- Email: [email protected]
Radio-frequency Stark effect modulation of single-molecule lines
Lumin=104=Rohini=Venkatachala=BG
Journal of Luminescence 86 (2000) 189}194
Radio-frequency Stark e!ect modulation of single-molecule lines Lothar Kador *, Tatiana Latychevskaia, Alois Renn, Urs P. Wild University of Bayreuth, Institute of Physics and **Bayreuther Institut fu( r Makromoleku( lforschung (BIMF)++, D-95440 Bayreuth, Germany Physical Chemistry Laboratory, Swiss Federal Institute of Technology, ETH-Zentrum, CH-8092 Zu( rich, Switzerland
Abstract Stark e!ect modulation experiments were performed on single-molecule lines of terrylene in crystalline matrices of n-hexadecane and naphthalene at low temperatures. Modulation frequencies in the MHz range were used. The resulting #uorescence excitation spectra are distinctly di!erent, depending on the relationship between the modulation frequency u and the molecular line width C. For u ;C, the single-molecule line exhibits a smooth broadening and apparent splitting into two components, whereas for u
of an electromagnetic wave. It is further demonstrated that Stark e!ect modulation in the radio-frequency regime can be used to record absorption signals of single molecules with good signal-to-noise ratio. 2000 Elsevier Science B.V. All rights reserved. PACS: 07.60.-j; 33.55.Be; 33.70.Jg; 78.40.-q Keywords: Single-molecule spectroscopy; Stark e!ect; Radio-frequency modulation; Interdigitating electrodes; Absorption signals; Terrylene; n-hexadecane; Naphthalene
1. Introduction The "rst spectroscopic investigation of single molecules in condensed matter was performed in an absorption experiment [1,2]. It was based on frequency-modulation (FM) spectroscopy in the MHz regime [3] to eliminate low-frequency laser noise; but a secondary modulation of the molecular ab-
* Corresponding author. Tel.: #49-921-55-3261; fax: #49921-55-3250. E-mail addresses: [email protected] (L. Kador), [email protected] (T. Latychevskaia)
sorption lines had to be applied to suppress residual amplitude modulation (RAM) [4] which leads to spurious signals and limits the sensitivity of FM experiments. Hence, a complicated double-modulation scheme resulted. Clear single-molecule signals could be detected, but the signal-to-noise ratio was only on the order of one to two, mainly due to the presence of overlapping weak signals from outof-focus molecules, since cleaved crystals of about 100 lm thickness were used. Soon afterwards, the #uorescence excitation technique was introduced, which provided much higher signal-to-noise ratios with a simpler set-up [5]. Hence, all subsequent experiments used this technique.
0022-2313/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 3 1 3 ( 9 9 ) 0 0 1 6 2 - 9
Lumin=104=Rohini=VVC=BG
190
L. Kador et al. / Journal of Luminescence 86 (2000) 189}194
Many di!erent spectroscopic investigations were performed on single molecules at low temperature. The most important advantages of studying single molecules are the complete absence of all ensemble-averaging e!ects and } at least in crystalline systems } the high spectral resolution on the order of 10}50 MHz, since the homogeneous line width can approach the lifetime limit at liquid-helium temperatures. Hence, spectral line shifts due to external perturbations such as electric "elds [6}10] or hydrostatic pressure [11}13] could be measured with high sensitivity. Also the e!ects of electric "elds in the radio-frequency (RF) regime were studied; the variation of the signal shape with RF amplitude and laser power showed that the interaction of single molecules with electromagnetic waves is described by the optical Bloch equations to a very high degree of accuracy [14,15]. In the present paper the signal shape of single-molecule lines under RF Stark modulation is investigated as a function of the modulation frequency. Moreover, it is demonstrated that RF modulation provides the possibility of detecting the absorption (rather than the #uorescence excitation) signal of a single molecule with good signal-to-noise ratio.
