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

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

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)

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

Na2 A-X coupling field wavefunctions

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

Coupling field transition choice

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 (699-29 or 899-29) Mechanical modulator

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)

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

AT Splitting vs. Coupling Laser Power Plot

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

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

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 = 4.77 MHz; Transit relaxation rate wt/2 = 0.38 MHz. E. Ahmed et. all, J. Chem. Phys. 124, 084308 (2006)

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

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).

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

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.

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

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 (699-29 or 899-29) Mechanical modulator

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:

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.

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.

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> L1,16874.14 0.0079 300 |2>  |3> L2, 15305.00 0.0502 278 |3>  |4> L3, 15204.10 0.1676 405 |4>  |5> L4, 12545.28 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 = 4.77 MHz; Transit relaxation rate wt/2 = 0.38 MHz.

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

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> L1,16874.14 0.0079 300 |2>  |3> L2, 15305.00 0.0502 405 |3>  |4> L3, 15204.10 0.1676 278 |4>  |5> L4, 12533.75 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 = 4.77 MHz; Transit relaxation rate wt/2 = 0.38 MHz.

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:

Extension to short range and large range?

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.

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

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)