule line. The average fluorescence intensity R e"~ increases linearly (quadratically in the case of TPE) with I for I << I~ns. As molecules out of resonance gain line intensity above I~n~, R en~ increases proportional to Vq- ( ~ I for TPE) at high power. RedS(I) of an ensemble excited at the laser frequency 12 is obtained by integration of the homogeneous lineshape function R(I, g2) over all molecular resonance frequencies to at fixed g2. Under OPE, assuming equal saturation intensity 1~"~ for all absorbers, R( I, 12) and R~"~(I) are [20]:

R ( I , 12) , R~

- -

I~ "s ( 1 2 - w ) 2 + ( l + I / I s Re"s(/)

"rrR~oNH 21~ "s

I ¢1 + I/I~ "s

ens

F

)(FenOsP E / 2 )

2

'

I ~[1 + I/I~ "s

In the case of OPE, the investigated ensemble had a number density of 1,1 molecules/MHz. The statistical fine structure and its correlation function are shown in Fig. 3. The dependences of R e"s and F~°PE on the excitation power are plotted in Fig. 4A and Fig. 4B, respectively. Both data sets were fit together, yielding the saturation intensity l~ns= 2.7 W / c m 1, the average high power count rate per

D. Walser et al. / Chemical Physics Letters 270 (1997) 16-22

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Lag [MHz]

~oo

8oo

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2 0 2 Relativefrequency[GHz]

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the statistical fine structure, the photon emission from each molecule is collected with a different efficiency according to its position relative to the center of V. The average single-molecule count rate calculated from a simulation of the statistical fine structure was determined to be 135-170 cps. In this simulation, the apparatus' collection efficiency was calculated for 100000 randomly distributed absorbers with molecular parameters R~ = 1900 cps, I s = 3 W / c m 2, /-OPE = 36 MHz contributing to the fine structure. Thus, the reduced average R~ is explained by different collection efficiencies for all the molecules in the probed volume.

6

100 ==

Fig. 3. OPE spectrum showing statistical fine structure at a wavelength of 444.0 nm, excitation power: 3.5 W / c m 2. The number of molecules per homogeneous linewidth was N H = 65 yielding a number density of 1.1 molecules per MHz. Again, the mirror symmetry shows the reproducibility of the fine structure signal. Inset: Cross correlation of the two symmetrical halves of the double scan, which was calculated instead of the autocorrelation of a single scan, with the advantage that the &function like peak originating from the noise was absent. The thick line is a Lorentzian fit with a F W H M of 116 MHz, corresponding to an average homogeneous linewidth of F~°sPE = 58 MHz.

8

= 4-; I:

s o ~ so

== 4O

0

20 40 60 ExcitationintensityI [W/cm2]

150 130

single molecule R~ = 160 cps and the low-power limit of the average homogeneous width F0°PE = 33 MHz. The ensemble linewidth is strongly power dependent (Fig. 4B) and shows far less fluctuations than the single molecule linewidth (Fig. 2B), because the spectral dynamics experienced by single absorbers are hidden in the ensemble. The representativity of the single molecule data in the previous paragraph is shown by the good agreement between I~n~ and I s, and between F0°P~ and the estimated F 0. The average R~ calculated from the ensemble measurements is 12 times smaller (160 cps) than the corresponding value obtained from single molecule data. In the apparatus, the aperture placed in the confocal plane of the laser focus strongly reduces the collection efficiency for molecules located outside the volume V. We assume that single molecule peaks are obtained from emitters located inside V, because they give rise to the strongest signals. When an ensemble of molecules is probed, as in the case of

, B

.