2. Experimental The experiments were performed on two crystalline systems, terrylene in n-hexadecane and terrylene in naphthalene. A tiny amount of the dye was simply dissolved in n-hexadecane which is liquid at room temperature. The solubility is so low that samples with the proper concentration for singlemolecule experiments could be prepared in this way. Doped crystal #akes of naphthalene were grown by co-sublimation at a temperature of the educt material of 1803C [16]. A few #akes were melted at about 803C to obtain small amounts of very dilute liquid solution. Electric RF "elds were applied to the samples by means of interdigitating electrodes which were evaporated on pyrex glass chips. Their width and the distance between them were each 18 lm. The electrodes were 250 nm thick and were covered with a 50-nm-thick protective layer of silicon car-
bide (SiC). In this way the electric "eld vector was oriented perpendicular to the k vector of the laser light. Radio-frequency signals between about 1 and 300 MHz were provided by a precision RF generator (Marconi 740A) whose output was ampli"ed by a wide-band RF power ampli"er (Kalmus 700LC). The magnitude of the electric "eld strength in the plane of the electrodes can be estimated, if we approximate each pair of electrodes by two thin, parallel, in"nite conducting half-planes with distance d. In this case the "eld strength at the center of the gap can be calculated exactly as (2/p);(;/d), where ; is the voltage between the half-planes [10]. A drop of the liquid sample material was placed on the pyrex chip and was quickly covered with a piece of microscope cover glass. Upon cooling, the material formed a polycrystalline layer of several microns thickness in close contact with the chip. For recording the #uorescence excitation signals of single moecules, the laser light was weakly focused onto the sample with an achromat lens. A microscope objective (NA"0.85) inside the cryostat was used to image the illuminated area of about 100 lm diameter on a video camera (Hamamatsu C2400-25) with image intensi"er. Hence, the spatially resolved #uorescence signals from all excited dye molecules in this area (and their position with respect to the electrodes) could be observed at a video rate of 25 frames/s [17]. The experimental set-up for detecting absorption signals is described in Section 4. All experiments were performed in super#uid helium at a temperature of about 1.8 K. 3. Fluorescence excitation spectra In the following we assume that the dye molecule under consideration exhibits a linear Stark e!ect, i.e., that its line shift due to an external "eld E is given by i l "! *l ) E, (1) # h The pyrex chips with the electrodes were purchased from the Fraunhofer-Institut fuK r FestkoK rpertechnologie, Munich, Germany.
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L. Kador et al. / Journal of Luminescence 86 (2000) 189}194
191
Fig. 1. Experimental [parts (a) and (c)] and calculated [parts (b) and (d)] #uorescence excitation signals of a single molecule exposed to an electric RF "eld. The modulation frequencies are 1 MHz [parts (a) and (b)] and 150 MHz [parts (c) and (d)]. The signals are shown as a function of laser frequency and RF amplitude (in arbitrary units). The experimental data were measured on the system terrylene in n-hexadecane, the theoretical signals were calculated according to Eqs. (2) [part (b)] and (3) [part (d)], respectively.
where *l is the di!erence of the permanent electric dipole moments in the excited and the ground state of the molecule, i the Lorentz factor determining the local electric "eld strength inside the solid matrix, and h is Planck's constant. Fluorescence excitation experiments on single molecules are performed in such a way that the red-shifted #uorescence is recorded for several milliseconds at each frequency position of the laser scan. This time is much longer than the oscillation periods of RF "elds (1 ls or below). Hence, the observed signal can be described by integrating the instantaneous #uorescence signal over one RF period. Two limiting cases have to be considered. If the RF frequency is small as compared to the molecular linewidth, u ;C, all relaxation processes de
termining the line width occur very fast and the line appears static on the time scale of the RF oscillation. In this case the averaged signal is simply given as
p S lim I(l)J [l!l !l cos(u t)] #
S C \ # dt 4p
(2)
(assuming Lorentzian line shape). Here l is the laser frequency, l the center frequency of the molecular line for E"0, and l the maximum frequency # excursion due to the linear Stark e!ect. In the opposite limit u
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L. Kador et al. / Journal of Luminescence 86 (2000) 189}194
oscillation. As a consequence, the molecular line develops side-bands whose spacing is exactly equal to the modulation frequency, similar to a phasemodulated electromagnetic wave. The measured signal has then the form > "J (2pl /u )" L #
lim I(l)J (l!l !n(u /2p))#(C/4p)
S L\ (3) with J denoting the Bessel function of "rst kind L and nth order. Fig. 1 shows experimental and theoretical #uorescence excitation signals as a function of laser frequency and RF amplitude. The experimental data were recorded on the system terrylene in nhexadecane, which has a line width of 40$2 MHz [18]. Hence, the RF frequencies of 1 MHz [parts (a) and (b)] and 150 MHz [parts (c) and (d)] correspond (approximately) to the two limits considered above. Experimental and theoretical signals agree very well. The di!erence between the smooth broadening and splitting at the low modulation frequency and the sideband structure at the high frequency is clearly visible. The apparent splitting into two components, which occurs for higher RF amplitudes at 1 MHz, is also reproduced in the calculated signal [Fig. 1(b)]; it is caused by the fact that the molecular line spends more time close to the turning points of its sinusoidal frequency excursion than at the center. The slow frequency shift of the experimental data in Fig. 1(c) is most probably due to a drift of the laser line.
