1. Marjatta Lyyra Physics Department, Temple University, Philadelphia, PA
Autler-Townes Effect as a Probe of Molecular Electronic Transition Dipole  Moments
Marjatta Lyyra
Physics Department, Temple University, Philadelphia, PA
Supported by NSF

2. Acknowledgements
Ergin Ahmed, Peng Qi, Omer Salihoglu, Bediha Beser and Svetlana Kotochigova, Physics Department, Temple University, USA
Annie Hansson, Stockholm University, Sweden
Li Li, Tsinghua University, Beijing, China
Sylvie Magnier, IUFM de Bretagne and Laboratoire de Physique des Atomes, Lasers, Molecules et Surfaces, CNRS et Université Rennes,Rennes Cedex, France
R. W. Field, MIT and John Huennekens, Lehigh University, USA

3. Outline
Introduction
AT splitting by triple resonance based extended  system
AT splitting by quadruple resonance excitation at large R
Conversion of AT splitting data to the R- dependence of e(R)

4. Introduction
Laser field, E
|1>
|2>
Transition Dipole Moment measurements using the Autler-Townes (AT) effect.
According to the R-centroid approximation,
is the R-centroid

5. Na2 A-X coupling field wavefunctions

6. Extended  Excitation Scheme
|3>
2 1Πg L2
|2>
A1u+
A1u+ L3
X 1g+ L1
|4>
|1>
X 1g+

7. Coupling field transition choice

8. Experimental Setup TiSa Sodium Heatpipe DCM R6G L3 M Verdi V10 M M
Lock-in
Amplifier
PMT
Monochromator BS
Sodium
Heatpipe L2
Verdi V10
DCM M L1
Sabre SBRC-DSW 25
R6G M
Lasers ( or )
Mechanical modulator

9. Autler – Townes split spectrum by L3
|3>
2 1Πg L2
|2>
A1u+
A1u+ L3 L1
|4>
X 1g+
|1>
X 1g+
L1: A 1u+(25,20) X 1g+(1,19)
L2: 21Πg(25,20)  A1u+(25,20)
L3: A1u+(25,20)— X 1g+(38,21)

10. Coupling Laser Power Study
(b)
(c)
(d)
(e)
(f)

11. AT Splitting vs. Coupling Laser Power Plot

12. AT Splitting vs. Coupling Laser Power
The electric field is calculated from the
experimentally measured laser power and spotsize
Note: Each rovibrational level has a set of magnetic sublevels (MJ), and for each of these levels the Rabi frequency is given by:
is an orientation factor. For R and P-branches of a
- transition and linearly polarized laser field
this factor is given by:
R- branch
P- branch

13. Density Matrix Formalism
The total Hamiltonian H for the system:
With the aid of the Rotating Wave Approximation the Hamiltonian H can be written in the following
form:
Density matrix equation of motion
in the interaction picture:
where  represents all relaxation terms:
We solve the density matrix equation of motion in the limit of steady state approximation.
Recorded Signal

14. Simulation E. Ahmed et. all, J. Chem. Phys. 124, 084308 (2006)
Excitation spectrum in the presence
of the coupling laser (Power 450mW)
OODR excitation spectrum
A1u+(25,20)— X 1g+(38,21)
1 = 28 MHz
2 = 52 MHz
1 = 28 MHz 2 = 52 MHz
The Rabi frequency 3 of the coupling
field is used as fitting parameter 3 = 755 ( 10) MHz.
Parameters:
Lifetime A 1u+ 2 = 12.5 ns, 21g 3 = 18.3 ns;
branching ratios W32/W3 = 0.076, W21/W2 = 0.001, W24/W2 = 0.16;
Doppler width 1.15 GHz;
Collisional dephasing rates ij/2 = MHz;
Transit relaxation rate wt/2 = 0.38 MHz.
E. Ahmed et. all, J. Chem. Phys. 124, (2006)

