DOCSLIB.ORG

Generalized Quantum Defect Methods in Quantum Chemistry Serhan

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Generalized Quantum Defect Methods in Quantum Chemistry Serhan Generalized Quantum Defect Methods in Quantum Chemistry by Serhan Altunata Submitted to the Department of Chemistry in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physical Chemistry at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2006 c Massachusetts Institute of Technology 2006. All rights reserved. Author............................................. ................. Department of Chemistry May 23, 2006 Certified by......................................... ................. Robert W. Field Haslam and Dewey Professor of Chemistry Thesis Supervisor Accepted by......................................... ................ Robert W. Field Chairman, Department Committee on Graduate Students This doctoral thesis has been examined by a Committee of the Department of Chemistry that included Professor Sylvia T. Ceyer (Chairman) Professor Jianshu Cao Professor Robert W. Field (Thesis Supervisor) 2 Generalized Quantum Defect Methods in Quantum Chemistry by Serhan Altunata Submitted to the Department of Chemistry on May 23, 2006, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physical Chemistry Abstract The reaction matrix of multichannel quantum defect theory, K, gives a complete pic- ture of the electronic structure and the electron nuclear dynamics for a molecule. The reaction matrix can be used to examine both↔ bound states and free electron scat- tering properties of molecular systems, which are characterized by a Rydberg/scattering electron incident on an ionic-core. An ab initio computation of the reaction matrix for fixed molecular geometries is a substantive but important theoretical effort. In this thesis, a generalized quantum defect method is presented for determining the reaction matrix in a form which minimizes its energy dependence. This reaction matrix method is applied to the Rydberg electronic structure of Calcium monofluo- ride. The spectroscopic quantum defects for the 2Σ+ ,2Π, 2∆, and 2Φ states of CaF are computed using an effective one-electron calculation. Good agreement with the experimental values is obtained. The Σ-symmetry eigenquantum defects obtained from the CaF reaction matrix are found to have an energy dependence characteristic of a resonance. The analysis shows that the main features of the energy-dependent structure in the eigenphases are a consequence of a broad shape resonance in the 2Σ+ Rydberg series. This short-lived resonance is spread over the entire 2Σ+ Rydberg series and extends well into the ionization continuum. The effect of the shape reso- nance is manifested as a global ”scarring” of the Rydberg spectrum, which is distinct from the more familiar local level-perturbations. This effect has been unnoticed in previous analyses. The quantum chemical foundation of the quantum defect method is established by a many-electron generalization of the reaction matrix calculation. Test results that validate the many-electron theory are presented for the quantum defects of the 1 + 1sσgnpσu Σu Rydberg series of the hydrogen molecule. It is possible that the reaction matrix calculations on CaF and H2 can pave the way for a novel type of quantum chemistry that aims to calculate the electronic structure over the entire bound-state region, as opposed to the current methods that focus on state by state calculations. 3 Thesis Supervisor: Robert W. Field Title: Haslam and Dewey Professor of Chemistry 4 Acknowledgments At the end of this long journey, it is my pleasure to extend my warm gratitude to the many wonderful people I have met over the years. One among these people takes a special precedence. My advisor, Prof. Robert W. Field, has given me the complete freedom to pursue my curiosity since the first day I arrived at MIT. He provided constant guidance, encouraging, smiling, and somehow, always knowing where to go next. He never told me I was wrong, even when he knew I was dead wrong, but always chose to wait and allow me to discover the truth on my own. As I look back upon what I have achieved, I realize that he has been the greatest teacher and mentor in my life. Thank you, Bob, for making this an extraordinary experience. None of this would have been possible without you. I would like to thank my parents for their love, support and raising me the way I am. I devote this thesis to them in our native language Turkish: Sevgili Annem ve Babam, Iste sonunda bu tezide bitirdim! Goztepe’nin kenar mahallesinde futbol oynayan kopuk cocugun buralara gelecegini bir tek siz gordunuz. Gozunuzu kirpmadan, varinizla, yokunuzla beni desteklediniz. Sizin sevginiz olmadan bunlarin hicbiri mumkun olmazdi. Tessekur kelimesi size az kalir. Hazirlanin, daha nice basarilara birlikte yuruyecegiz. Bu