4. Absorption signals Radio-frequency Stark e!ect modulation can also be used to record absorption signals of single molecules. In this case a tiny change of the laser power transmitted through the sample (on the order of 10\) must be detected so that it is necessary to eliminate the strong technical laser noise, which is most prominent in the kHz range and below. The experimental set-up is shown schematically in Fig. 2. The laser light was now tightly focused by the microscope objective in the cryostat. An achromat lens (focal length 80 mm) and a camera
Fig. 2. Experimental set-up for recording absorption signals of single molecules: (MO) microscope objective; (S) sample; (APD) avalanche photodiode; (RF) RF generator; (PS) RF power splitter; (AMP) RF ampli"ers; (M) double-balanced mixer; (LPF) 5 MHz low-pass "lter; (PMPA) post-mixer preampli"er; (RC) RC circuit with adjustable time constant.
objective (focal length 58 mm) were used to focus the transmitted light on a fast avalanche photodiode with integrated preampli"er (EG&G C30950F; cut-o! frequency 100 MHz). The RF component of the photocurrent was ampli"ed and demodulated in a double-balanced mixer (Mini Circuits GRA-6), which received its local-oscillator signal from the Marconi RF generator. The spatial position of the observed single molecules was determined by the laser focus in this case, but it was not as readily visible as with the camera set-up described in Section 2. Since the single-molecule lines are shifted periodically on the frequency axis and the shift is detected phase-sensitively, this technique can be regarded as an optical analog of a standard experiment in electron paramagnetic resonance (EPR). Hence, the demodulated signal should be proportional to the derivative of the molecular line shape, provided that the molecule exhibits a purely linear Stark e!ect and that the RF "eld strength is su$ciently low. An example of a single-molecule absorption signal is presented in Fig. 3. The system was terrylene in n-hexadecane, the modulation frequency 1 MHz. The voltage at the IF (intermediate-frequency), i.e., output port of the mixer was ampli"ed and smoothed with a time constant of about 300 ms; the corresponding signal has been plotted versus the optical frequency. The laser was scanned from
Lumin=104=Rohini=VVC=BG
L. Kador et al. / Journal of Luminescence 86 (2000) 189}194
Fig. 3. Absorption signal of a single terrylene molecule in nhexadecane at 572.097 nm. The direction of the laser scan was reversed at the frequency position 2 GHz. Shown is the ampli"ed and smoothed output (IF) signal of the mixer. Modulation frequency, 1 MHz.
lower to higher frequencies over an interval of 2 GHz and then at the same rate back in reversed direction. Hence, two copies of the line appear in the "gure, which demonstrates the reproducibility. Besides the strong line, also some weaker features appear in both halves of the plot; they are probably due to out-of-focus molecules or molecules with improper orientations. The signal-to-noise ratio of the strong line is at least 10. The absorption signals of several terrylene molecules in the matrices n-hexadecane and naphthalene were recorded. Some of them had the expected derivative-like shape, but in both matrices also molecules were found whose signals extended mainly to one side from the baseline, with the lobe in the other direction being weak or almost absent [19]. This e!ect is tentatively ascribed to the possibility that the corresponding molecules have both linear and quadratic contributions to their Stark shift. Future experiments will clarify this point.
