ISSN 1054-660X, Laser Physics, 2007, Vol. 17, No. 4, pp. 583–589.
QUANTUM INFORMATION
AND QUANTUM COMPUTATION
© MAIK “Nauka /Interperiodica” (Russia), 2007.
Original Text © Astro, Ltd., 2007.
UV-VIS Absorption Spectroscopy of Large Molecules
for Applications in Matter Wave Interferometry
N. Gotsche, H. Ulbricht, and M. Arndt*
Fakultät für Physik, Universität Wien, Boltzmanngasse 5, Wien, A-1090 Austria
*e-mail: [email protected]
Received November 9, 2006
Abstract—We study the optical properties of various large molecules with respect to their suitability for new
matter wave interference and detection schemes. Optical phase gratings for molecules will only be compatible
with a sufficiently small absorption cross section visible while optical detection schemes may exploit strong
UV resonances. We compare UV-VIS spectra of various biomolecules, such as amino acids, polypeptides, and
proteins, with those of new perfluoroalkylated molecules and carbon nanotubes, and we discuss their suitability
for coherent matter wave experiments.
PACS numbers: 33.20.Ea, 33.20.Kf, 33.20.Lg, 39.10.+j, 39.30.+w, 78.67.Ch
DOI: 10.1134/S1054660X07040433
1. NEW TECHNIQUES
FOR MATTER WAVE INTERFEROMETRY
WITH LARGE MOLECULES
The physics of matter waves is a well-established
research field and coherence experiments with massive
objects have become textbook examples of quantum
physics [1]. This also includes recent experiments with
ultra-cold and weakly-bound degenerate atomic
ensembles [2, 3], as well as studies with strongly-bound
large and hot molecules [4].
Coherence experiments with large molecules are of
interest for various reasons: on the one hand, they permit the exploration of elementary principles of quantum physics on a size and mass-scale that has not been
experimentally tested so far. The internal complexity of
molecules gives rise to various new decoherence
effects—such as, for instance, thermally induced decoherence [5]—that cannot be observed in simpler atomic
systems. But, also, applications in molecule metrology
and molecule nano-lithography are conceivable. Diffraction and interferometry of molecules has been previously explored with cold dimers—such as I2 [6], He2
[7], and Na2 [8]—as well as with polyatomic helium
clusters [9]. Beams of thermo-stable molecules even
allowed for the extension of the mass and complexity
range to small biomolecules and fullerene derivatives
composed of up to more than 100 atoms [10].
in Fig. 1. The first grating prepares the coherence of the
incident molecular beam. The central, optical grating
serves as the diffraction, while the third structure acts as
a scanning mask for the interferometrically generated
molecular density pattern. The horizontal laser beam
(B) at the end is used for detection through photo-ionization or laser induced fluorescence. For all optical
interactions—grating and detection—it is important to
know the spectral properties of those molecules that
might be interesting for matter wave interferometry. In
the present paper, we therefore discuss the absorption
spectra of various biomolecules, novel perfluoroalkylated particles, and carbon nanotubes.
Since the molecular beam sources will be very different for all of these particle classes, here we compare
spectra of molecules in solution. One might expect sol-
To push the mass limit in molecular matter wave
interferometry even further, we need new concepts for
the coherent manipulation of complex objects. Brezger
et al. [11] suggested implementing a new interferometer type: a Kapitza–Dirac–Talbot–Lau interferometer
(KDTLI) will combine the near-field setup of the Talbot–Lau interferometer [12, 13] with the Kapitza–
Dirac effect [14], i.e. with optical gratings for molecules [15]. The idea of such an experiment is sketched
583
G1
G2
A
G3
B
Fig. 1. A Kapitza–Dirac–Talbot–Lau interferometer contains one standing light wave (A) and often one optical
detection beam (B).
584
GOTSCHE et al.
vent induced spectral shifts and changes in the extinction coefficient, but experiments with fullerenes [16]
indicate that at least for nonpolar molecules the similarity between gas phase and solvent based spectra is so
high that our procedure is justified for our purposes.