80

. @

~, 110 90

~ 7o "3

50 30 10

10 20 30 ExcitationintensityI [W/cm2]

40

Fig. 4. Analysis of the statistical fine structure at different laser intensities. (A) Power dependence of the average fluorescence intensity R ens. The solid line is a least squares fit to Re"S(1)= FI1/I + 1/I~ ns + BI, where the last term takes into account additional background signal, 1~ns is the ensemble saturation intensity and F = (TrR=NH)/(21~ns). (B) Power dependence of the average homogeneous linewidth, deduced from the cross correlation of the two symmetrical halves of a scan. The solid line is a least squares OPE fit to FeO~E(l)= Fc;.e,sV/l + I / I ~ "s. Both data sets were fit simultaneously, resulting in the values 1~n s = 2.7 W / c m 2, F = 6000 cm 2 W - i s - I, B = 100 cm 2 W - J s - 1 an d /"o°ePnEs= 33 MHz The relative errors of _+59% for l~ns, -1-18% for F and _+21% for Fo°eE have the same meaning as in Fig. 2.

D. Walser et a l . / Chemical Physics Letters 270 (1997) 16-22

In the case of TPE, the number density of the ensemble was 0.5 molecules/MHz. The number of single-molecule lines observed in OPE spectra was at least twice the number observed under TPE 4. This effect has already been discussed in [5]. The average homogeneous linewidth was about 95 MHz with fluctuations of + 10% from scan to scan, and there was no power dependence. Saturation of the fluorescence intensity could not be achieved, as the laser power available was not high enough, thus I~n~ > 20 W / c m 2. For comparison, the single-molecule saturation intensity I s was between 7 and 13 M W / c m 2 in this sample. We point out a few reasons for this discrepancy which did not appear in OPE experiments. Because the TPE rate is proportional to the square of the probing power, it depends more strongly on the position of the molecule with respect to the beam center compared to the OPE rate. Moreover, the TPE rate is more sensitive to the angle between the wavevector of the laser field and the molecular transition dipole. The detected single molecules may have a slightly larger tilt than the ensemble average. Additionally, the blue light intensity available was much higher than /~ns, thUS even molecules in unfavorable conditions could be excited at a high rate. This was not the case for TPE, where, consequently, single molecules with lowest saturation intensities were ens TPE selected, and I s < / ~ n s is not surprising. On the other hand, the F TPE from single molecule data is close to the ensemble value, what does not contradict the above considerations.

4. Conclusion Single molecules of DPOT in tetradecane have been investigated with respect to their behavior under one- and two-photon excitation. The spectral number density in OPE was two to three times the one in TPE spectra. The homogeneous linewidths probed by TPE were two to three times broader than under OPE. This was also the case for molecules which were detectable under one- and two-photon

4 The ratio depended on the focal spot position on the microcrystal and on the alignment of the aperture in the confocal plane; the highest ratio measured was 6:1.

21

excitation simultaneously ('type 3'). We believe that the broadening occurs due to spectral diffusion induced by localized matrix excitations upon highpower IR irradiation. The effect must be saturated in the investigated power range, as no dependence of F TPE on the laser intensity was observed, neither for single molecules, nor for the ensemble. The large uncertainty in single-molecule linewidths under OPE may be caused by light-induced spectral jumps, but this argument is not yet established. The differences between the two excitation processes could be observed for individual molecules as well as for ensembles which were studied by statistical fine structure investigations.

Acknowledgements Careful proof reading by Elizabeth Donley is gratefully acknowledged. This work was financially supported by the Swiss National Science Foundation and by ETH Ziarich.

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[16] T. Plakhotnik, D. Walser, A. Renn, U.P. Wild, Phys. Rev. Lett. 77 (1996) 5365. [17] K. Barth, W. Richter, J. Lumin. 64 (1995) 63. [18] W. Richter, M. Lieberth, D. Haarer, J. Opt. Soc. Am. B 9 (1992) 715.

[19] A.S. Bonanno, J.M. Olinger, P.R. Griffiths, in: Near Infra-red Spectroscopy, K.I. Hildrum, T. lsaksson, T. Naes, A. Tandberg (Eds.), Ellis Horwood, Chichester, 1992, p. 19. [20] A. Yariv, Quantum Electronics, 3rd ed., Wiley, New York, 1988, pp. 176-179.