Coherent population transfer and dark resonances in SO2
T. Halfmann and K. Bergmann
Fachbereich Physik der Universität, 67653 Kaiserslautern, Germany
~Received 12 February 1996; accepted 20 February 1996!
Highly efficient population transfer between the ~0,0,0! and the ~9,1,0! vibrational levels of the
electronic ground state X̃ 1 A 1 of SO2 is demonstrated. The process relies on stimulated Raman
scattering with adiabatic passage induced by two suitably delayed ultraviolet laser pulses with
nearly transform-limited bandwidth. A transfer efficiency of 100% is achieved. The associated dark
resonance is observed. Properties of the latter are compared for delayed and fully overlapping
pulses. © 1996 American Institute of Physics. @S0021-9606~96!03516-4#
INTRODUCTION
The collision dynamics and spectroscopy of highly vibrationally excited molecules are themes of great current
interest.1 In thermal equilibrium such levels are not populated but methods to access them have recently been developed. These methods differ in the degree of flexibility, efficiency, selectivity, and experimental complexity. A
successful and widely used technique to transfer population
relies on stimulated emission pumping ~SEP!.1,2 A pump laser transfers population to a suitable level in an electronically
excited state, followed by a dump laser, which transfers part
of that population to the targeted vibrational level of the
electronic ground state. When the fluence of the laser pulses
is high enough, as much as one-third of the population can
be transferred from the initial to the final level. Some population will remain in the electronically excited state, and
from there it reaches other vibrational levels by spontaneous
emission. It is straightforward to implement the SEP method
with pulsed multimode lasers because coherence properties
of the radiation are not important. Coherence may even be
detrimental to an experimentally robust transfer process, because Rabi oscillations3 will be induced.
The coherence of the radiation needs to be invoked to
achieve a significantly higher transfer efficiency from the
initial to the final level. In fact, chirped pulse multiphoton
excitation schemes, such as those recently proposed4 can
transfer a substantial fraction of the thermal population of
low lying levels to high lying ones. The technique of coherent population transfer with delayed pulses, proposed some
time ago5 and experimentally demonstrated later,6 is a
method capable of achieving a transfer efficiency of unity,
which implies perfect selectivity. This method relies on
stimulated Raman scattering with adiabatic passage
~STIRAP!. The STIRAP method is now well established for
diatomic molecules. It has been successfully implemented
with cw lasers in the visible6,7 and in the infrared8 using
molecular beams, where the particles fly through the spatially displaced laser beams. The technique has been used in
crossed beams collision experiments.7 It has also been implemented for multilevel systems9 and in the context of atomic
interferometry and laser cooling.10 Pulsed laser work dealing
with atoms11 or molecules12 has been reported as well.
A necessary condition for the success of the transfer pro7068
J. Chem. Phys. 104 (18), 8 May 1996
cess is a counterintuitive sequence of the laser pulses, with
the Stokes laser pulse, coupling the intermediate and final
level, arriving before the pump laser pulse, which couples
the initial and the intermediate level. It is straightforward to
rationalize the striking features of STIRAP by using the
dressed state picture. When the two laser frequencies involved are tuned to the two-photon resonance with the initial
and final level, then one of the eigenstates of the strongly
coupled system ~comprising initial, intermediate, and final
bare states u1&, u2&, and u3&, respectively! reads6,13
u a 0 & 5cos Q u 1 & 2sin Q u 3 &
~1!
with tan Q5VP /VS where V P and V S are the Rabi frequencies related to the pump laser and the Stokes laser, respectively. The Rabi frequency is given by V P,S 5 m E P,S /\
where m is the dipole moment of the respective transition
and E P,S the electric field of the radiation. Since we are
dealing with delayed laser pulses, the Rabi frequencies and
their ratio is time dependent. Therefore the mixing angle Q
varies with time.
Important properties of the STIRAP transfer process can
be seen from Eq. ~1!. Unlike the other two dressed states
u a 1 & and u a 2 & of a three states system,6 the dressed state
u a 0 & has no component of the radiatively decaying bare state
u2&. Radiative decay will not occur as long as the system is in
u a 0& .
In a geometrical picture we visualize a three dimensional
Hilbert space spanned by the state vectors of the bare states
u1&, u2&, and u3&. The molecule is initially in the bare state u1&.
At early times when only the Stokes laser is present, we have
cos Q51. The state vector uC&, which describes the population distribution among the bare states, as well as the
dressed-state vector u a 0 & , are both lined up parallel to u1&.