Also, for polar biomolecules the trend of the spectrum
is sufficiently clear in guiding our choice for future
molecular beam experiments.
ters, as one-photon absorption gratings seem to be feasible [19]. It is understood, however, that many technical
difficulties would have to be overcome in the future:
molecular beams of nanotubes, as well as their sorting by
mass and chirality, will provide a whole scientific community still with challenging work for several years.
2. CHOICE OF MOLECULES
Biomolecules are interesting candidates for matter
wave interferometry as they exist essentially in a monodisperse form. They exhibit large polarizabilities and
electric dipole moments. They are characterized by
chirality, appear in different conformations and isomers, and, therefore, offer various new handles for
investigations of coherence and decoherence with massive objects. Small biomolecules, such as tetraphenlyporphyrins, have already been successfully used in de
Broglie interferometry before [10]. A new Kapitza–
Dirac–Talbot–Lau interferometer installed in our lab is
designed to be compatible with such high masses for
beam velocities of up to 300 m/s. Recent experiments
showed that pulsed laser desorption of pure biomaterials into an adiabatically expanding noble gas jet allows
the beam formation for molecules at least up to the
complexity level of medium-sized polypeptides [17].
Futhermore, we were successful in creating rather
intense neutral beams of both tryptophan and gramicidin, which we could detect in a multiphoton ionization
process at a 266 nm excitation wavelength. Tryptophan
is an aromatic amino acid with a mass of 204 amu. The
polypeptide gramicidin is composed of 15 amino acids
with a mass of about 1900 amu. Sources and detectors
for neutral gas-borne proteins are still a challenge, but
Weickhardt et al. [18] already described the successful
detection of neutral insulin (C257H383N65O77S6, m ~
5800 amu) and one may hope to reach even further to
cytochrome C (m ~ 12000 amu) or myoglobin (m ~
16700 amu).
Perfluorinated molecules have recently also
attracted interest for matter wave experiments since
they have low polarizabilities and high vapor pressures.
Here, we study for the first time the optical properties
of such molecules, which are four to nine times more
massive than the fullerene C60. Since they do not have
any simple common name, we designate them here by
their mean molecular mass as perfluoro2634
(C62H36F93NOSi2), perfluoro2934 (C68H36F105NOSi2),
perfluoro3379 (C96H48Cl2F102P2Pd), and “perfluoroalkylated buckyball” (C60[(CF2)11CF3]n).
Carbon nanotubes are also intriguing candidates for
future matter wave experiments: they exist in a large
range of sizes, exhibit lower ionization potentials than
biomolecules, have interesting aspect ratios, huge
polarizabilities, and an enormous mechanical stability.
Together with metal clusters they appear to be good
candidates for purely optical Talbot–Lau interferome-
All molecular materials were first dissolved in their
appropriate solvents in well-defined concentrations,
filled in a thin suprasil cuvette and then submitted to
absorption spectroscopy inside a Varian Cary G5 photo
spectrometer.
Tryptophan and gramicidin were dissolved in ethanol.
Insulin, myoglobin, and cytochrome C were studied in
water, perfluoro2634 and perfluoro2934 in methanol,
perfluoro3379 and the perfluoroalkylated buckyballs in
perfluorooctane, C60 in toluene, and the carbon nanotubes
again in water—after functionalization (see below).
Most of these molecules occur with a unique
mass—except for the natural small isotopic spread.
Only gramicidin, the perfluoroalkylated buckyball, and
the functionalized carbon nanotubes still deserve a further discussion.
Gramicidin D is mixture of gramicidin A (80–85%),
gramicidin B (6–7%), gramicidin C (10–15%), and
gramicidin D (<1%). They all differ by the exchange of
a single amino acid—which introduces only minor
changes in the spectra and a mass variation on the percent-level—which is acceptable for the proposed de
Broglie interferometry experiments.