15. Transition Dipole Moment Measurements Results
Transition dipole moment of Na2 as function
of the internuclear distance
A1u+
(v',J')
X1g+
(v'',J'')
Debye
FCF
Rc, Å
e(Rc),
Debye
28, 20
42, 21
1.86
0.036
4.57
9.76
33, 20
46, 19
2.75
0.083
5.16
9.54
33, 20
51, 21
2.09
0.046
4.90
9.71
33, 20
43, 21
3.06
0.105
5.40
9.44
34, 20
44, 21
2.6
0.077
5.57
9.40
34, 20
44, 19
2.75
0.086
5.51
9.39
34, 20
48, 21
1.79
0.035
5.31
9.51
35, 20
35, 19
1.79
0.037
5.77
9.31
10, 20
20, 21
2.53
0.067
4.00
9.75
10, 20
17, 21
2.03
0.044
3.82
9.70
10, 20
23, 21
3.87
0.155
4.30
9.84
8, 20
20, 21
3.02
0.094
4.18
9.83
14, 20
27, 19
3.08
0.098
4.44
9.85
20, 20
34, 19
5.37
0.301
4.71
9.79
29, 20
44, 21
2.02
0.043
5.03
9.73
25, 20
38, 21
5.50
0.322
4.82
9.70

16. Conclusion
This technique allows experimental measurement of the transition dipole moment between the ground and first excited states, as function of the internuclear distance from the experimentally measured coupling field (E3) and a simulation of the recorded AT split spectrum.
We are in the process of measuring the transition dipole moment of X1g+ A1u+ of Li2 as function of the internuclear distance to understand better the role of perturbations. In that case spin-orbit interaction is very week.
We are extending the experimentally accessible R- range of the transition dipole moment measurements by implementing an excitation scheme involving four CW lasers (quadruple resonance).

17. CW all-Optical Quadruple Resonance Spectroscopy of Sodium Dimer
Ergin Ahmed, Peng Qi, Marjatta Lyyra,
Physics Department, Temple University, Philadelphia, PA
Supported by NSF

18. Quadruple Resonance Technique: Introduction
We report the first cw all-optical quadruple resonance excitation experiment with all excitations steps being coherently driven by a combination of four tunable lasers.
We have constructed a theoretical model to simulate the experimentally observed signal based on density matrix formalism, which can be used also to identify optimal laser wavelengths as well as laser propagation geometry for observation of the Autler-Townes splitting.
This excitation technique is very general and can be used to probe transitions to electronic states at large inter-nuclear distance. The Autler-Townes effect associated with this technique can be used as a way of investigating the internuclear distance dependence of the transition dipole moment function at larger internuclear distance than before.
The technique also allows for general access to highly excited electronic states at large internuclear distance with high resolution and thus can be used to probe Rydberg states in high vibrational levels, which are difficult to reach otherwise starting from the thermal population in the ground state.

19. Excitation Schemes Excitation scheme B Excitation scheme A Recorded
21Πg
(v=19,J=20)
A1Σu+
(v´=22,J´=20)
X1Σg+
(v´´=1,J ´´=21)
|3
21Πg
(v=19,J=20)
A1Σu+
(v´=22,J´=20)
X1Σg+
(v´´=1,J ´´=21)
41Σg+(v=14,J=21)
|3
|5
Recorded
Signal L3 L3 L2 L2 L4
A1Σu+
(v´=23,J´=20)
|4>
A1Σu+
(v´=23,J´=22)
|4>
A1Σu+
(v´=23,J´=20)
|2>
|2> L4
Recorded
Signal
|5 L1 L1
X1Σg+
(v´=36,J´=19)
|1
|1

20. Experimental Setup TiSa DCM Sodium Heatpipe DCM R6G L4 M Verdi V10 L3
Inova 400
DCM BS
Lock-in
Amplifier
PMT
Monochromator BS
Sodium
Heatpipe L2
Verdi V10
DCM M L1
Sabre SBRC-DSW 25
R6G M
Tunable lasers: Coherent
autoscan ( or )
Mechanical modulator

21. Density Matrix Formalism
The total Hamiltonian H for the system:
The molecular part of the Hamiltonian Hmol:
The interaction part of the Hamiltonian Hmol:
With the aid of the Rotating Wave Approximation the Hamiltonian H can be written in the interaction picture in the following form:
Density matrix equation of motion
in the interaction picture:
 represents the relaxation rates:

22. Diagram of the Excitation and Decay Processes
Excitation scheme A
Excitation scheme B
1,1
W32
W21
W34
W41
W52
W54
4,4
3,3
2,2
W32
W21
W34
W41
W45
3,3
4,4
2,2
1,1
*Levels |6> and |7> represents all other ro-vibrational levels of the ground and first excited electronic
states, respectively. They are not coherently coupled to the system.