When the Stokes laser pulse gives way to the pump laser
pulse, the mixing angle Q increases from 0° to 90°, i.e.,
u a 0 & rotates and eventually lines up antiparallel to u3& at late
times. Efficient population transfer occurs if the state vector
uC& remains aligned with u a 0 & , i.e., if it follows the rotation
of the latter.
Adiabatic following requires sufficiently strong coupling
of the bare states, so that the consequent Stark splitting separates the eigenvalues of the dressed states.6,13 In a three-state
system, adiabatic following occurs when
0021-9606/96/104(18)/7068/5/$10.00
© 1996 American Institute of Physics
Downloaded¬01¬Apr¬2002¬to¬134.253.26.10.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright,¬see¬http://ojps.aip.org/jcpo/jcpcr.jsp
T. Halfmann and K. Bergmann: Coherent population transfer and dark resonances in SO2
VD t @1,
7069
~2!
where Dt is the width of the laser pulses, assuming that the
pump and Stokes laser Rabi frequencies are about equal.6
The adiabatic following condition needs to be modified when
phase fluctuations of the laser pulses are appreciable on the
time scale of the interaction. Phase fluctuations that lead to a
substantial increase of the laser bandwidth are detrimental to
the success of the transfer process.14 When the transfer in a
multistate system is considered, crossings of dressed-state
eigenvalues may occur and a more detailed analysis is required. Such complications may result from Zeeman
splittings9 or fine and hyperfine interactions15 or from a high
density of states. In particular, they may be detrimental when
nearby levels are radiatively coupled to intermediate states,
but are separated in energy from the considered levels by less
than the Rabi frequency.
For the experiments on SO2 discussed in this paper, the
three-state picture is adequate. Hyperfine splitting does not
occur because the nuclear spins are zero for the most abundant isotopes of sulphur and oxygen. The density of states
near the final level is low enough to allow full resolution of
individual eigenstates. Although the states involved have a
nonzero angular momentum, the m-level degeneracy causes
no problems, since the lasers are linearly polarized parallel to
each other and only Dm50 transitions are involved. Therefore, the population transfer occurs within several unrelated
three-state systems in parallel, each one labeled by a different magnetic quantum number.16
EXPERIMENT
Our experiment is as follows. A pulsed beam of SO2
molecules, seeded in argon with a concentration of 2%, expands from a stagnation pressure of 300 mbar through a 0.8
mm diam. nozzle into a vacuum chamber. The beam is collimated by a 0.8 mm diam. skimmer placed 20 mm downstream of the nozzle. The residual transverse Doppler width,
for excitation with a laser which crosses the molecular beam
axis at right angle, is 230 MHz. The pump laser at l5227
nm and the Stokes laser at l5300 nm couple the ~0,0,0!
vibration ground level of SO2 in the X̃ 1 A 1 electronic
state17,18 to the vibrational level ~9,1,0! of the X̃ 1 A 1 state via
the ~1,1,0! level of the electronic C̃ 1 B 2 state;19 see Fig. 1.
The sequence of rotational levels is 2 02 , 3 03 , 2 02 .
The radiation from two cw single-mode dye lasers at
l5600 nm and l5579 nm is amplified in pulsed dye amplifiers, pumped by the second harmonic of an injection-seeded
Nd:YAG laser. The amplified radiation at 600 nm is frequency doubled in KD*P crystal and provides the Stokes
laser radiation with a typical pulse energy of 200 mJ. The
width of this pulse @half-width at 1/e of E(t)# is 3.1 ns as
measured with a high speed 2 GHz analog-bandwidth digital
oscilloscope. The radiation from the other amplifier at 579
nm is first frequency doubled and then mixed with the fundamental frequency of the Nd:YAG laser to yield typically
500 mJ of pump laser radiation. The width of this pulse is 2.7
ns. The pump radiation is mildly focused to a diameter of 0.8
FIG. 1. SO2 energy levels and the pump, Stokes and probe laser transitions.
Relevant wavelengths are given in nm. The bandwidth of the former two
pulses is nearly transform limited. A multimode dye laser provides the probe
laser pulse.
mm and the Stokes beam has a diameter of 2.5 mm near the
axis of the molecular beam. The resulting Rabi frequencies
are about 73109 s21 for pump and Stokes pulse, which
yields VDt'20. The time delay of the pulses at the molecular beam axis is controlled by sending the pump pulse
through an adjustable folded optical delay line. The population transferred to the ~9,1,0! level is probed by fluorescence
from the ~1,2,0! level of the C̃ 1 B 2 state induced by a multimode excimer pumped dye laser which is delayed by 300
ns relative to the pulses for the STIRAP process.