The perfluoroalkylated buckyballs were not mass
selected in the chemical production process and, thus,
still contain different numbers of (identical) side chains
[(CF2)11CF3]n—with n varying between one and ten.
Quadrupole mass spectroscopy on an effusive beam
revealed that about 80% of the material was decorated
by between seven and nine such side chains, with
C60[(CF2)11CF3]7 being the dominant contribution that
was taken as a reference to determine the molarity and
extinction estimates below.
The single-walled carbon nanotubes (HiPCO
SWCNT) were purchased (CNI, Houston, United
States) as a powdery mixture of bundled tubes. Following published recipes [20], we first sonicated them
(Branson horn sonifier, 5 h, <100 W) in an aqueous
solution to enforce their individualization in soap
micelles. The following centrifugation at 30000 rpm
separated the still remaining tube bundles from the
individualized single tubes. Our own AFM measurements confirm that this process yields a typical distribution of isolated tubes with a diameter distribution
peaked at ~1 nm and a length distribution between 200
and 900 nm. The optical spectra are known not to vary
strongly with length. And, although an interference
experiment would probably have to use further short-
3. UV-VIS ABSORPTION SPECTROSCOPY
LASER PHYSICS
Vol. 17
No. 4
2007
UV-VIS ABSORPTION SPECTROSCOPY OF LARGE MOLECULES
Optical density, cm–1
Molarity, mmol/l
0.12
4
0.10
585
0.08
0.06
3
0.04
0.02
2
0
0.5
1.0
1.5
2.0
2.5
3.0
Optical density, cm–1
1
0
200
400
600
800
1000
1200
Wavelength, nm
Fig. 2. Concentration dependent absorption spectra of myoglobin. The concentration ranges from 0.17 to 1.85 g/l. The inset shows
the evaluation of the molar extinction coefficient according to Beer’s law at 633 (solid squares), 532 (upright triangles), and 266 nm
(inverted triangles).
ened tubes, we may take the optical properties of our
sample already as a reference.
Absorption spectra for all molecules were recorded
for a set of different molecular concentrations to eliminate multiple scattering and saturation of the solvents.
Bleaching and optical saturation were also avoided in
all cases by keeping the samples in the dark when
unused and by maintaining the probe intensity below
10 µW/cm2.
The wavelength dependent molar extinction coefficient ε(λ) (in units [L mol–1 cm–1]) was then determined
according to Beer’s law from the optical density
I(λ)
ε ( λ )lC = – log ⎛ ----------⎞ ,
⎝ I0 ⎠
(1)
where l is the thickness of the optical cell (in centimeters) and I and I0 are the measured transmission spectra
with or without the dissolved molecules.
The optical density for different molecule concentrations (molarities C) is shown in Fig. 2 for the example of myoglobin. We evaluate the extinction coefficient ε from a linear fit to this curve, as shown in the
inset in Fig. 2. The effects of saturation or incomplete
solvation would show up as a deviation from the
straight line. The error bar on the extinction coefficient
LASER PHYSICS
Vol. 17
No. 4
2007
is mainly due to the weighing tolerances in the preparation of the solutions.
The molecular absorption cross section (in units of
cm2) is then derived from the extinction coefficient (in
units
[l/mol/cm])
according
to
σ(λ)
=
1000ε(λ)/(NA log(e)), where NA is the Avogadro number
and e is Euler’s number.
Absolute absorption coefficients were also determined independently for all molecules in a separate
measurement at the specific laser frequency of
632.8 nm to calibrate the spectra. For calibration purposes, we also recorded spectra of rhodamin B and
tryptophan. Their literature spectra [21, 22] were found
to be in very good agreement with our data. All other
molecules were treated in a similar way. Their spectra
are displayed in Fig. 3.
From traces, as those appearing in Fig. 3, we can
extract the extinction coefficients and absorption cross
sections for the wavelengths 266, 532, and 1064 nm,
which are of particular interest for ionization, laser
induced fluorescence, optical phase gratings, and possibly
optical traps. Their values are summarized in the table.