23. Density Matrix Equations (scheme A)
where:
Each equation involving the time derivative of the off diagonal matrix elements on the left side has a complex conjugate equation.
The set of equations are solved in the limit of steady state approximation, along with a condition for conservation of the population.

24. Experimental Results and Simulations– excitation scheme A
Quadruple resonance single channel fluorescence spectra from level |5>. Comparison
between coherently driven and spontaneous decay only |3>|4> transition.
|3
|5
Transition
Laser, cm-1
FCF
Beam radius,m
|1>  |2>
L1,
0.0079
300
|2>  |3>
L2,
0.0502
278
|3>  |4>
L3,
0.1676
405
|4>  |5>
L4,
0.1898
660 L2 L3 L4
|4>
|2> L1
|1>
Parameters for the simulation:
Lifetime A 1u+ 2 = 12.5 ns, 21g 3 = 18.3 ns, 41g+ 4 = 12.2 ns,
Rabi frequencies 1=56MHz, 2=104MHz, 3=228MHz
Doppler width 1.15 GHz;
Collisional dephasing rates ij/2 = MHz;
Transit relaxation rate wt/2 = 0.38 MHz.

25. Experimental Results – excitation scheme B
Quadruple resonance single channel fluorescence spectra from level |4>. Autler-Townes effect as a function of the coupling (L4) laser power.
|3 L3 L2
|4>
|2> L4
|5 L1
|1

26. Simulations
excitation scheme B
Simulation of the experimental fluorescence spectra from level |4> with 4 as adjustable parameter
Transition
Laser, cm-1
FCF
Beam radius,m
|1>  |2>
L1,
0.0079
300
|2>  |3>
L2,
0.0502
405
|3>  |4>
L3,
0.1676
278
|4>  |5>
L4,
0.2324
505
Parameters for the simulation:
Lifetime A 1u+ 2 = 12.5 ns, 21g 3 = 18.3 ns;
Rabi frequencies 1=58MHz, 2=91MHz, 3=185MHz
Doppler width 1.15 GHz;
Collisional dephasing rates ij/2 = MHz;
Transit relaxation rate wt/2 = 0.38 MHz.

27. Transition Dipole Moment Measurement
excitation scheme B
Autler-Townes (AT) splitting versus the coupling (L4) laser power.
Note: Each rovibrational level has set of magnetic sublevels (MJ), and for each of this level the Rabi frequency is given by:
is a orientation factor. For R-branch - transition
and linearly polarized laser field it has the form:

28. Extension to short range and large range?

29. Conclusions: ongoing and future work
We have demonstrated that coherence effects such as the AT splitting can be used as a precision probe of electronic transition dipole moment function and its R dependence in multiple resonance experiments.
The R-centroid approximation is limited to the first moment of the
R variable. Higher order moments of R can be used to fit the experimental data to a more desirable functional form.
In regions of R where laser wavelengths are not available intensity based transition moment data can be normalized through an overlap region to the same absolute scale as the Autler-Townes splitting based data.
The AT splitting techniques can also be used to control singlet triplet mixing ratios. Preliminary experiments are in progress.

30. Diagram of the Excitation and Decay Processes
W54
W32
W21
W31
W34
W36
W35
W24
W26
W56
W51

31. Cascade Excitation Scheme
|1>
|2>
|3>
2 1Πg L2
A1u+
A1u+ L1
X 1g+
L1: A 1u+(8,13) X 1g+(0,14)
L2: 21Πg(4,14)  A1u+(8,13)