5. Conclusions The e!ects of electric "elds in the radio-frequency regime on single-molecule lines were investigated. The "elds were applied by means of interdigitating gold electrodes evaporated on a glass chip. With an electrode spacing of 18 lm, voltages of a few volts
193
were su$cient to generate "eld strengths above 1 kV/cm. The #uorescence excitation signals are distinctly di!erent in the two limiting cases that the modulation frequency is either much lower or much higher than the molecular line width. Whereas in the "rst case the line exhibits a smooth broadening and apparent splitting with increasing RF amplitude, it develops side-bands in the second case. The latter phenomenon is analogous to phase or frequency modulation of an electromagnetic wave. It was also demonstrated that Stark e!ect modulation in the MHz range e$ciently eliminates low-frequency laser noise so that absorption signals of single molecules can be recorded with good signal-to-noise ratio using a single-modulation technique. This method can be regarded as an optical analog to standard EPR experiments.
Acknowledgements We would like to thank P. Ny!eler and R. Weiner for important help in the electronic design and H. Bach for the preparation of the naphthalene samples. Financial support from the ETH ZuK rich is gratefully acknowledged.
References [1] W.E. Moerner, L. Kador, Phys. Rev. Lett. 62 (1989) 2535. [2] L. Kador, D.E. Horne, W.E. Moerner, J. Phys. Chem. 94 (1990) 1237. [3] G.C. Bjorklund, Opt. Lett. 5 (1980) 15. [4] E.A. Whittaker, M. Gehrtz, G.C. Bjorklund, J. Opt. Soc. Am. B 2 (1985) 1320. [5] M. Orrit, J. Bernard, Phys. Rev. Lett. 65 (1990) 2716. [6] U.P. Wild, F. GuK ttler, M. Pirotta, A. Renn, Chem. Phys. Lett. 193 (1992) 451. [7] M. Orrit, J. Bernard, A. Zumbusch, R.I. Personov, Chem. Phys. Lett. 196 (1992) 595. [8] L. Kador, A. MuK ller, W. Richter, Mol. Cryst. Liq. Cryst. 291 (1996) 23. [9] F. Kulzer, R. Matzke, C. BraK uchle, Th. BascheH , J. Phys. Chem. A 103 (1999) 2408. [10] Ch. Brunel, Ph. Tamarat, B. Lounis, J.C. Woehl, M. Orrit, J. Phys. Chem. A 103 (1999) 2429. [11] M. Croci, H.-J. MuK schenborn, F. GuK ttler, A. Renn, U.P. Wild, Chem. Phys. Lett. 212 (1993) 71. [12] A. MuK ller, W. Richter, L. Kador, Chem. Phys. Lett. 241 (1995) 547.
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[13] T. Iwamoto, A. Kurita, T. Kushida, Chem. Phys. Lett. 284 (1998) 147. [14] Ch. Brunel, B. Lounis, Ph. Tamarat, M. Orrit, Phys. Rev. Lett. 81 (1998) 2679. [15] Ph. Tamarat, F. Jelezko, Ch. Brunel, A. Maali, B. Lounis, M. Orrit, Chem. Phys. 245 (1999) 121. [16] H. Bach, Ph.D. Thesis ETH ZuK rich, 1998.
[17] Th. Irngartinger, A. Renn, U.P. Wild, J. Lumin. 66&67 (1996) 232. [18] W.E. Moerner, T. Plakhotnik, Th. Irngartinger, M. Croci, V. Palm, U.P. Wild, J. Phys. Chem. 98 (1994) 7382. [19] L. Kador, T. Latychevskaia, A. Renn, U.P. Wild, J. Chem. Phys. 111 (1999) 8755.