In Fig. 4, we also show an absorption spectrum of
both isolated (left) and mixed (bundled and isolated)
single-walled carbon nanotubes. The graph immediately shows that absorption is rather significant over
300000
532 nm
GOTSCHE et al.
266 nm
586
Cytochrom C
140
Myoglobin
120
100
80
200000
60
40
100000
pFC60
0
70
Gramicidin
60
Rhodamin B
50
0
150000
Insulin
100000
C60
40
30
20
50000
10
0
Cross section, 10–17 cm2
Molar extinction coefficient, l/mol cm
20
0
Perfluoro 3379
Perfluoro 2934
10000
5
4
Perfluoro 2634
Tryptophan
3
2
5000
1
0
200
400
600
0
800
Wavelength, nm
Fig. 3. Molar extinction and absorption cross sections for molecules with potential interest for matter wave interferometry. One
requirement for the molecules to be suitable for green optical phase gratings is to have a sufficiently low extinction at 532 nm, the
wavelength of the phase grating laser.
the entire spectrum and it varies only by about a factor
of two for all wavelengths from the ultraviolet to the
infrared.
The overall sloped background on the blue side of
the spectrum is caused by a plasmon resonance, which
can be found in bundled and individualized tubes. The
peak structure in the near-infrared is related to electronic transitions in individual tubes in the ensemble,
and the rather good contrast after centrifugation is a
clear indication of the high degree of individualization
of the tubes in the solvent.
We use again Beer’s law (1) to obtain the concentration of individualized tubes after sonication and centrifugation. We know that the spectrum is composed of two
parts: the ubiquitous plasmon—exhibited by both the
bundles and the individual tubes—and the resonant features of the individualized tubes. The latter become
much more detailed and dominant in the course of cen-
trifugation which sequentially removes the more dense
remaining bundles. We, thus, evaluate a concentration
of individual tubes after centrifugation of 13(2) mg/l
from an initial concentration of 50(2) mg/l of bundles.
4. SUITABILITY FOR MATTER WAVE
INTERFEROMETRY
Within a matter wave experiment based on an optical phase grating—such as the Kapitza–Dirac-Talbot–
Lau interferometer—the interaction of the molecules
with the central laser light grating (at 532 nm) should
be conservative and mediated by the optical dipole
force alone.
Scattered or spontaneously emitted photons have to
be avoided as they impart a random recoil on different
molecules, thus washing out the interference pattern.
LASER PHYSICS
Vol. 17
No. 4
2007
UV-VIS ABSORPTION SPECTROSCOPY OF LARGE MOLECULES
587
Optical properties of all molecules at those laser wavelengths which are supposed to be important for optical detection, diffraction, and trapping
Molecule
Tryptophan
Gramicidin
Insulin
Cytochrom C
Myoglobin
Perfluoro2634
Perfluoro2934
Perfluoro3379
Perflouroalkylated C60
C60
C70
Rhodamin B
ε [l/mol/cm]
σ [cm2] @ 266 nm
ε [l/mol/cm]
σ [cm2] @ 532 nm
ε [l/mol/cm]
σ [cm2] @ 1064 nm
4.8(1) × 103
1.85(5) × 10–17
2.43(8) × 104
9.3(3) × 10–17
7.1(3) × 103
2.7(1) × 10–17
1.73(8) × 104
6.6(3) × 10–17
2.71(2) × 104
1.04(1) × 10–16
2.5(1) × 102
9.46(2) × 10–19
7.9(2) × 102
3.01(6) × 10–18
7.7(4) × 103
2.9(1) × 10–17
6 × 104
2 × 10–16
–
19 ± 1
7.2(2) × 10–20
4.3(2) × 102
1.64(8) × 10–18
4.6(2) × 103
1.77(8) × 10–17
9.3(4) × 103
3.6(2) × 10–17
6.5(1) × 103
2.52(2) × 10–17
63 ± 2
2.41(6) × 10–19
–
13 ± 1
5.2(2) × 10–20
