ABSTRACT CIRCULAR POLARIZATION SPECTROSCOPY: DISORIENTATION 133 2 CROSS-SECTION IN THE Cs 6p P3=2 LEVEL BY USING TWO-PHOTON TWO-COLOR NANO-SECOND PULSED LASER by Ramesh Marhatta We have experimentally investigated the disorientation cross-section of the cesium J = 3/2 excited-level atom by using two-photon two-color nano-second pulsed dye lasers in the presence of argon buffer gas. Alignment and orientation 2 in the 6p P3=2 level were produced with a circularly polarized light. The circular polarization degree was measured with the pump (¸ = 852.112 nm) and probe 2 laser (¸ = 603.409 nm) to obtain disorientation cross-section in the 6p P3=2 level cesium due to collision with the ground level argon atoms over the Zeeman population. The disorientation cross-section was extracted, using non-linear square fit, from the measured circular polarization spectra as a function of argon gas pressure. We obtained the value of disorientation cross-section as 151(42) A˚2 which matches with the theory. CIRCULAR POLARIZATION SPECTROSCOPY: 133 2 DISORIENTATION CROSS-SECTION IN THE Cs 6p P3=2 LEVEL BY USING TWO-PHOTON TWO-COLOR NANO-SECOND PULSED LASER A Thesis Submitted to the Faculty of Miami University in partial fulfillment of the requirements for the degree of Master of Science Department of Physics by Ramesh Marhatta Miami University Oxford, Ohio 2007 Advisor Bur¸cinS. Bayram Reader Douglas Marcum Reader Samir Bali Contents 1 Introduction 1 2 Properties of Cesium 3 3 Theory of Polarization Spectra 7 3.1 Excitation Scheme . 7 3.2 Selection Rules . 8 3.3 Alignment and Orientation . 9 3.4 Density Matrix Formulation . 11 3.5 Circular Polarization Spectra . 13 3.5.1 Linear and Circular Polarization of Light . 13 3.5.2 Intensity and Circular Polarization Degree . 16 3.6 Fine and Hyperfine Interactions . 18 3.6.1 Fine Structure . 18 3.6.2 Hyperfine Structure . 21 3.7 Hyperfine Depolarization Effects on Circular Polarization Spectra 22 4 Experimental Apparatus 25 4.1 Lasers . 25 4.1.1 Nd:YAG Laser . 25 4.1.2 Dye Laser . 25 4.2 Free Spectral Range . 29 4.3 Circular Polarization Set-up . 29 4.4 Cesium Cell . 31 5 Overview of Experimental Measurement 33 6 Signal Detection Scheme 36 7 Systematic Effects 38 7.1 Effect of Power of Laser . 39 7.2 Effect of Temperature . 40 ii 8 Rate Equation Analysis and Results 41 8.1 Rate Equation Analysis . 41 8.2 Polarization as a Function of Buffer Gas Pressure . 45 9 Conclusion and Future Directions 48 A Production and Detection of Linear and Circularly Polarized light Using Jone’s Matrices 51 B Calculation of Circular Polarization Degree 54 C LabVIEW Program 57 D Apparatus 60 iii List of Tables 2.1 Properties of naturally occurring 133Cs atoms. 5 3.1 Table for coupling constants used in the calculations. 22 5.1 Some important parameters involved in the experiment. 35 8.1 Our work on the circular depolarization with argon buffer gas in 2 2 the 6s S1=2 ! 10s S1=2 transition. 46 8.2 The alignment and orientation depolarization cross-section of the 133 2 Cs 6p P3=2 J = 3/2 atoms. 46 8.3 Some important parameters used in the experiment . 47 133 2 2 B.1 The alignment and orientation in the Cs 6p P1=2 and 6p P3=2 states. 56 B.2 Clebsch-Gordan coefficients used in the experiment . 56 iv List of Figures 2.1 Cesium D1 and D2 lines. 4 2.2 Vapor pressure and number density of cesium atoms. 6 3.1 Excitation of atoms. 7 3.2 Grotrian diagram showing the excitation and emission scheme. 8 3.3 Selection rule. 9 3.4 Aligned axially symmetric system. 10 3.5 Oriented axially symmetric system. 11 3.6 Collision and detection frame. 12 3.7 Transition of electrons from s to p level. 13 3.8 Combination of two linearly polarized waves to form a resultant linearly polarized wave. 14 3.9 Combination of two linearly polarized waves to form circularly po- larized wave. 15 3.10 Circular polarization of light. 15 3.11 Energy level diagram of Cs. 17 3.12 Hydrogen atom from the electron’s perspective. 19 3.13 Hyperfine splitting of the levels of 133Cs. 21 3.14 Overlap time of the pump and probe lasers. 23 4.1 Experimental apparatus. 26 4.2 Pumping scheme of experiment. 27 4.3 Littman-Metcalf cavity configuration. 28 4.4 Cesium cell. 31 4.5 View of the oven wrapped with heating tape and aluminum foil. 32 5.1 Micrometer tuning curve of laser 1. 33 5.2 Geometry of the experiment . 34 7.1 Effect of power of laser 1 on circular polarization degree. 39 7.2 Effect of power of laser 2 on circular polarization degree. 40 7.3 Effect of temperature of cell on the circular polarization degree. 40 8.1 Population mixing among the Zeeman coherence . 