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Development of Optoelectronic Devices and Computational Tools for the Production and Manipulation of Heavy Rydberg Systems

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Development of Optoelectronic Devices and Computational Tools for the Production and Manipulation of Heavy Rydberg Systems Development of Optoelectronic Devices and Computational Tools for the Production and Manipulation of Heavy Rydberg Systems by Jeffrey Philippson A thesis submitted to the Department of Physics, Engineering Physics and Astronomy in conformity with the requirements for the degree of Master of Science Queen’s University Kingston, Ontario, Canada September, 2007 Copyright c Jeffrey Philippson, 2007 Abstract Experimental and theoretical progress has been made toward the production and ma- nipulation of novel atomic and molecular states. The design, construction and char- acterization of a driver for an acousto–optic modulator is presented, which achieves a maximum diffraction efficiency of 54 % at 200 MHz, using a commercial modulator. A novel design is presented for a highly sensitive optical spectrum analyzer for displaying laser mode structure in real time. Utilizing programmable microcontrollers to read data from a CMOS image sensor illuminated by the diffraction pattern from a Fabry– P´erot interferometer, this device can operate with beam powers as low as 3.3 µW, at a fraction of the cost of equivalent products. Computational results are presented analyzing the behaviour of a model quantum system in the vicinity of an avoided crossing. The results are compared with calculations based on the Landau–Zener formula, with discussion of its limitations. Further computational work is focused on simulating expected conditions in the implementation of a technique for coherent con- trol quantum states atomic and molecular beams. The work presented provides tools to further the aim of producing large, mono–energetic populations of heavy Rydberg systems. i Acknowledgements I would like to thank the people whose help and support has facilitated the completion of this thesis... First and foremost, I would like to convey my sincere gratitude for the help, advice, patience and understanding shown by my supervisor Ralph Shiell. His knowledge and enthusiasm are a source of constant inspiration to me. Matt Ugray and Tefo James Toai were collaborators on the optical spectrum an- alyzer project presented in chapter 4, they both made significant contributions and were both a pleasure to work with. Figure 4.2 was created by MU. In addition, I would like to thank Ken Sutherland for early work on optimising a Fabry–P´erot interference pattern and Jonathan Murrell for useful discussions concerning CMOS image sensors. I wish to thank Edward Wilson for his assistance with the use of various machine tools and Ralph Fredrick for useful discussions concerning the design of electronic devices. James Fraser is my Queen’s University co–supervisor; I wish to express my thanks for his support during my time at Queen’s. Finally I want to extend my gratitude to the entire physics department at Trent University for making me feel welcome, for stimulating discussions and for generally being a wonderful group of people. ii Dedicated to Mary and Peter, truly special people who are a source of constant inspiration. iii Contents Abstract i Acknowledgments ii List of tables vii List of figures viii List of Acronyms xi Chapter 1: Introduction 1 1.1 Research goals ............................... 2 1.2Structureofthethesis.......................... 3 Chapter 2: Literature Review 5 2.1Rydbergatoms.............................. 5 2.2HeavyRydbergsystems......................... 8 2.3Developmentofscientificinstruments.................. 10 Chapter 3: Construction and Characterization of a Driver for an Acousto– Optic Modulator 12 3.1 Acousto–optics .............................. 13 3.1.1 TheBraggregime......................... 14 3.1.2 TheRaman–Nathregime..................... 16 3.1.3 Acousto–optic modulators .................... 17 3.2AOMdriver................................ 18 3.2.1 Design............................... 19 3.2.2 RFissues............................. 21 3.2.3 Construction........................... 30 iv 3.2.4 Characterization......................... 31 Chapter 4: Real Time Laser Mode Structure Analysis 35 4.1Producinganinterferencepattern.................... 37 4.2Theimagesensor............................. 38 4.2.1 Configurationsettings...................... 39 4.2.2 Imagesensorcharacterization.................. 41 4.2.3 Theimagesensorcircuit..................... 42 4.3Thedisplay................................ 43 4.3.1 Timing............................... 44 4.4Themicrocontrollers........................... 46 4.4.1 Memory.............................. 47 4.4.2 Clocking.............................. 49 4.4.3 Inputs/outputs .......................... 51 4.4.4 Theprogram........................... 