3.2(2) × 102
1.23(6) × 10–18
3.8(1) × 103
1.47(6) × 10–17
3.6(3) × 102
1.4(1) × 10–18
1.26(1) × 103
4.80(4) × 10–18
88 ± 6
3.4(2) × 10–19
–
–
2.59(4) × 104
9.9(2) × 10–17
2.2(1) × 103
8.4(4) × 10–18
4 × 103
1 × 10–17
7.6(1) × 102
2.89(4) × 10–18
2.0(5) × 10–17 [16]
5.36(9) × 104
2.05(3) × 10–16
709 ± 34
2.7(1) × 10–18
1 × 102
3 × 10–19
17 ± 1
6.4(2) × 10–20
2.6(1) × 102
1.0(2) × 10–18
One can argue that the optical absorption event
itself—followed by an internal conversion instead of an
emission process—would not destroy the interference,
since it is a phase coherent process which always shifts
the molecular fringe pattern by the same amount. However, the Poissonian nature of the laser light statistics
implies that each molecule will absorb a different number of photons. Additionally, the superposition of
unshifted, shifted, and multishifted curves then also
reduces the interference contrast—even though it does
not necessarily completely destroy it [15].
polarizability and the absorption cross section, both at
the wavelength of the diffracting laser beam.
Large particles are permitted to exhibit a higher
absorption cross section than smaller ones, since one
can afford to work at lower laser intensities. The phase
acquired by the molecules during the passage through
the laser field
It is, therefore, generally preferable that the wavelength of the optical phase grating is far detuned with
respect to all major molecular transition. Yet, it is also
known that complex molecules, such as the fullerenes,
as well as many of the objects discussed in the present
work, have “resonances” that span several ten to hundred nanometers—at least when the molecules emerge
from thermal beams.
can still be high at a low laser intensity—and, thus, low
absorption probability—if the polarizability is sufficiently high. Molecules are, therefore, assumed to be
suitable candidates for a KDTL interferometer if their
α/σ (532 nm) is comparable to or bigger than that of C70.
However, it has recently been shown that KDTL
interferometry can be achieved with C70 [23], even
though it exhibits a finite absorption. It, thus, turns out
that the figure-of-merit for phase gratings is defined by
the ratio of α/σ (532 nm), i.e. by the ratio of the optical
LASER PHYSICS
Vol. 17
No. 4
2007
t1
φ =
∫ ( αE ( r, t )/2 ) dt
2
(2)
t0
4.1. Biomolecules
A glance at the table reveals that the absorption
coefficient of tryptophan and gramicidin at 532 nm is
between more than a factor of one hundred and a factor
often smaller than that of C70. It is very reasonable to
assume that these values will still stay way below the
values of C70 in gas phase experiments.
588
GOTSCHE et al.
Optical density, cm–1
0.8
0.7
0.04
1225 nm
703 nm
1003 nm
Concentration, g/l
0.02
0
0.6
0.4 0.8 1.2 1.6
Optical density, cm–1
0.5
0.4
400
600
800
1000 1200
400 600
Wavelength, nm
800
1000 1200
Fig. 4. Left: Absorption spectrum of isolated and purified carbon nanotubes (see text). Right: Absorption spectra of unpurified tube
samples at concentrations between 10 and 50 mg/l. Since this sample was not centrifuged, it provides us with concentration information: the off-resonant optical densities are identical for individualized tubes and bundles. The inset in the left panel shows the
connection between the concentration and the optical density (squares 1225, circles 1003, and triangles 703 nm).