42 v 8.2 Weighted non-linear least square fit of the circular polarization spectrum of Cs. 46 B.1 Transition of electrons by right circularly polarized light. 54 C.1 Interface of the LCVR. 57 C.2 Medowlark LCR subVI. 58 C.3 takedata3 sub.vi. 58 ¯ C.4 Stepper motor subVI. 59 C.5 Get Spectrum program to take wave form of fluorescence signal. 59 D.1 Experimental apparatus. 60 D.2 Flowing dye laser 1 oscillator in the Littman-Metcalf design. 61 D.3 Dye flowing machine for laser 1. 61 D.4 Static dye laser 2 oscillator in Littman-Metcalf cavity. 62 D.5 Dye laser 2 amplifier. 62 D.6 A view of quarter wave plate, Glan-Thompson polarizer and the LCR . 63 D.7 Boxcar averager/integrator. 63 D.8 DAQ board connected between a computer and the boxcar aver- ager/integrator. 64 vi ACKNOWLEDGMENTS It is the greatest moment to express my sincere thanks to my research advisor Dr. Bur¸cinS. Bayram for her continuous support, encouragement and guidance throughout my research. Her readiness and availability at all times to answer my questions are worthy to praise. She created a favorable environment for me to learn very basic knowledge in research. This paved the path to my brighter future. Also, I would like to appreciate the work of graduate student Seda Kin and undergraduate assistants Jacob Hinkle and Morgan Welsh who contributed a lot in this research. It is my pleasure to thank the machinist Michael Eldridge for his support in this research. I would like to appreciate my thesis committee members Dr. Samir Bali and Dr. S. Douglas Marcum for reading the manuscript and giving me valuable suggestions. I would also like to acknowledge the Department of Physics at Miami University, faculties, and staffs for offering me a great opportunity and support to undertake this project. I cannot simply say thanks to my wife Ranju and daughter Rajshree for their inspiration throughout my study at Miami University. Finally, I wish lifetime happiness to the Bayram’s family. vii Chapter 1 Introduction Lasers have wide applications in various fields of science and technology. With the invention of solid-state laser, gas laser, and dye laser, new areas of research are open to scientists. Scientists have been taking advantages using lasers in research because lasers are coherent, monochromatic and travel a long distance without much loss of energy and without divergence. Scientists are interested in the study of photon-matter interaction to under- stand the properties and behavior of the atoms and molecules. Laser light sources have been used in the study of interaction of photon with matter, photoionization or photodissociation, stimulated Raman spectroscopy, polarization spectroscopy, atoms trapping and cooling, electromagnetic induced transparency [1, 2] and so on. Nowadays lasers open up new possibilities for research. Since dye laser is tunable, it is used to study single photon, two-photon resonance (this research) and multi-photon excitation to study the lifetime of different atomic levels, decay rate and atomic ionization [3]. Two-photon excitation process has been mainly used to study the hyperfine structure [4] of atoms and quantum beat spectroscopy in the resolved hyperfine levels. In our research we use circularly polarized pulsed laser to study the collisional dynamics of the excited state of 133Cs atom colliding with ground level argon atoms. The main idea of this research is to measure the circular polarization de- 2 2 2 133 gree of 6s S1=2 ! 6p P3=2 ! 10s S1=2 transition in Cs atom and to extract the disalignment and disorientation cross-section. We investigated circular polariza- 133 2 2 2 tion spectrum of the Cs 6s S1=2 ! 6p P3=2 ! 10s S1=2 transition and measured polarization degree through two-photon double resonance with argon buffer gas at different pressures ranging from 5 to 100 Torr. We can gain valuable information on relaxation rates of electronic moments and the state-multipole-dependent depolarization cross-section by studying the depolarization in excited level alkali atoms under the influence of collision with noble gases. The study of collision between alkali atoms and noble gas is important for numerous applications, particularly for remotely sensing the composition of planetary atmospheres, the interstellar medium, and fusion plasmas [5]. 1 The study of collisional dynamics is not new, but recent advances in tech- nique for cooling and trapping of atoms has enormously increased the interests in this area. For example, high-resolution molecular spectroscopy of colliding cold atoms has become a leading experimental technique to investigate the collisional dynamics and to accurately determine the potential curves of molecules.