52 4.4.5 Themicrocontrollercircuit.................... 57 4.5Systemcharacterization......................... 57 4.6Futuredevelopments........................... 61 Chapter 5: Power Supplies 63 5.1 Current supply .............................. 63 5.1.1 Initialdesign........................... 63 5.1.2 A low power current supply ................... 66 5.2 Voltage supply .............................. 68 Chapter 6: The Adiabatic Theorem of Quantum Mechanics: Beyond the Landau–Zener Approximation 69 6.1Themodelsystem............................. 70 6.1.1 Diabaticstates.......................... 71 6.1.2 Adiabaticstates.......................... 72 6.2Theadiabatictheorem.......................... 75 6.2.1 TheLandau–ZenerApproximation............... 76 6.2.2 BeyondtheLandau–Zenerapproximation............ 79 Chapter 7: Adiabatic Population Transfer 82 7.1The3–levelsystem:Λconfiguration................... 83 7.1.1 FeaturesoftheΛsystem..................... 83 v 7.1.2 CoherentPopulationTrapping.................. 85 7.1.3 Adiabaticpopulationtransfer.................. 88 7.1.4 DeparturefromRamandetuning................ 91 7.2The4–levelsystem–doubleΛconfiguration.............. 92 7.2.1 FeaturesofthedoubleΛsystem................. 92 7.2.2 Decouplingthe4thlevel..................... 95 Chapter 8: Conclusions and Future Work 97 Bibliography 105 A Assembly Code for PIC Microcontrollers 106 A.1 SensorPIC code.............................. 106 A.2 DisplayPIC code............................. 112 B Deriving the Hamiltonian for the Time-Dependent Adiabatic State 119 C Adiabatic Theorem MATLAB Code 121 C.1Analyzingtheeffectofdifferingfieldprofiles.............. 121 C.2 Comparing numerical results with calculations using the Landau–Zener formula.................................. 123 D MATLAB Simulation of Population Dynamics in a 4–Level System 125 vi List of Tables 3.1 Specifications of the IntraAction ATM–200–1A1 AOM ......... 18 3.2ListofMini-CircuitsRFcomponentsfortheAOMdriver....... 30 4.1 Micron MT9M001C12STM imagesensor,configurationregisters.... 39 4.2 Memory available and memory used in the PIC18F2320 and PIC18LF2320 microcontrollers.............................. 47 vii List of Figures 2.1 Potential energy curves for the Li2 molecule.............. 9 3.1Energylevelschemesforthetwostableisotopesoflithium...... 13 3.2Photon–phononscatteringdiagram................... 15 3.3AOMoperatingintheBraggregime.................. 17 3.4AOMoperatingintheRaman–Nathregime.............. 17 3.5 Block diagram illustrating the AOM driver............... 19 3.6AOMdrivercircuitdiagrams....................... 21 3.7 A model RF circuit:source,transmissionlineandload........ 26 3.8 Geometry of a twisted pair transmission line. ............... 26 3.9Twistedpairpowertransmissionanalysis................ 28 3.10 AOM driver PCB layouts......................... 32 3.11 Image of the completed AOM driver................... 33 3.12 Tuning current supply for the variable attenuator . .......... 34 3.13 Tuning the RF power supplied to the amplifier using the attenuator . 34 3.14 Dependence of diffraction efficiency on acoustic frequency for the AOM– driversystem............................... 34 3.15 Tuning the diffraction efficiency of the AOM–driversystem...... 34 4.1Theoriginoflasermodestructure.................... 35 4.2Lasermodestructureanalysis,schematicdiagram........... 36 4.3Schematicdiagramoftheimagesensorcircuit............. 42 viii 4.4 Layout of the PCB fortheimagesensor................. 44 4.5Temporalvariationindisplayintensity................. 45 4.6Timeaveragedintensityfordifferentrow–enddelays.......... 46 4.7 Pin configuration for the PIC18F2320 .................. 51 4.8 Flow chart illustrating program operation ............... 53 4.9Schematicdiagramofthecircuithousingthemicrocontrollers.... 58 4.10 Layout of the PCB forthemicrocontroller............... 59 4.11Displayingsinglemodelaseroperation................. 60 4.12Displayingmultimodelaseroperation.................. 60 4.13Imagesensorcalibrationcurve...................... 61 5.1 Emitter–follower current supply ..................... 64 5.2 An image of the high power, current source power supply ....... 66 5.3 Current supply final design . ..................... 67 5.4 An image of the voltage source power supply .............. 68 6.1Anavoidedcrossinginmolecularpotentialenergycurves....... 70 6.2Levelenergiesofthediabaticandadiabaticstates........... 73 6.3 Comparing the results of a numerical solution with the Landau–Zener solution.................................. 79 6.4 Adiabatic state populations and energies for different field ramp profiles 80 7.1Energylevelschemeofa3–levelsysteminaΛconfiguration..... 84 7.2Rabifloppingina3–levelΛsystem................... 86 7.3Coherentpopulationtrappingina3–levelΛsystem.......... 86 7.4 Coherent population trapping in a 3–level Λ system, examined in the dark/absorbingbasis........................... 87 7.5ChangeinRabifrequenciesduetoalinearelectricfieldramp....
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