Journal of Luminescence 86 (2000) 189}194
Radio-frequency Stark e!ect modulation of single-molecule lines Lothar Kador *, Tatiana Latychevskaia, Alois Renn, Urs P. Wild University of Bayreuth, Institute of Physics and **Bayreuther Institut fu( r Makromoleku( lforschung (BIMF)++, D-95440 Bayreuth, Germany Physical Chemistry Laboratory, Swiss Federal Institute of Technology, ETH-Zentrum, CH-8092 Zu( rich, Switzerland
Abstract Stark e!ect modulation experiments were performed on single-molecule lines of terrylene in crystalline matrices of n-hexadecane and naphthalene at low temperatures. Modulation frequencies in the MHz range were used. The resulting #uorescence excitation spectra are distinctly di!erent, depending on the relationship between the modulation frequency u and the molecular line width C. For u ;C, the single-molecule line exhibits a smooth broadening and apparent splitting into two components, whereas for u
of an electromagnetic wave. It is further demonstrated that Stark e!ect modulation in the radio-frequency regime can be used to record absorption signals of single molecules with good signal-to-noise ratio. 2000 Elsevier Science B.V. All rights reserved. PACS: 07.60.-j; 33.55.Be; 33.70.Jg; 78.40.-q Keywords: Single-molecule spectroscopy; Stark e!ect; Radio-frequency modulation; Interdigitating electrodes; Absorption signals; Terrylene; n-hexadecane; Naphthalene
1. Introduction The "rst spectroscopic investigation of single molecules in condensed matter was performed in an absorption experiment [1,2]. It was based on frequency-modulation (FM) spectroscopy in the MHz regime [3] to eliminate low-frequency laser noise; but a secondary modulation of the molecular ab-
* Corresponding author. Tel.: #49-921-55-3261; fax: #49921-55-3250. E-mail addresses: [email protected] (L. Kador), [email protected] (T. Latychevskaia)
sorption lines had to be applied to suppress residual amplitude modulation (RAM) [4] which leads to spurious signals and limits the sensitivity of FM experiments. Hence, a complicated double-modulation scheme resulted. Clear single-molecule signals could be detected, but the signal-to-noise ratio was only on the order of one to two, mainly due to the presence of overlapping weak signals from outof-focus molecules, since cleaved crystals of about 100 lm thickness were used. Soon afterwards, the #uorescence excitation technique was introduced, which provided much higher signal-to-noise ratios with a simpler set-up [5]. Hence, all subsequent experiments used this technique.
0022-2313/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 3 1 3 ( 9 9 ) 0 0 1 6 2 - 9
Lumin=104=Rohini=VVC=BG
190
L. Kador et al. / Journal of Luminescence 86 (2000) 189}194
Many di!erent spectroscopic investigations were performed on single molecules at low temperature. The most important advantages of studying single molecules are the complete absence of all ensemble-averaging e!ects and } at least in crystalline systems } the high spectral resolution on the order of 10}50 MHz, since the homogeneous line width can approach the lifetime limit at liquid-helium temperatures. Hence, spectral line shifts due to external perturbations such as electric "elds [6}10] or hydrostatic pressure [11}13] could be measured with high sensitivity. Also the e!ects of electric "elds in the radio-frequency (RF) regime were studied; the variation of the signal shape with RF amplitude and laser power showed that the interaction of single molecules with electromagnetic waves is described by the optical Bloch equations to a very high degree of accuracy [14,15]. In the present paper the signal shape of single-molecule lines under RF Stark modulation is investigated as a function of the modulation frequency. Moreover, it is demonstrated that RF modulation provides the possibility of detecting the absorption (rather than the #uorescence excitation) signal of a single molecule with good signal-to-noise ratio.
2. Experimental The experiments were performed on two crystalline systems, terrylene in n-hexadecane and terrylene in naphthalene. A tiny amount of the dye was simply dissolved in n-hexadecane which is liquid at room temperature. The solubility is so low that samples with the proper concentration for singlemolecule experiments could be prepared in this way. Doped crystal #akes of naphthalene were grown by co-sublimation at a temperature of the educt material of 1803C [16]. A few #akes were melted at about 803C to obtain small amounts of very dilute liquid solution. Electric RF "elds were applied to the samples by means of interdigitating electrodes which were evaporated on pyrex glass chips. Their width and the distance between them were each 18 lm. The electrodes were 250 nm thick and were covered with a 50-nm-thick protective layer of silicon car-
bide (SiC). In this way the electric "eld vector was oriented perpendicular to the k vector of the laser light. Radio-frequency signals between about 1 and 300 MHz were provided by a precision RF generator (Marconi 740A) whose output was ampli"ed by a wide-band RF power ampli"er (Kalmus 700LC). The magnitude of the electric "eld strength in the plane of the electrodes can be estimated, if we approximate each pair of electrodes by two thin, parallel, in"nite conducting half-planes with distance d. In this case the "eld strength at the center of the gap can be calculated exactly as (2/p);(;/d), where ; is the voltage between the half-planes [10]. A drop of the liquid sample material was placed on the pyrex chip and was quickly covered with a piece of microscope cover glass. Upon cooling, the material formed a polycrystalline layer of several microns thickness in close contact with the chip. For recording the #uorescence excitation signals of single moecules, the laser light was weakly focused onto the sample with an achromat lens. A microscope objective (NA"0.85) inside the cryostat was used to image the illuminated area of about 100 lm diameter on a video camera (Hamamatsu C2400-25) with image intensi"er. Hence, the spatially resolved #uorescence signals from all excited dye molecules in this area (and their position with respect to the electrodes) could be observed at a video rate of 25 frames/s [17]. The experimental set-up for detecting absorption signals is described in Section 4. All experiments were performed in super#uid helium at a temperature of about 1.8 K. 3. Fluorescence excitation spectra In the following we assume that the dye molecule under consideration exhibits a linear Stark e!ect, i.e., that its line shift due to an external "eld E is given by i l "! *l ) E, (1) # h The pyrex chips with the electrodes were purchased from the Fraunhofer-Institut fuK r FestkoK rpertechnologie, Munich, Germany.