arada en buyuk cim bom! I would like to warmly thank Prof. Jianshu Cao for his valuable collaboration and guidance. I have truly enjoyed working with him on my semiclassical Rydberg wavepacket project, which bore my first, and probably the most memorable, paper in Physical Review A. Prof. Sylvia T. Ceyer is also greatly acknowledged for the valuable comments she has provided as my thesis committee chair. I would like to thank the members of the Robert W. Field group for helping me merge my theoretical studies with experimental work. I have learnt much from them and benefited greatly from fruitful discussions on spectroscopy. Specifically, I feel privileged to have worked with Vladimir Petrovic and Bryan Wong on various challenging and interesting theoretical projects. I would also like to thank Ryan Thom, who has patiently answered my endless questions on a wide range of topics 5 in spectroscopy. My special thanks goes to our past member Jason O. Clevenger for welcoming me to the Rydberg project when I first joined the Robert W. Field group. I would like to express my gratitude to the members of the MIT theoretical group. It has been a great pleasure to share a work space with them. They have made many precious contributions to my scientific knowledge through discussions and our com- petitive problem solving sessions. I would like to thank Steve Presse, Jim Witkoskie, Xiang Xia, Shilong Yeng, Jianlan Wu, Chiao-Lun Cheng, and Ophir Flomenbo for making the zoo an enjoyable and welcoming environment. I would like to thank my sister, Selen, for being the wise guide in my life. She has shown me the right choices and helped me to navigate many of the challenges of graduate school. She is a great buddy to have. I would like to thank Cindy for her continuous support and caring. She has been my source of inspiration during both the pleasant times and the hardships that I have experienced during my stay at MIT. I would like to thank her for being part of my life. 6 Contents 1 Introduction 37 1.1 HistoricalAccountofMQDT . 38 1.2 CurrentProgress ............................. 48 1.2.1 Connection between the Effective Hamiltonian and MQDT .. 51 2 Formalism of Multichannel Quantum Defect Theory 67 2.1 Introduction................................ 67 2.2 CoulombScattering............................ 68 2.2.1 AsymptoticLimit......................... 72 2.2.2 Behavior of the Coulomb functions at r =0 .......... 75 2.2.3 ContinuumNormalization . 75 2.2.4 SolutionsatNegativeEnergy . 77 2.2.5 BoundStatesoftheCoulombpotential . 77 2.2.6 Phase-Amplitude Form of the Coulomb Functions . 78 2.2.7 PlotsoftheCoulombFunctions . 79 2.2.8 CoulombScatteringMatrix . 85 2.2.9 Bound States as Poles of the Coulomb Scattering Matrix ... 87 2.3 SingleChannelTheory .......................... 90 2.3.1 BoundStates ........................... 93 2.3.2 CollisionEigenstates . 94 2.3.3 ScatteringWave.......................... 94 2.3.4 Applications of the Single Channel Theory: Alkali Atoms... 95 2.4 MultichannelTheory ........................... 99 7 2.4.1 The Case where All Channels are Closed: Bound States . 101 2.4.2 The Case for All Channels Open: Continuum . 108 2.4.3 The Case of a Mixture of Closed and Open Channels: Autoion- izingResonances ......................... 110 2.4.4 TheFrameTransformation. 111 2.5 ResonanceScatteringTheory . 118 2.5.1 ShapeResonances. 122 2.5.2 FeshbachResonances . 122 2.6 Conclusions ................................ 132 3 Calculation of the Short-Range Reaction Matrix from First Princi- ples 135 3.1 Introduction................................ 135 3.2 Theory................................... 139 3.2.1 SolutionsoftheZero-OrderEquations . 141 3.2.2 CoupledEquations . 143 3.2.3 Iterative Procedure to Calculate the K-Matrix. 144 3.2.4 The Energy Dependence of the Reaction Matrix . 148 3.2.5 The Transformation between K(ǫ) and K¯ ........... 152 3.3 Conclusions ................................ 154 3.4 MathematicalAppendixA . 160 3.5 MathematicalAppendixB . 161 3.6 MathematicalAppendixC . 162 4 Electronic Spectrum of CaF 165 4.1 Introduction................................ 165 4.2 ApplicationandResults . 167 4.2.1 Analytical Continuation of the Integer K Matrix to Negative Energy............................... 183 4.3 PhotoionizationofCaF. 187 4.4 Conclusions ................................ 197 8 4.5 MathematicalAppendix . 200 5 Broad Shape Resonance Effects in CaF Rydberg States 203 5.1 Introduction................................ 203 5.2 ResultsandDiscussion . .. .. 207 5.3 Violation of Mulliken’s Rule Caused by the Shape Resonance..... 216 5.4 Conclusions ................................ 222 6 Many Electron Generalization of the ab initio Reaction Matrix Cal- culation 225 6.1 Introduction................................ 225 6.2 The Variational K-MatrixTheory. 227 6.2.1 The N-electronIon-CoreHamiltonian.