The literature values for the polarizability amounts
to 23 Å3 for tryptophan and 580 Å3 for insulin [24]. For
the polarizability of larger proteins, such as cytochrome and myoglobin, it is justifiable to assume a proportionality of mass and polarizability as in hydrocarbons [25]. This rule is also consistent with the known
data for amino acids and polypeptides as well as the
fullerenes. Cytochrome C (12000 amu) and myoglobin
(16700 amu) may, thus, be described by a static polarizability of 1200 and 1700 Å3, respectively. These
polarizabilities exceed the fullerene value by factors of
15 and 20, respectively, whereas the absorption cross
sections remain comparable to those of C70. The large
width of all resonance lines implies that even on a slope
of the absorption peak these values will change only by
a small factor.
We can, therefore, conclude that all selected biomolecules possess optical properties which are compatible
with optical phase gratings as their α/σ (532 nm) values
exceed that of C70.
4.2. Perfluoralkylated Molecules
The polarizability of perfluoralkylated molecules
has not yet been determined experimentally. In order to
obtain a realistic estimate for future experiments, we
refer to simulations for perfluoro2934 and
perfluoro2634 using the Gaussian software. Generally,
the response of a molecule to an external electric field
will depend on the frequency of the laser field, on the
temperature dependent configuration of the molecule,
on the vibrational and rotational states, and more. It
turns out, however, that the values vary by not more
than 50% even for rather strong molecular deformations. This permits sufficiently reliable predictions
about the suitability of a molecule as a potential candidate in interference experiments.
The static polarizability is computed to be about
90 Å3 for both perfluoro2934 and perfluoro2634, i.e., it
is nearly identical to the fullerene value. The values
presented here describe the static polarizability, but,
like for the fullerenes, the absence of dipole allowed
transitions in the entire visible frequency band implies
that the static value describes the polarizability over the
visible range within about a factor of two [26].
Since the polarizability of all perfluorinated particles is nearly identical with that of C70 it suffices to
compare their absorption cross section at 532 nm. The
table reveals that the absorption of C70 surpasses all perfluorinated particles even though they latter contain up
to eight times as many atoms. Thermal beams of these
massive objects have recently been demonstrated in our
lab. Perfluoralkylated molecules are, therefore, very
LASER PHYSICS
Vol. 17
No. 4
2007
UV-VIS ABSORPTION SPECTROSCOPY OF LARGE MOLECULES
promising candidates for matter wave interferometry in
the multi-kDa mass range.
4.3. Carbon Nanotubes
The spectra evidently show significant absorption at
532 nm—and essentially all visible wavelengths. This
has two reasons: on the one hand, the existence of a
π-plasmon, which is common to all tube types—and on
the other hand, the individual resonances that are related
to the diameter and chirality of the tubes. With present
techniques and mass selection alone, a phase grating
seems, therefore, rather difficult to implement for
SWCNTs. It should, however, be noted that optical phase
gratings may be again be feasible as soon as chiralityselected tubes become available. Also, the polarizability
of metallic tubes is known to surpass the simple polarizability-to-mass extrapolation. While this extrapolation
works fine for hydrocarbons, the polarizability of metallic tubes may be more than tenfold higher.
Complimentary to that, it is interesting to see, that
matter wave interferometry may also be based on optical absorption gratings, where the term absorption now
refers to the fact that a molecule might be removed
from the molecular beam, when it passes the antinode
of a standing laser light beam. For reasons similar to
those given above, this is, however, only viable if the
removal of the molecule is achieved for instance in single-photon ionization/shelving, and this usually means
with the help of highly energetic light.
The ionization potentials of biomolecules and perfluoroalkylated are generally situated in the range of 9–
12 eV, i.e. way beyond all existing laser photon energies.
In contrast, carbon nanotubes have ionization potentials smaller than 7 eV, which are well accessible for
VUV excimer lasers, such as a F2 laser at 157 nm. Nanotubes might, therefore, be well suited for absorptive
diffraction gratings and also for detection schemes
based on absorptive processes [19]; this holds independent of their internal properties and individual chirality.
Summarizing, we can say that for all molecules
studied here, the optical transitions and polarizabilities
are such that optical gratings are generally conceivable.