TRANSFER EFFICIENCY: RESULTS AND DISCUSSION
Figure 2 shows fluorescence induced by the probe laser.
The signal is proportional to the population of the final
~9,1,0! level. The lower trace shows the signal S FCP obtained
when the Stokes laser is blocked and population in the final
level is established by spontaneous emission from the intermediate level ~Franck–Condon pumping of population!. The
upper trace shows the signal S STIRAP when the Stokes laser
pulse participates in the transfer process. The signal S FCP has
been multiplied by a factor of 10 to be visible on the same
scale. If this particular case, the STIRAP process enhances
the population in the final level by more than two orders of
magnitude.
The absolute transfer efficiency is derived from the ratio
of the two signals S STIRAP and S FCP . This is possible since
the spontaneous transition rate from the intermediate to the
final level, given by the Franck–Condon factor F and the
rotational line-strength factor H are known. The value of the
Franck–Condon factor was taken from dispersed laser induced fluorescence spectra18 to be F51.960.1%. The linestrength factor for the 3 03 – 2 02 rotational transition for an
J. Chem. Phys., Vol. 104, No. 18, 8 May 1996
Downloaded¬01¬Apr¬2002¬to¬134.253.26.10.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright,¬see¬http://ojps.aip.org/jcpo/jcpcr.jsp
7070
T. Halfmann and K. Bergmann: Coherent population transfer and dark resonances in SO2
FIG. 3. Variation of the measured transfer efficiency ~filled squares! as the
delay Dt between pump and Stokes pulse is changed. Complete population
transfer is achieved for 25 ns<Dt<23 ns ~STIRAP regime!. Results from
a density matrix calculation with Rabi frequencies V P 53.83109 s21 and
V S 57.03109 s21 are shown in open circles.
FIG. 2. Population in the final level X̃~9,1,0!, measured by the probe laser
induced fluorescence with and without Stokes laser, as the frequencies are
tuned across two-photon resonance. The pump pulse is delayed 3.6 ns relative to the Stokes pulse. The trace obtained when the Stokes laser is off, is
shifted downward from zero for better visibility.
asymmetric top molecule is calculated to be H50.428.20
However, unlike for Na2 or Ne* in molecular beams interacting cw with lasers,6,9 the interaction time of the molecules
with the laser fields is short compared to the spontaneous
emission lifetime. Therefore the consequences of Rabi oscillations needs to be considered.15 If the pulse energy would
show no shot-to-shot variation, the fraction of the population
transferred to the intermediate level at the end of the pump
laser pulse would vary between zero and 100%, sensitively
dependent on the pulse area. For a pulse area which is sufficiently large ~equivalent to ten or more Rabi cycles during
the interaction with a single pulse, i.e., under conditions of
strong saturation! and for pulse-to-pulse fluctuations which
are sufficiently strong, the predicted excitation probability
exhibits also large pulse-to-pulse variations. However, on average, half of the population will reside in the intermediate
state at the end of the pump laser pulse. In the present case
strong saturation is fulfilled for all magnetic sublevels, including the one with the weakest coupling strength. Therefore, the transfer efficiency T is determined according to the
formula
T52FH
S
S STIRIAP
nabsorb
3G
S FCP
nDoppler
D
.
~3!
The value of the function G~nabsorb /nDoppler! depends on the
one- or two-photon saturation broadened linewidth and the
related Doppler width. Since the STIRAP process involves
an absorption and emission process, a partial compensation
of the Doppler shift occurs. The velocity components v' ,
perpendicular to the molecular beam axis, of molecules
which can participate in the two-photon process, largely exceeds the maximum value of v' , determined by the divergence of the collimated molecular beam. We have also confirmed experimentally that the saturation broadened signalphoton absorption linewidth for a pulse energy >10 mJ
exceeds the residual Doppler width of 230 MHz. Therefore,
all molecules in the collimated molecular beam participate in
the excitation leading to S FCP as well as in the transfer process yielding S STIRAP and we have G( n absorb /nDoppler!51.
From data such as those shown in Fig. 2 we derive
S STIRAP /S FCP5255625 in very good agreement with
S STIRAP /S FCP5246 expected for 100% transfer efficiency (T
51! from Eq. ~3!.