Load more

Recommended publications
  • Lectures 8-9: Multi-Electron Atoms Energy Levels in Alkali Metals
    Lectures 8-9: Multi-electron atoms Energy levels in alkali metals o Alkali atoms: in ground state, contain a set of Z - 1 completely filled subshells with a single valence electron in the next s subshell. o Alkali atom spectra o Electrons in p subshells are not excited in any low-energy processes. s electron is the single optically active electron and core of filled subshells can be ignored. o Central field approximation o Shell model o Effective potentials and screening o Experimental evidence for shell model PY3004 PY3004 Energy levels in alkali metals Hartree theory o In alkali atoms, the l degeneracy is lifted: states with the same principal quantum number n o For multi-electron atom, must consider Coulomb interactions between its Z electrons and its and different orbital quantum number l have different energies. nucleus of charge +Ze. Largest effects due to large nuclear charge. o Relative to H atom, alkali terms lie at lower energies due to increased Coulomb attraction of o Must also consider Coulomb interactions between each electron and all other electrons in nucleus. This shift increases the smaller l is. atom. Effect is weak. o For larger values of n, i.e., greater orbital radii, the terms are only slightly different from o Assume electrons are moving independently in a spherically symmetric net potential. hydrogen. o The net potential is the sum of the spherically symmetric attractive Coulomb potential due to o Also, electrons with small l are more strongly bound and their terms lie at lower energies. the nucleus and a spherically symmetric repulsive Coulomb potential which represents the average effect of the electrons and its Z - 1 colleagues.
    [Show full text]
  • Who Named the Quantum Defect? \ A
    - -? 90 gy Who Named the Quantum Defect? \ A. R. P. Rau Department of Physics and Astronomy, Louisiana State University Baton Rouge, LA 70803 and Mitio Inokuti Physics Division, Argonne National Laboratory, Argonne, EL 60439-4843 Abstract The notion of the quantum defect is important in atomic and molecular spectroscopy and also in unifying spectroscopy with collision theory. In the latter context, the quantum defect may be viewed as an ancestor of the phase shift. However, the origin of the term "quantum defect" does not seem to be explained in standard textbooks. It occurred in a 1921 paper by Schrodinger, preceding quantum mechanics, yet giving the correct meaning as an index of the short-range interactions with the core of an atom. We present the early history of the quantum-defect idea, and sketch its recent developments. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi- bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer- ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
    [Show full text]
  • Topics in Atomic Physics
    TOPICS IN ATOMIC PHYSICS C. E. Burkhardt Department of Physics St. Louis Community College St. Louis, MO 63135 & J. J. Leventhal Department of Physics University of Missouri - St. Louis St. Louis, MO 63121 CHAPTER 1 - BACKGROUND ..................................................................................................... 1 1.1 Introduction ........................................................................................................................... 1 1.2 The Bohr model of the atom..................................................................................................2 1.3 Numerical values and the fine structure constant .................................................................. 9 1.4 Atomic dimensions – is a0 a reasonable atomic diameter? .................................................. 11 1.5 Localizing the electron: Is a point particle reasonable? ....................................................... 13 1.6 The classical radius of the electron...................................................................................... 14 1.7 Atomic units. ....................................................................................................................... 15 CHAPTER 2 - ANGULAR MOMENTUM................................................................................... 18 2.1 Introduction ......................................................................................................................... 18 2.2 Commutators .....................................................................................................................