Lumin=104=Rohini=VVC=BG
L. Kador et al. / Journal of Luminescence 86 (2000) 189}194
191
Fig. 1. Experimental [parts (a) and (c)] and calculated [parts (b) and (d)] #uorescence excitation signals of a single molecule exposed to an electric RF "eld. The modulation frequencies are 1 MHz [parts (a) and (b)] and 150 MHz [parts (c) and (d)]. The signals are shown as a function of laser frequency and RF amplitude (in arbitrary units). The experimental data were measured on the system terrylene in n-hexadecane, the theoretical signals were calculated according to Eqs. (2) [part (b)] and (3) [part (d)], respectively.
where *l is the di!erence of the permanent electric dipole moments in the excited and the ground state of the molecule, i the Lorentz factor determining the local electric "eld strength inside the solid matrix, and h is Planck's constant. Fluorescence excitation experiments on single molecules are performed in such a way that the red-shifted #uorescence is recorded for several milliseconds at each frequency position of the laser scan. This time is much longer than the oscillation periods of RF "elds (1 ls or below). Hence, the observed signal can be described by integrating the instantaneous #uorescence signal over one RF period. Two limiting cases have to be considered. If the RF frequency is small as compared to the molecular linewidth, u ;C, all relaxation processes de
termining the line width occur very fast and the line appears static on the time scale of the RF oscillation. In this case the averaged signal is simply given as
p S lim I(l)J [l!l !l cos(u t)] #
S C \ # dt 4p
(2)
(assuming Lorentzian line shape). Here l is the laser frequency, l the center frequency of the molecular line for E"0, and l the maximum frequency # excursion due to the linear Stark e!ect. In the opposite limit u
Lumin=104=Rohini=VVC=BG
192
L. Kador et al. / Journal of Luminescence 86 (2000) 189}194
oscillation. As a consequence, the molecular line develops side-bands whose spacing is exactly equal to the modulation frequency, similar to a phasemodulated electromagnetic wave. The measured signal has then the form > "J (2pl /u )" L #
lim I(l)J (l!l !n(u /2p))#(C/4p)
S L\ (3) with J denoting the Bessel function of "rst kind L and nth order. Fig. 1 shows experimental and theoretical #uorescence excitation signals as a function of laser frequency and RF amplitude. The experimental data were recorded on the system terrylene in nhexadecane, which has a line width of 40$2 MHz [18]. Hence, the RF frequencies of 1 MHz [parts (a) and (b)] and 150 MHz [parts (c) and (d)] correspond (approximately) to the two limits considered above. Experimental and theoretical signals agree very well. The di!erence between the smooth broadening and splitting at the low modulation frequency and the sideband structure at the high frequency is clearly visible. The apparent splitting into two components, which occurs for higher RF amplitudes at 1 MHz, is also reproduced in the calculated signal [Fig. 1(b)]; it is caused by the fact that the molecular line spends more time close to the turning points of its sinusoidal frequency excursion than at the center. The slow frequency shift of the experimental data in Fig. 1(c) is most probably due to a drift of the laser line.
