VOLUME 83, NUMBER 10 PHYSICAL REVIEW LETTERS 6SEPTEMBER 1999
Measurement of x
3
for Doubly Vibrationally Enhanced Four Wave Mixing Spectroscopy
Wei Zhao and John C. Wright
Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706
(Received 26 April 1999)
We report the measurement of the third order susceptibility x
3
for doubly vibrationally enhanced
four wave mixing in the model system, acetonitrile. Two resonances multiplicatively increase the
mixing efficiency if there is mode coupling and provide an additional spectral dimension for vibrational
spectroscopy that greatly improves its resolution. Such methods promise to have important applications
for vibrational spectroscopy of complex materials.
PACS numbers: 42.65.An, 33.20.Ea, 33.80. – b
Vibrational spectroscopy is widely used for studying
materials because it provides molecular level character-
ization. Its use is often hindered in complex materials
because spectral congestion and line broadening obscure
transitions. There is great interest in developing multi-
resonant six wave mixing (SWM) spectroscopies that can
increase selectivity [1–7]. A different approach uses
multiresonant four wave mixing (FWM) and indeed,
selective enhancements and line narrowing have been
demonstrated with FWM for electronic transitions at cryo-
genic temperatures [8]. In this paper, we extend FWM to
vibrational resonances and report the first measurement of
the multiplicative vibrational enhancement of x
3
. The
measurement of a doubly vibrationally enhanced (DOVE)
x
3
shows the feasibility for multidimensional vibrational
spectroscopies.
There are many nonlinear processes that must be consid-
ered [3]. Figure 1 shows the important nonlinear processes
for this work. In the DOVE-IRFWM process [Fig. 1(a)],
coherent sources drive the acetonitrile CH
3
CN absorp-
tions near the n
2 C—
—
—
N stretch at v
2
2253 cm
21
and
the n
2
1n
4 (C—
—
—
N 1 C—C stretch) combination band
at v
1
3164 cm
21
. A third beam at 532 nm generates
the output coherence by a two photon Raman process
that destroys the n
4
excitation. The Mukamel diagram in
Fig. 1(a) shows how the bra and ket parts of the coherence
r
i ,j
evolve along three different time ordered pathways [9].
Each pathway can be resonantly enhanced (see Fig. 1) and
described quantitatively by [3]
r
db
µ
V
ac
V
ab
V
cd
D
ca
D
da
D
db
1
V
ac
V
ab
V
cd
D
ca
D
cb
D
db
1
V
ac
V
ab
V
cd
D
ab
D
cb
D
db
∂
r
aa
, (1)
where each term corresponds to a pathway. Here, V
ij
is
the Rabi frequency, m
ij
E2¯ h, of the transition between
states i and j , m
ij
is the transition moment, E is the
resonant laser field, D
ij
v
ij
2v
k
2 i G
ij
, v
ij
is the
frequency difference between states i and j , v
k
is the laser
frequency, and G
ij
is the dephasing rate. This equation can
be rewritten in the form
r
db
V
ac
V
ab
V
cd
D
ba
D
ca
µ
1
D
da
1
i G
a
db
D
da
D
db
1
i G
a
cb
D
cb
D
db
∂
r
aa
,
(2)
where G
a
ij
G
ij
2G
ia
2G
aj
2G
aa
and G
ij
is the pure
dephasing rate of the ij transition. The last two terms
vanish in the limit of no pure dephasing [3]. The second
FWM process is shown in Fig. 1(b). If state c is an
electronic state, this process is coherent anti-Stokes Raman
spectroscopy (CARS) [9] but if state c is a vibrational state,
it is a DOVE Raman process given by [3]
r
da
V
ac
V
cb
V
bd
D
ca
D
ba
D
da
r
aa
. (3)
FIG. 1. The resonances for DOVE with three input frequen-
cies (v
1
, v
2
, v
3
) and the output signal v
4
. The horizon-
tal lines indicate resonant vibrational or nonresonant electronic
states. The solid and dotted vertical arrows indicate resonances
associated with the ket or bra part of the coherence. The letters
in the bottom Mukamel diagrams represent state changes in the
ij of the r
ij
density matrix.
1950 0031-9007 99 83(10) 1950(4)$15.00 © 1999 The American Physical Society