Additional independent evidence for complete population transfer is derived from the data of Fig. 3, which shows
the characteristic variation of the transfer efficiency T with
the delay Dt of the Stokes laser pulse relative to the pump
laser. The overall agreement with numerical calculations
based on the Liouville equation16 ~open circles in Fig. 3! is
excellent. The simulation study uses the measured temporal
profile of the pulses and includes an average over the measured pulse-to-pulse energy fluctuations of 14%. For negative delay ~the STIRAP configuration, where the Stokes laser
pulse preceeds the pump laser pulse! a transfer efficiency of
100%, within the given errors bars, is observed for the range
23 ns.Dt.25 ns.The plateau of T(Dt) is clear qualitative
evidence for a transfer efficiency of nearly unity, even in a
case when quantitative analysis according to Eq. ~3! is unreliable because of the uncertainty of the value of some of the
factors involved. The plateau is characteristic of the adiabatic
following process. It develops when the adiabaticity criterion, such as the one given in Eq. ~2!, is well fulfilled. In that
case a small deviation from the optimal configuration ~pulse
energies, pulse delay! is not detrimental.
DARK RESONANCE: RESULTS AND DISCUSSION
When complete population transfer occurs through the
state u a 0 & we expect, according to Eq. ~1!, the fluorescence
J. Chem. Phys., Vol. 104, No. 18, 8 May 1996
Downloaded¬01¬Apr¬2002¬to¬134.253.26.10.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright,¬see¬http://ojps.aip.org/jcpo/jcpcr.jsp
T. Halfmann and K. Bergmann: Coherent population transfer and dark resonances in SO2
FIG. 4. Dark resonances of the fluorescence induced by the pump laser, as
the Stokes laser frequency is tuned across the two-photon resonance. The
data shown in the panel to the left are obtained with delayed pulses
~STIRAP configuration!, while the Raman configuration ~delay Dt50! leads
to the results shown in the panel to the right. Although the maximum value
of V P is reduced by a factor of 10 in the latter case, the residual fluorescence of the dark resonance is negligibly small.
from the intermediate level will vanish, provided the pump
and Stokes laser frequencies are tuned to the two-photon
resonance between the initial and final level. Figure 4 shows
this dark resonance for the STIRAP configuration ~Stokes
laser pulse proceeds the pump laser pulse! and for the Raman
configuration ~the two laser pulses coincide!, which was recently applied to coherent fluorescence-dip ~or ion-dip! spectroscopy by Neusser and co-workers.21 At first glance it is
surprising that the residual fluorescence from the intermediate level at two-photon resonance is no more than a few
percent in the latter case, despite the reduction of the pump
laser Rabi frequency by a factor of ten, while it is about 20%
in the former case. The explanation is as follows.
The adiabaticity criterion in its simplest form, Eq. ~2!,
can be rewritten as6
Q̇! u D v u ,
~4!
i.e., the rate of change of the mixing angle during the interaction must be small compared to the separation Dv from the
nearest nonzero dressed-state eigenvalue. Violation of the
condition imposed by Eq. ~4! results in diabatic coupling the
other dressed states, which include a component of the radiatively decaying bare states. Thus, if V S @ V P at early times
and the state u a 0 & is initially exclusively populated, the residual fluorescence at two-photon resonance is a measure of
7071
the degree of diabatic coupling. The consequences of Eq. ~4!
are best seen in the geometrical picture briefly discussed in
the Introduction.
When the objective is population transfer, the state vector uC& must follow the 90° rotation of u a 0 & from the orientation parallel to u1& into the orientation antiparallel to u3&.
Therefore the mean value of the lhs of Eq. ~4!, averaged over
the interaction time of pulse overlap D t 0 , is ^ Q̇& STIRAP
5 p /(2D t 0 ). When the objective of dark resonance spectroscopy with overlapping laser pulses, and provided the
pulse shape and width of both pulses are identical, the mixing angle does not change, ^Q̇&Raman50 and Eq. ~4! is trivially fulfilled. However, in this case we do not have cos Q51
initially, and radiatively decaying states are also populated,
which excludes the observation of a pronounced dark resonance. A deep dark resonance can be recovered in the Raman
configuration if the width D t P of the pump laser pulse is
smaller than the width D t S of the Stokes laser pulse, as
realized in the experiments by Neusser and co-workers,21
and in this work. For D t P ,D t S and Dt50 we have
V P /V S ! 1 at the beginning and at the end of the interaction. The mixing angle reaches a maximum value of
max
arctan(V P /V S )!1 for V max
before returning to zero.
