S.B. BayramPhysics 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, 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.

133Cs I=7/2 6p2P1/2 34(3.4)ns A=291.90(13) MHz g(1) =0.344 g(2) =0 6p2P3/2 33(3.3)ns A=50.34(6) MHz B=-0.38MHz g(1) =0.344 g(2) =0.219

23Na I=3/2 3p2P1/2 16.2(5)ns A=94.3(1) MHz g(1) =0.377 g(2) =0 3p2P3/2 16.1(5)ns A=18.69(9)MHz B=2.90(21)MHz g(1) =0.555(2) g(2) =0.297(1)

Population mixing among the Zeeman sublevelsJ=1/2 Jʹ=3/2 Jʹʹ=1/2,5/2

Rate equation analysis of Zeeman populations

Populated by linearly polarized lighty

Populated by circularly polarized lighty

2

)(3)(

2

1)(N

2

)(3)(

2

1)(N

1/2

1/2

tOtNt

tOtNt

o

o

J=1/2 Jʹ=3/2 Jʹʹ=1/2

J=1/2 Jʹ=1/2 Jʹʹ=1/2

34.03II

IIPC

oO

PNtN )( 3/pooo OO

Net rate of change:

Time dependent solutions in the limit of steady state approximation

tP etN

1)( )1(

3)( t

o

po

oetO

6.0516

15

II

IIP

//

//L

o

o

A

A

CsArvoAro

0.1)(

45

2

)(15P

)2(

)1(

C

tgA

tgO

o

o

)1(1

)1(1

)()(

)1(

t

t

o

oc

eT

eTtg

pP

o

Experimental Results from Atomic PolarizationSpecies σ2 (Å2) σ1 (Å2) σ2 / σ1 References Technique

Cs-Ar 186 (58) Bayram [1] TPS

Cs-Ar 151 (42) 1.23 (4) Bayram [2] TPS

Cs-Ar 288 (72) 234 (34)188 (38)

1.23 (18) Guiry [5]Fricke [6]

Ze-S high BOP

Cs-Kr 294 (45)273

Bayram [3]Okunevich [10]

TPSTheory

Cs-Ar 9.25(1.4) Bayram [4]

Na-Ar 196 (22) Bayram [5] TPS

Na-Ar 200 (30) 228 (13)308 (31)

Cook [7]Gay [8]Elbel [9]

PS-tuningZe-Scan B Ha-E

Na-Xe 357 (21) Bayram [5] TPS

376 (38) Elbel [9]

[1] Bayram et al., Phy. Rev. A 73, 042713 (2006)

[2] Bayram et al., Phys. Rev. A78, 033403 (2008)

[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).

J=3/2

J=3/2

J=1/2

22 44 66 88 1010 1212 1414 1616 1818 2020 2222 2424

0

10000

20000

30000

pro

be

pu

mp

fluo

resc

en

ce

21u

51+

g

61+

g

X1+

g

Ene

rgy

(cm

-1)

Internuclear Distance R (Å )

A1+

u

41+

g

31+

g

B1u

3s+3s

Na2

3s+4s

3s+3p

3p+3d

-6022.02

3s+4p

3s+5s

cw

Study of Collision Dynamics of Excited Molecules:Excitation Scheme of Na2

Na2 Experimental Setup

Sodium Heatpipe Oven 300o C with 4 mTorr Ar15 mTorr vacuum @ 22o C 4-arm cooling with tap water

Coherent 699-01

Wavemeter0.001 cm-1

Ti:Sapphirepulsed

DCM

Dye Laser 552 nm

CC

DCoherentVerdi V10

Millenia 532 10 W

Nd: YAG 532

1.5-m SPEX

PC

PMT filter PMT

etalontuning

Boxcar

PC

Argon gas line

100MHz, 7.5W 1 GHz

Vertical Polarizer

Vertical Polarizer

LCR

0 5 10 15 20 250

5

10

15

20

25Na

2 61+

g - B1

u Franck - Condon Factors

61+

g

B 1

u 0.01000

0.02344

0.03516

0.04688

0.09375

0.1406

0.1641

0.1875

0.2344

0.2578

0.2813

0.3750

0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

35

40Na

2 X1+

g - A1+

u Franck - Condon Factors

v'' (X1+

g )

v '

