Peng Qi 1, O. Salihoglu 1, E. Ahmed 1, S. Kotochigova 1,J. Huennekens 2, A. Marjatta Lyyra 1 Peng Qi 1, O. Salihoglu 1, E. Ahmed 1, S. Kotochigova 1, J.

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Presentation transcript:

Peng Qi 1, O. Salihoglu 1, E. Ahmed 1, S. Kotochigova 1,J. Huennekens 2, A. Marjatta Lyyra 1 Peng Qi 1, O. Salihoglu 1, E. Ahmed 1, S. Kotochigova 1, J. Huennekens 2, A. Marjatta Lyyra 1 1.Physics Department, Temple University, Philadelphia, PA 2.Physics Department, Lehigh University, Bethlehem, PA Experimental Mapping of the Li 2 A 1 Σ u + ~ X 1 Σ g + Electronic Transition Dipole Moment μ e (R) by Autler-Townes Splitting

Introduction Li 2 vs. Na 2 We expect that ab initio calculations for Li 2 are more accurate than those for Na 2 We expect better agreement between experiment and theory for Li 2 than for Na 2 Both pseudopotential and relativistic ab initio calculations are available

cross section of laser beam profile Excitation scheme and Experimental Setup |1> |2> |3> L1L1 L2L2 L3L3 |4> X 1  g + (1,9) X 1  g + (19,11) A 1  u + (17,10) A 1  u + (20,10) |5> F 1 Σ g + (16,11) Excitation scheme M5 Lock-inAmplifier M4 f2 R6G TiS M3M1M2f1 M6 M7 f3 SPEX + PMT DCM Dichroic Mirror chopper

Density Matrix The 4-level system Hamiltonian in the interaction picture Detunings : Rabi frequency : The density matrix equation of motion Decay rate : |3>|2> |1> |4> L2 L1 L3

Simulation W 56 W 54 W 32 W 21 W 31 W 34 W 36 W 35 W 24 W 26 W 51

Simulation Transition dipole moment Matrix element was varied to give the best fit! Experimentallymeasured Experimentallymeasured

Measuring the amplitude E of the electric field For a Gaussian beam we have: Using razor blade technique one can measure where C is: d - beam waist, the radius at which the intensity drops 1/e 2 from the maximum value of I 0

Determine Transition Dipole Moment I |v,J> rovibronic wavefunctions LEVEL program was used to calculate the overlap and R moment between different vibrational wavefunctions. R-Centroid Approximation J. Tellinghuisen, The Franck-Condon Principles In Bound-Free Transitions, Advances in Chemical Physics Vol. 60, From experiments

Determine Transition Dipole Moment II i th R-centroid J. Tellinghuisen, The Franck-Condon Principles In Bound-Free Transitions, Advances in Chemical Physics Vol. 60, Coefficients μ i are obtained by a multidimensional fit (Origin ® ), i max =3 were used in the fit

Results

Conclusions We have mapped the transition dipole moment (TDM) between ground state and first excited state of Li 2. The experimental results showed excellent agreement with ab initio calculation as expected.

Prof. Li Li, Tsinghua University Prof. R. W. Field, M. I. T. Prof. S. Magnier, Rennes, France Prof. R. Le Roy, University of Waterloo (Level program) Bill Stevenson, Temple University Ed Kaczanowicz, Temple University Acknowledgements This work is supported by NSF.