P ! VS
The lhs, averaged over the interaction time, is ^ Q̇ & Raman
5(1/D t P )arctan(VP /VS). ^ Q̇& Raman decreases with decreasing V P and increasing V S , while the residual fluorescence in
the STIRAP configuration decreases with further increasing
Rabi frequencies V P and V S . Obviously, it is easier to prevent diabatic coupling in the Raman configuration, and dark
resonances with less residual fluorescence at two-photon
resonance are to be expected, as observed in the experiment
~see Fig. 4!. This observation is closely related to the phenomenon of electromagnetically induced transparency,22
where an alternative picture is used to describe the process.
When a strong Stokes laser causes dynamic Stark splittings
of the upper level, the absorption of a ~weak! pump laser,
tuned to the one-photon resonance, is zero due to destructive
interference of the contributions from the two Stark components. A detailed numerical and experimental study of the
diabatic coupling processes will be the subject of a future
publication.
CONCLUSION
We have shown that the technique of coherent population transfer can be applied to populate very high-lying vibrational levels of a polyatomic molecule. An efficiency of
100% for transfer from the vibrational ground level to the
~9,1,0! vibrational level of SO2 in the electronic ground state
has been achieved. This demonstrates that experiments involving polyatomic molecules in selectively excited high lying vibrational levels are possible. We also demonstrate that,
and explain why, the amount of residual fluorescence at the
center of the dark resonance is different for the delayed pulse
configuration on one hand and the Raman configuration with
overlapping pulses on the other hand.
J. Chem. Phys., Vol. 104, No. 18, 8 May 1996
Downloaded¬01¬Apr¬2002¬to¬134.253.26.10.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright,¬see¬http://ojps.aip.org/jcpo/jcpcr.jsp
7072
T. Halfmann and K. Bergmann: Coherent population transfer and dark resonances in SO2
ACKNOWLEDGMENTS
E. Tiemann ~Hannover! and K. Yamanouchi ~Tokyo!
kindly provided us with spectroscopic data of SO2 from their
unpublished work. This work was supported by the Deutsche
Forschungsgemeinschaft and by the Stiftung für Innovation
Rheinland–Pfalz through the Lasercenter in Kaiserslautern.
Partial support through the EU network ‘‘Laser Controlled
Dynamics of Molecular Processes and Applications,’’
4050PL93-2602, is also acknowledged. We thank B. W.
Shore for valuable comments on the manuscript.
1
Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping,
edited by H. L. Dai and R. W. Field ~World Scientific, Singapore, 1995!.
2
C. H. Hamilton, J. L. Kinsey, and R. W. Field, Annu. Rev. Phys. Chem.
37, 493 ~1986!; X. Yang, J. M. Price, and A. Wodke, J. Phys. Chem. 97,
3944 ~1990!; J. M. Price, C. A. Rogaski, X. Yang, and A. Wodke, Chem.
Phys. 175, 83 ~1993!; R. Tuomi, J. A. Mack, and A. M. Wodtke, Science
265, 1831 ~1994!.
3
B. W. Shore, The Theory of Coherent Atomic Excitation ~Wiley, New
York, 1990!, Sec. 2.
4
S. Chelkowski and G. N. Gibson, Phys. Rev. 52, 3417 ~1995!.
5
J. Oreg, F. T. Hioe, and J. H. Eberly, Phys. Rev. A 29, 690 ~1984!.
6
U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, J. Chem. Phys.
92, 5363 ~1990!; H. G. Rubahn, E. Konz, S. Schiemann, and K. Bergmann, Z. Phys. D 22, 401 ~1991!.
7
P. Dittmann, J. Martin, G. Coulston, H. Z. He, and K. Bergmann, J. Chem.
Phys. 97, 9472 ~1992!; P. Dittmann, Ph.D. thesis, Universität Kaiserslautern, Kaiserslautern, 1993; M. Külz, A. Kortyna, M. Keil, B. Schellhaab,
J. Hauck, K. Bergmann, W. Meyer, and D. Weyh, Phys. Rev. A ~to be
published!.
8
C. Liedenbaum, S. Stolte, and J. Reuss, Phys. Rep. 178, 1 ~1989!; J. Reuss
and N. Dam, in Applied Laser Spectroscopy, edited by M. Inguscio and
W. Demtröder ~Plenum, New York, 1990!; N. Dam, L. Oudejans, and J.
Reuss, Chem. Phys. 140, 217 ~1990!.