(A1

+ u ) 0.000

0.01000

0.02500

0.05000

0.1000

0.2000

0.3320

J"=30

33 66

0

10000

20000

30000

v'=13

v=8

v'=6

prob

e

pum

p

fluor

esce

nce

61+

g

X1+

g

Ene

rgy

(cm

-1)

Internuclear Distance R (Å )

A1+

u

B1u

Na2

-6022.02

cw

v"=0

Triple Resonance Spectroscopy

Triple Resonance Excitation & Emission Scheme

6600.034316562.8306B1Σu+ (13,20) X1Σg

+ (14,21)|4> |1>

4050.26611705.353961Σ g (8,J=J’±1) B1Πu (13,J±1)|3> |4>

0.15018021.7307A1Σu+ (7, J’) 61Σ g (8,J’ ±1)|1> |2>

0.11215426.111X1Σg+ (0,30) A1Σu

+ (7,J’=30±1)|1> |2>

Franck-Condon Factor

Laser wavenumbers

cm-1

Transition

Doppler width 1.15 GHz; Laser 1 bandwidth: 1 GHz

L1 power: 300 mW

L2 power: 2 mW with 18 kW peak power

L3 power: 1.5 W average power

1542

6.11

1 cm

-118

02.7

307

cm-1

fluo

resc

ence

16562.8306 cm-1

cw

11705.3539 cm-1

X1Σg

A1Σu

61Σg (8,J)SE

P

PUM

P

(13,J±1)

(0,30)

(3, Jʹʹ)

(7, Jʹ)

B1u

540 550 560 570 580 590 600 61020000

40000

60000

80000

Inte

nsi

ty (

arb

itra

ry)

wavelenght

• The molecule is in a particular rovibrational level of the A 1u+

• The molecules then populated in 61g+ by a pump laser – initial orientation is created by a

circularly (linearly) polarized pump laser. Probe laser further populates B 1u+

• The molecule undergoes a collision which transfer some of the orientation to a

neighboring rovibrational level of the 61g+

• This disorientation or amount of orientation can be probed by a probe laser which causes

stimulated emission down to B 1u+

Measurement of Collisional Orientation Transfer

-Jʹ+1 -Jʹ+ 2 Jʹ+2 Jʹ+1

-J -J+1 -J+ 2 J+2 J+1 J

-Jʹ -Jʹ +1 -Jʹ + 2 Jʹ +2 Jʹ +1 Jʹ

mʹʹ

mʹ

m

PUMP

PROBE

Δm=0 Linear polarization

Δm= -1 Left circular polarization

Δm=±1

Conclusion

• We have calculated and measured the state multipoles in the excited states of Cs

• We have calculated and measured the effects of nuclear hyperfine depolarization as a

function of the delay time of the probe.

• Extracted the anisotropy-dependent collisional depolarization cross sections from the

polarization spectrum.

• We have demonstrated time-evolution of state multiples using PUMP-PROBE

(Stimulated Emission Pump) scheme in conjunction with PROBE-delayed-detection

technique. To extract the collisional cross section, a theoretical model based on the

density matrix formalism was developed.

• Using the triple resonance spectroscopy we are currently working on the collisional

transfer of population and orientation in Na2.

Acknowledgments & References

• Prof. M. Lyyra from Temple U. for providing Coherent 699-01 laser

• Dr. Jim Gord from Dayton WPAF Base for providing Ti:sapphire laser

• Prof. W. Stwalley from UConn for providing DCM mirror set

• Prof. R. Le Roy, University of Waterloo (Level program)

• Students: Ceylan Guney (Visiting Scholar), Oleg Popov (Ph.D. U. Of California, Riverside)

View from our laboratory

Phill Arndt (grad), Briana Vamosi (1st yr), Patrick Boyle (2nd yr).

Briana shows Patrick and Jacob how to align counter propagating beams.