For biomolecules and perfluoralkylated particles, phase
gratings will be the diffraction elements of choice,
while carbon nanotubes are predicted to be appropriate
candidates for absorptive ionization gratings. For all of
these particles, matter wave interferometry itself will
also be a useful method to determine the polarizabilities
with higher accuracy.
ACKNOWLEDGMENTS
Our studies are funded by the Austrian Science Foundation (FWF) within the projects START Y177 and SFB
F1505. We thank Paul Fagan for donating the perfluoroalkylated buckyballs, the group of Romano Rupp for
lending us their Cary spectrometer, Wilfried Ellmeier for
LASER PHYSICS
Vol. 17
No. 4
2007
589
access to the ultra-centrifuge, Hans Kuzmany for the
possibility to use the AFM, and Hans-Günter Löw and
Sarayut Deachapunya for helpful discussions.
REFERENCES
1. L. Bergmann and C. Schaefer, Optics of Waves and Particles (Gruyter, New York, 2002).
2. E. Cornell and C. E. Wieman, Rev. Mod. Phys. 74, 875
(2002).
3. W. Ketterle, Rev. Mod. Phys. 74, 1131 (2002).
4. M. Arndt, K. Hornberger, and A. Zeilinger, Phys. World
18, 35 (2005).
5. L. Hackermüller, K. Hornberger, B. Brezger, et al.,
Nature 427, 711 (2004).
6. Ch. J. Bordé, N. Courtier, F. Du Burck, et al., Phys. Lett.
A 188, 187 (1994).
7. W. Schöllkopf and J. P. Toennies, Science 266, 1345
(1994).
8. M. S. Chapman, C. R. Ekstrom, T. D. Hammond, et al.,
Phys. Rev. Lett. 74, 4783 (1995).
9. L. W. Bruch, W. Schöllkopf, and J. P. Toennies, J. Chem.
Phys. 117, 1544 (2002).
10. L. Hackermüller, S. Uttenthaler, K. Hornberger, et al.,
Phys. Rev. Lett. 91, 90408 (2003).
11. B. Brezger, M. Arndt and A. Zeilinger, J. Opt. B 5, S82
(2003).
12. J. F. Clauser and M. W. Reinsch, Appl. Phys. B 54, 380
(1992).
13. B. Brezger, L. Hackermüller, S. Uttenthaler, et al., Phys.
Rev. Lett. 88, 100404 (2002).
14. P. L. Kapitza and P. A. M. Dirac, Proc. Camb. Philos.
Soc. 29, 297 (1933).
15. O. Nairz, B. Brezger, M. Arndt, and A. Zeilinger, Phys.
Rev. Lett. 87, 160401 (2001).
16. P. F. Coheur, M. Carleer, and R. Colin, J. Phys. B 29,
4987 (1996).
17. M. Marksteiner, G. Kiesewetter, L. Hackermuller, et al.,
Acta Phys. Hung. B 20 (2006).
18. C. Weickhardt, L. Draack, and A. Amirav, Anal. Chem.
75, 5602 (2003).
19. E. Reiger, L. Hackermuller, M. Berninger, and M. Arndt,
Opt. Comm. 264, 326 (2006).
20. M. J. O’Connell et al., Science 297, 593 (2002).
21. J. Lindsey, http://omlc.ogi.edu/spectra/PhotochemCAD/
html/ (1998).
22. D. B. Wetlaufer, Adv. Protein Chem. 17, 303 (1962).
23. S. Gerlich, L. Hackermüller, K. Hornberger, et al., submitted (2007).
24. S. K. Lee, Y. Polyakova, and K. H. Row, Bull. Korean
Chem. Soc. 24, 1757 (2003); http://bioinf.charite.de/
superdrug.
25. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York,
1954).
26. M. S. Dresselhaus, G. Dresselhaus, and P. C. Eklund,
Science of Fullerenes and Carbon Nanotubes, 2nd ed.
(Academic, San Diego, 1998).