9
B. W. Shore, J. Martin, M. Fewell, and K. Bergmann, Phys. Rev. A 52,
566 ~1995!; J. Martin, B. W. Shore, and K. Bergmann, ibid. 52, 583
~1995!; Phys. Rev. A ~submitted!; K. Bergmann, J. Martin, and B. W.
Shore, in Proc. of the Conference on Coherence and Quantum Optics VII,
edited by J. Eberly, L. Mandel, and E. Wolf ~Plenum, New York, 1996!.
10
P. Marte, P. Zoller, and J. L. Hall, Phys. Rev. A 44, R4118 ~1991!; P.
Pillet, C. Valentin, R. L. Yuan, and J. Yu. ibid. 48, 845 ~1993!; L. S.
Goldner, C. Gerz, R. J. Spreeuw, S. L. Rolston, C. I. Westbrook, W. D.
Phillips, P. Marte, and P. Zoller, ibid. 72, 997 ~1994!; J. Lawall and M.
Prentiss, Phys. Rev. Lett. 72, 993 ~1994!; M. Weitz, B. C. Young, and S.
Chu, ibid. 73, 2563 ~1994!; L. Lawall, S. Kulin, B. Saubamea, N. Bigelow, M. Leduc, and C. Cohen-Tannoudji, in Proc. of the 4th International
Workshop on Laser Physics ~Moscow, 1995!, Laser Physics 6, 1 ~1996!.
11
B. Broers, H. B. van Linden van den Heuvell, and L. D. Noordam, Phys.
Rev. Lett. 69, 2062 ~1992!.
12
S. Schiemann, A. Kuhn, S. Steuerwald, and K. Bergmann, Phys. Rev.
Lett. 71, 3637 ~1993!.
13
J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, Phys. Rev. A
40, 6741 ~1989!; K. Bergmann and B. W. Shore, Sec. 9 in Ref. 1.
14
A. Kuhn, G. W. Coulston, G. Z. He, S. Schiemann, W. S. Warren, and K.
Bergmann, J. Chem. Phys. 96, 4215 ~1992!.
15
A. Kuhn, Ph.D. thesis, Universität Kaiserslautern, Kaiserslautern, 1995.
16
B. W. Shore, Sec. 6 in Ref. 3.
17
F. J. Lovas, J. Phys. Chem. Ref. Data 14, 395 ~1985!; K. Yamanouchi, H.
Yamada, and S. Tsuchiya, J. Chem. Phys. 88, 4664 ~1988!; Y. Morina, M.
Tanimoto, and S. Saito, Acta Chem. Scand. A 42, 346 ~1988!.
18
K. Yamanouchi, S. Takeuchi, and S. Tsuchiya, J. Chem. Phys. 92, 4044
~1990!.
19
J. C. D. Brand, P. H. Chiu, A. R. Hoy, and H. D. Bist. J. Mol. Spec. 60,
43 ~1976!; A. R. Hoy and J. C. D. Brand, Mol. Phys. 36, 1409 ~1978!; S.
Becker, C. Braatz, J. Lindner, and E. Tiemann, Chem. Phys. Lett. 208, 15
~1993!; J. E. Szankowski, Diplomarbeit, Universität Hannover, Hannover,
1994; K. Yamanouchi, M. Okunishi, Y. Endo, and S. Tsuchiya, J. Mol.
Struc. 352, 541 ~1995!
20
P. C. Cross, R. M. Hainer, and G. W. King, J. Chem. Phys. 12, 210
~1994!; D. Papousek and M. R. Aliev, Molecular Vibrational-Rotational
Spectra ~Elsevier, Amsterdam, 1982!.
21
R. Sussmann, R. Neuhauser, and H. J. Neusser, J. Chem. Phys. 100, 4784
~1994!; R. Sussmann, R. Neuhauser, and H. J. Neusser, J. Chem. Phys.
103, 3315 ~1995!; R. Neuhauser, R. Sussmann, and H. J. Neusser, Phys.
Rev. Lett. 74, 3141 ~1995!.
22
K. J. Boller, A. Imamoglu, and S. E. Harris, Phys. Rev. Lett. 67, 3062
~1991!.
J. Chem. Phys., Vol. 104, No. 18, 8 May 1996
Downloaded¬01¬Apr¬2002¬to¬134.253.26.10.¬Redistribution¬subject¬to¬AIP¬license¬or¬copyright,¬see¬http://ojps.aip.org/jcpo/jcpcr.jsp