Experimental Mapping of the Absolute Value of the Transition Dipole Moment Function μe(R) of the Na2 A1Σu+ - X1Σg+ Transition E. Ahmed1, B. Beser1, P. Qi1, S. Kotochigova1, A. M. Lyyra1 and J. Huennekens2, 1Physics Department, Temple University 2Physics Department, Lehigh University

Overview New approach for measuring the absolute transition dipole moment μ of molecular rovibronic transitions between the ground and the excited states by a 4- level extended Λ scheme. Using the R-centroid method, we determine the electronic transition dipole moment μe(R) as function of the internuclear distance R. To extend the range of accessible transitions beyond the ones available with the extended Λ scheme we have demonstrated a new 4-laser excitation scheme.

Extended  Excitation Scheme X 1g+ |1> |2> |3> L1 L2 L3 |4> A1u+ 2 1Πg 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) Autler-Townes split spectrum ______________________________ Annie Hanson, Peng Qi and Li Li

Experimental Setup and AT Splitting vs. Coupling Laser Power TiSa M Verdi V10 M M Lock-in Amplifier PMT Monochromator Verdi V10 L2 BS Sodium Heatpipe Oven DCM L1 M R6G M Sabre SBRC-DSW 25 Lasers (699-29 or 899-29) Mechanical modulator

Simulation – Density Matrix Formalism 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 = 4.77 MHz; Transit relaxation rate wt/2 = 0.38 MHz. E. Ahmed et. al., J. Chem. Phys. 124, 084308 (2006)

Electronic Transition Dipole Moment Calculating from the Experimentally Measured Dipole Moment Matrix Elements ith R-centroid R-centroid Approximation J. Tellinghuisen, The Franck-Condon Principle in Bound-Free Transitions, Advances in Chemical Physics Vol. 60, 1985

Electronic Transition Dipole Moment as function of R A1u+ (v',J') X1g+ (v'',J') ,Debye 25,20 38,21 5.65 28, 20 42, 21 2.02 28, 20 40, 21 3.40 28, 20 43, 21 3.33 28, 20 41, 21 4.45 33, 20 43, 21 3.20 33, 20 43, 19 3.26 33, 20 46, 19 2.96 33, 20 48, 21 3.38 33, 20 51, 21 2.10 34, 20 44, 21 2.66 AT based results using 34, 20 44, 19 2.82 Intensity based results (J. Huennekens) 34, 20 48, 21 1.97 35, 20 45, 19 1.82 10, 20 20, 21 2.58 10, 20 17, 21 2.01 10, 20 23, 21 4.00 8, 20 20, 21 3.10 14, 20 27, 19 3.18

In collaboration with Peng Qi Quadruple Resonance Spectroscopy In collaboration with Peng Qi Na2 energy levels

Experimental Results and Simulations – Stimulated Emission Quadruple resonance single channel fluorescence spectra from level |5>. Comparison between coherently driven and spontaneous decay only |3>|4> transition. |3 |5 Transition Laser wavenumbers, cm-1 Franck-Condon Factor we, m L2 L3 L4 |1>  |2> X1Σg+ (1,21) A1Σu+ (22,20) 16874.14 0.0079 300 |4> |1>  |2> A1Σu+ (22,20)21Πg (19,20) 15305.00 0.0502 280 |2> |3>  |4> 21Πg (19,20) A1Σu+ (23,20) 15204.10 0.1676 405 |4>  |5> A1Σu+ (23,20)41Σg+ (14,21) 12545.28 0.1898 660 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 = 4.77 MHz; Transit relaxation rate wt/2 = 0.38 MHz.

The total Hamiltonian H for the system: Density Matrix Formalism Density matrix equation of motion in the interaction picture: W32 W34 W54 W52 The total Hamiltonian H for the system: W41 W21 represents all relaxation terms: W32 W34 W45 W21 W41

Experimental Results – Autler-Townes Splitting |3 L3 L2 |4> |2> L4 |5 L1 |1

Simulations-Density Matrix Formalism Simulation of the experimental fluorescence spectra from level |4> with 4 as adjustable parameter 505 0.2324 12533.75 A1Σu+ (23,20) X1Σg+ (36,19) |4>  |5> 278 0.1676 15204.10 21Πg (19,20) A1Σu+ (23,20) |3>  |4> 405 0.0502 15305.00 A1Σu+ (22,20)21Πg (19,20) |1>  |2> 300 0.0079 16874.14 X1Σg+ (1,21)  A1Σu+ (22,20) we, m Franck-Condon Factor Laser wavenumbers, cm-1 Transition 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 = 4.77 MHz; Transit relaxation rate wt/2 = 0.38 MHz.

Conclusion Using the extended Λ scheme we have measured the absolute value of the transition dipole moment between A1Σu+ and X1Σg+ states of Na2 for a number of rovibrational transitions. Using the R-centroid method, we have investigated the internuclear distance R dependence of e(R). To extend the range of accessible transitions, we have demonstrated a new 4-laser excitation scheme . To predict and simulate the experimental spectra, a theoretical model based on the density matrix formalism was developed.

Acknowledgments Prof. L. Li, Tsinghua University Prof. R. W. Field, MIT Prof. S. Magnier, Rennes, France Prof. R. Le Roy, University of Waterloo (Level program) Annie Hansson Teodora Kirova Jianmei Bai Omer Salihoglu Bill Stevenson Ed Kaczanowicz

The total Hamiltonian H for the system: Density Matrix Formalism Density matrix equation of motion in the interaction picture: The total Hamiltonian H for the system: represents all relaxation terms:

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.

Diagrams 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.

Using razor blade technique one can measure Measuring the amplitude E of the electric field For a Gaussian beam we have: - beam waist, the radius at which the intensity drops 1/e2 from the maximum value of I0 Using razor blade technique one can measure where C is: d

-Transition dipole moment matrix element Transition Dipole Moment Measurements Using the Autler-Townes (AT) effect The AT splitting arises from the two dressed States |2> Laser field, E |1> -Transition dipole moment matrix element Laser field, E |1> |2> Probe Laser Laser field, E |1> |2> Probe Laser d