S.B. Bayram Physics Department, Miami University, Oxford, OH Collision Dynamics of Excited Atoms and Molecules Briana Vamosi (UG, Chemistry) Patrick Boyle (UG, Physics) Jacob McFarland (UG, Physics) Phill Arndt (G, roup Members Suppo ting International Symposium on Molecular Spectrosc June 17, 2014
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S.B. Bayram Physics Department, Miami University, Oxford, OH Collision Dynamics of Excited Atoms and Molecules Briana Vamosi (UG, Chemistry) Patrick Boyle.
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Briana Vamosi (UG, Chemistry) Patrick Boyle (UG, Physics)
Jacob McFarland (UG, Physics)Phill Arndt (G, Physics)
Current Group Members Supported by
69th Meeting International Symposium on Molecular Spectroscopy June 17, 2014
• Focus: Anisotropy transfer arising from collisions between diatomic molecules and rare-gas atoms. Goal: To measure collision cross sections for transfer of rotational orientation Na2-argon system using polarization spectroscopy. The recent experimental discovery of collisional transfer of anisotropy in heteronuclear molecular system prompted us to investigate whether this effect is general or shows unusual behavior in different molecules.
• Atomic Polarization Measurement in the excited state of atoms using PUMP-PROBE (Stimulated Emission Pump -SEP) with PROBE -delayed detection technique
• Time-resolved polarization measurement which depends on the anisotropy (alignment, orientation) created in the excited state by a PUMP laser.
• From the polarization measurement we extract collisional cross section using rate equation analysis
• Application of Polarization Measurement in sodium molecules using three-step sequence cw-PUMP-PROBE scheme - we are currently working on this experiment.
Measurement of polarization from analysis of the emitted light is a very powerful method gaining information about the inelastic collision process between the electronically excited molecules and other collision partners.
Overview & Motivation
Density Matrix Formalism
Polarization of an excited state ensemble of atoms with J by – (2J+1)x(2J+1)
Irreducible tensor components of density matrix
)';'()1()('
' qMMkJJCJT MJk
MMMM
kq
'MM
)...)(( kkqJT kq
4-axially symmetric multipoles up to k=2J
Off-diagonal elements represent coherences diagonal elements represent populations in the Zeeman levels
Symmetry relations can be used to reduce nonzero components: q=0 components survive- coherences are not Generated between Zeeman sublevels.
Axially symmetric multipoles can be created up to k=2J
k=0 monopole (population) N
k=1 magnetic dipole moment (orientation)
k=2 electric quadrupole moment (alignment)
k=3 magnetic octupole momentk= 4 electric hexadecapole …
m
z
JJ
mma
JJ
JO
)1(
)(
)1(
2
0
m
z
JJ
JJmma
JJ
JJA
)1(
)]1(3[)(
)1(
3 2222
0
<A0> = -4/5 Jʹ = 3/2<A0> = 0 Jʹ = 1/2
State Multipole Moments :Dynamical information about the excited state
)...)(( kkqJT kq
Atomic polarization is represented here as a surface whose radius is given by the probabillity to find the maximum projection of angular momentum along each direction.
A J=2 atomic state, initially aligned along the x axis in a z-directed electric field.
Alignment Orientation
z z
Polarized Atoms Visualized by Multiple Moments
Rochester & Budker, AJP, vol. 69, 450 (2001)
Aligned axially symmetric system, invariant under reversal of z-axis. No net angular momentum of the system.
Intensity of fluorescence and polarization in terms of anisotropy
2sincos),(2
3
2cos2cossin),(4
3)(cos),(
2
11
3
1),,(
1
222
2
ofi
ofiofi
o
OJJh
AJJhPAJJhII
Greene and Zare, Ann. Rev. Phys. Chem., vol.33, 119 (1982)
(φ,θ, χ) are Euler angles relating the collision frame to the detector frameβ is polarization state of lighth(Ji,Jf) is a function that depends only on the angular momentum of Ji and Jf
II
IIPL
//
//
)(16
)(3)(
0
0
tA
tAtPL
5/4)0(0 tA
2/3'J
14.0)0( tPL
852.12 nm
387.92 nm
894.72 nm
Spectroscopy by Stimulated Emission Pumping
-0.8
-0.6
-0.4
-0.2
0.0
volta
ge(
V)
time(s)
390 ns
13 ns
Stimulated emission signal
Cesium
)cos();'()12(
)1'2)(12()( '
2
'
)( tIkJFJFWI
FFtg FF
FF
k
Time Evolution of the Polarization in the 8p 2P3/2
)(20
)(3
)()(16
)()(3)2(
)2(
)2(0
)2(0
tg
tg
tgtA
tgtAPL
Blum, Density matrix theory & applications, Plenum press, 1981.
Polarizer
home-made dye lasers in Littman-Metcalf cavity
Perturbation coefficient
Probe delay line
0 20 40 60 80 100 120-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
Time (ns)
Pola
riza
tion
(%
)
Time Evolution of Polarization: Quantum Beats
PUMP-SEP Polarization Spectroscopy with SEP-delayed detection technique allows us to map out the time evolution of polarization.
2'
2
'
)(
)(1
);'(
)12(
)1'2)(12(
FFFF
k IkJFJFW
I
FFg
Excited State Perturbation Coefficients
Perturbation coefficient need to be integrated over time if the excitation and decay times are not resolved: quantum beat disappears but net effect may still be visible through depolarization of emitted light.
M.D. Havey and L.L. Vahala, J. Chem. Phys. 86 (3), 1648 (1987)Andersen and Bartschat, Polarization, Alignment, and Orientation in Atomic Collisions, Springer, 2001
A summary of data used to calculate hyperfine depolarization coefficient and values for g (1) and g (2)
for common alkai isotopes is given in Havey et al.
[3] Bayram et al., Opt. Comm., vol. 282, 1567-1573 (2009)
[4] Bayram et al., J. Quant. Spectrosc. Radiat. Transfer, 113, 2066 (2012)
[5] Bayram et al. Phys. Rev. A 86, 062503 (2012).
[5] J. Guiry and L. Krause, Phys. Rev. A 14, 2034 (1976); [6] Fricke et al., Phys. Rev. 163, 45 (1967); [7] Cook et al., Phys. Rev. A 47, 340 (1993); [8] J.-C. Gay and W. B. Schneider, Z. Phys. A 278, 211 (1976); [9] M. Elbel, B. Kamke, and W. B. Schneider,Physica (Amsterdam) 77, 137 (1974). [10] A.I. Okunevich and V.I. Perel, Soviet Physics JETP 31, 356 (1970).