4. Absorption signals Radio-frequency Stark e!ect modulation can also be used to record absorption signals of single molecules. In this case a tiny change of the laser power transmitted through the sample (on the order of 10\) must be detected so that it is necessary to eliminate the strong technical laser noise, which is most prominent in the kHz range and below. The experimental set-up is shown schematically in Fig. 2. The laser light was now tightly focused by the microscope objective in the cryostat. An achromat lens (focal length 80 mm) and a camera
Fig. 2. Experimental set-up for recording absorption signals of single molecules: (MO) microscope objective; (S) sample; (APD) avalanche photodiode; (RF) RF generator; (PS) RF power splitter; (AMP) RF ampli"ers; (M) double-balanced mixer; (LPF) 5 MHz low-pass "lter; (PMPA) post-mixer preampli"er; (RC) RC circuit with adjustable time constant.
objective (focal length 58 mm) were used to focus the transmitted light on a fast avalanche photodiode with integrated preampli"er (EG&G C30950F; cut-o! frequency 100 MHz). The RF component of the photocurrent was ampli"ed and demodulated in a double-balanced mixer (Mini Circuits GRA-6), which received its local-oscillator signal from the Marconi RF generator. The spatial position of the observed single molecules was determined by the laser focus in this case, but it was not as readily visible as with the camera set-up described in Section 2. Since the single-molecule lines are shifted periodically on the frequency axis and the shift is detected phase-sensitively, this technique can be regarded as an optical analog of a standard experiment in electron paramagnetic resonance (EPR). Hence, the demodulated signal should be proportional to the derivative of the molecular line shape, provided that the molecule exhibits a purely linear Stark e!ect and that the RF "eld strength is su$ciently low. An example of a single-molecule absorption signal is presented in Fig. 3. The system was terrylene in n-hexadecane, the modulation frequency 1 MHz. The voltage at the IF (intermediate-frequency), i.e., output port of the mixer was ampli"ed and smoothed with a time constant of about 300 ms; the corresponding signal has been plotted versus the optical frequency. The laser was scanned from
Lumin=104=Rohini=VVC=BG
L. Kador et al. / Journal of Luminescence 86 (2000) 189}194
Fig. 3. Absorption signal of a single terrylene molecule in nhexadecane at 572.097 nm. The direction of the laser scan was reversed at the frequency position 2 GHz. Shown is the ampli"ed and smoothed output (IF) signal of the mixer. Modulation frequency, 1 MHz.
lower to higher frequencies over an interval of 2 GHz and then at the same rate back in reversed direction. Hence, two copies of the line appear in the "gure, which demonstrates the reproducibility. Besides the strong line, also some weaker features appear in both halves of the plot; they are probably due to out-of-focus molecules or molecules with improper orientations. The signal-to-noise ratio of the strong line is at least 10. The absorption signals of several terrylene molecules in the matrices n-hexadecane and naphthalene were recorded. Some of them had the expected derivative-like shape, but in both matrices also molecules were found whose signals extended mainly to one side from the baseline, with the lobe in the other direction being weak or almost absent [19]. This e!ect is tentatively ascribed to the possibility that the corresponding molecules have both linear and quadratic contributions to their Stark shift. Future experiments will clarify this point.
5. Conclusions The e!ects of electric "elds in the radio-frequency regime on single-molecule lines were investigated. The "elds were applied by means of interdigitating gold electrodes evaporated on a glass chip. With an electrode spacing of 18 lm, voltages of a few volts
193
were su$cient to generate "eld strengths above 1 kV/cm. The #uorescence excitation signals are distinctly di!erent in the two limiting cases that the modulation frequency is either much lower or much higher than the molecular line width. Whereas in the "rst case the line exhibits a smooth broadening and apparent splitting with increasing RF amplitude, it develops side-bands in the second case. The latter phenomenon is analogous to phase or frequency modulation of an electromagnetic wave. It was also demonstrated that Stark e!ect modulation in the MHz range e$ciently eliminates low-frequency laser noise so that absorption signals of single molecules can be recorded with good signal-to-noise ratio using a single-modulation technique. This method can be regarded as an optical analog to standard EPR experiments.
Acknowledgements We would like to thank P. Ny!eler and R. Weiner for important help in the electronic design and H. Bach for the preparation of the naphthalene samples. Financial support from the ETH ZuK rich is gratefully acknowledged.
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