Tracking molecular wave packets in cesium dimers by coherent Raman scattering

PHYSICAL REVIEW A 86, 023421 (2012)

Tracking molecular wave packets in cesium dimers by coherent Raman scattering
Luqi Yuan,' Dmitry Pestov,2 Robert K. Murawski,3 Gombojav O. Ariunbold,4'5 Miaochan Zhi,' Xi Wang,'
Vladimir A. Sautenkov,1'6 Yuri V. Rostovtsev,7 Torsten Siebert,1,8 and Alexei V. Sokolov'
'Texas A&M University, College Station, Texas 77843, USA
2Biophotonic Solutions Inc., 1401 East Lansing Drive, Suite 112, East Lansing, Michigan 48823, USA
3Department of Physics, Drew University, Madison, New Jersey 07940, USA
4The University of Arizona, College of Optical Sciences, Tucson, Arizona 85721, USA
5School of Physics and Electronics, National University of Mongolia, Ulaanbatar 210646, Mongolia
6Joint Institute for High Temperatures of Russian Academy of Sciences, 13-2 Izhorskaya Str., Moscow 125412, Russia
7Department of Physics, University of North Texas, Denton, Texas 76203, USA
8lnstitut fir Experimentalphysik, Freie Universitat Berlin, Arnimallee 14, 14195 Berlin, Germany
(Received 5 April 2012; published 31 August 2012)
We explore wave-packet dynamics in the ground X '11+ and excited B 'Hu states of cesium dimers (Cs2). In
particular, we study the dependence of the wave-packet dynamics on the relative timing between femtosecond
pump, Stokes, and probe pulses in a nondegenerate BOXCARS beam geometry, which are commonly used
for coherent anti-Stokes Raman scattering (CARS) spectroscopy. The experimental results are elucidated by
theoretical calculations, which are based on the Liouville equations for the density matrix for the molecular
states. We observe oscillations in CARS signals as functions of both Stokes and probe pulse delays with respect
to the pump pulse. The oscillation period relates to the wave-packet motion cycle in either the ground or excited
state of Cs2 molecules, depending on the sequence of the input laser pulses in time. The performed analysis
can be applied to study and/or manipulate wave-packet dynamics in a variety of molecules. It also provides an
excellent test platform for theoretical models of molecular systems.

DOI: 10.1103/PhysRevA.86.023421 Pi
I. INTRODUCTION
Femtosecond laser pulses have been used to study the
transient ultrafast dynamical processes in molecular systems
and launched a research field, which is called femtochemistry
[1,2]. The study of the vibrational and rotational wave
packets in molecules on femtosecond time scale has been of
interest for several decades [3]. Recently, the vibrational and
rotational wave-packet dynamics in different molecules have
been observed by adopting the two-color, pump probe [4-6]
and coherent femtosecond four-wave mixing (FWM) spec-
troscopic [7-10] techniques. Resonant coherent anti-Stokes
Raman scattering (CARS) spectroscopy has been used to
extract a time-dependent wave function of a reacting molecule
[11]. It has been shown that the phase-matching condition
in the FWM process is crucial in monitoring the molecular
dynamics at single-laser-shot level [12,13]. The effect of the
impulsive excitation and the momentum transfer [14,15] exists
in the FWM experiment with ultrashort pulses.
Coherent laser control of the quantum dynamics in the
physicochemical processes has been studied [2,16]. In particu-
lar, temporal coherent control on ultrashort time scale in atomic
rubidium vapor has been reported [17,18]. The study of quan-
tum interference of molecular eigenstates has led to a method
to manipulate the wave packets with promising applications
in various coherent control techniques [19]. Two-dimensional
spectroscopy has served as a useful tool, which provides a
clear physical picture of the wave-packet temporal evolution
[20]. Coherent optical response in gas has been revealed by
using the Fourier transform of two-dimensional spectroscopic
measurements [21,22]. A time-dependent perturbation theory
has been adopted to understand various FWM processes
[23-25]. Density matrix formalism [26] has proved to be

ACS number(s): 33.80.-b, 33.80.Wz, 78.47.nj, 42.65.Re
an important tool to interpret molecular coherent processes
observed in femtosecond experiments [27,28].
In the present work, we study ultrafast wave-packet
dynamics in cesium dimers by using the CARS technique
in the nondegenerate BOXCARS beam arrangement. The
main advantage of our experimental configuration is the
ability to perform two-dimensional types of measurements.
In particular, the measured CARS signal is studied as a two-
dimensional function of pump-Stokes and pump-probe delays.
In order to model these experiments, we adopt the Liouville's
equation for the density matrix for the electronic excited
(B 'Hu) and ground (X 1'+) states with the appropriate
Franck-Condon factors. The electric dipole moment between
the (B 'Hu) and (X 'Eg) states could be approximated to
be a constant if the locations of the nuclei are not displaced
far from the equilibrium [29]. In our experiment, we note
that the rotational levels are also heavily populated. However,
for simplicity's sake, the rotational contributions have been
neglected in the theoretical model with the Franck-Condon
principle.
Our paper is organized as follows. We present the experi-
mental setup and theoretical model in the next two sections. In
Sec. IV, the experimental and theoretical results are analyzed
in detail. We summarize our results in the last section.
II. EXPERIMENTAL SETUP
The Cs2 wave-packet dynamics is studied via a two-
color CARS scheme. The input pump, Stokes, and probe
beams are arranged in the folded-BOXCARS geometry. The
experimental setup is shown in Fig. 1.

1050-2947/2012/86(2)/023421(10)

023421-1

2012 American Physical Society

Yuan, Luqi; Murawski, Robert K.; Ariunbold, Gombojav O.; Zhi, Miaochan; Wang, Xi; Sautenkov, Vladimir A. et al. Tracking molecular wave packets in cesium dimers by coherent Raman scattering. [College Park, Maryland]. UNT Digital Library. http://digital.library.unt.edu/ark:/67531/metadc103258/. Accessed August 30, 2014.