    [Show full text]
  • Chapter 1: Quantum Defect Theory
    Chapter 1: Quantum Defect Theory I. THE HYDROGEN ATOM Rydberg atoms are excited states of atoms with a large principle quantum number, where the Rydberg electron is only weakly bound to the ionic core. This weak binding makes Rydberg atoms very sensitive to external perturbations and results in a wide range of unique features. To understand the basic properties of Rydberg atoms, it is instructive to first look at the solution of the hydrogen atom. In atomic units, the Hamiltonian is given by p2 1 H = − ; (1) 2µ r where position and momentum operators are canonically conjugated and µ = 1 − 1=mp is the reduced math according to the proton mass mp ≈ 1836. To solve the hydrogen problem, we first introduce the angular momentum operators Li = "ijkxjpk (2) 2 2 2 2 and its square L = Lx + Ly + Lz. Then, we can write the Hamiltonian as p2 L2 1 H = r + − : (3) 2µ 2µr2 r The angular momentum part can be solved independently from the radial part, using the angular momentum algebra. The eigenvalues of L2 are given by l(l + 1), with l being a non- negative integer. Each eigenvalue of L2 is 2l + 1-fold degenerate. This degenerate manifold can be expressed in terms of eigenvectors of Lz, having integer eigenvalues m with jmj ≤ l. The radial part can be solved by expressing the radial momentum term in its coordinate representation, resulting in 1 @2 l(l + 1) 1 H = − r + − : (4) 2µr @r2 2µr r The resulting Schr¨odingerequation can then be solved using standard techniques [1].
    [Show full text]
  • Arxiv:1907.02776V1 [Physics.Atom-Ph] 5 Jul 2019 Bosons, K Is a Metastable Fermion
    Precision measurement of the ionization energy and quantum defects of 39K I Michael Peper,∗ Felix Helmrich, Jonas Butscher, Josef Anton Agner, Hansj¨urgSchmutz, Fr´ed´ericMerkt,y and Johannes Deiglmayrz Laboratory of Physical Chemistry, ETH Z¨urich, 8093 Z¨urich,Switzerland (Dated: July 8, 2019) We present absolute-frequency measurements in ultracold 39K samples of the transitions from the 4s1=2 ground state to np1=2 and np3=2 Rydberg states. A global nonlinear regression of the −1 np1=2 and np3=2 term values yields an improved wave number of 35 009:813 971 0(22)sys(3)stat cm 39 for the first ionization threshold of K and the quantum defects of the np1=2 and np3=2 series. In 0 0 addition, we report the frequencies of selected one-photon transitions n s1=2 np3=2, n dj np3=2, 0 0 n fj0 ndj and n gj0 nfj and two-photon transitions nfj0 npj determined by millimeter-wave spectroscopy, where j is the total angular momentum quantum number. By combining the results from the laser and millimeter-wave spectroscopic experiments, we obtain improved values for the quantum defects of the s1=2, d3=2, d5=2, fj and gj states. For the dj series, the inverted fine structure was confirmed for n ≥ 32. The fine-structure splitting of the f series is less than 100 kHz at n = 31, significantly smaller than the hydrogenic splitting, and the fine structure of the g series is regular for n ≥ 30, with a fine-structure splitting compatible with the hydrogenic prediction.
    [Show full text]
  • Spectroscopy of High Energy Rydberg States of Magnesium
    Eth Zurich,¨ Trapped Ion Quantum Information Group Semester Project Spectroscopy of high energy Rydberg states of Magnesium Theo Dressler Prof. Jonathan Home Dr. Matt Grau Christoph Fischer April 15, 2019 Abstract The Rydberg energy states of magnesium atoms for different an- gular momentum quantum states are measured. Transitions in a mag- nesium gas cloud are driven using lasers of wavelength 285 nm for a transition into the first excited state, and 375 nm to drive a transition into a Rydberg state. Unexpected states at energies in between the theoretically predicted energy states of different angular momentum are discovered in combination with the expected transitions. Addition- ally in contradiction to the possible transitions, following the dipole selection rules, angular momentum states are reached which should not be possible: from a p-state to another p-state. This experiment determines the energies of the realized states of Magnesium atoms. 1 Contents 1 Introduction 3 2 Quantum Defect and Excitation Theory 4 3 Experimental Set-up 6 4 Measurement Method 9 5 Spectroscopy Results 12 5.1 Possible Transition . 17 5.2 Transition Characteristics . 19 5.3 Diversity of Spectral Lines . 20 1 5.4 n P1 Correspondence . 21 5.5 High Rydberg states close to ionization . 23 6 Discussion and Determination of Quantum defect parame- ters 24 2 1 Introduction Magnesium ions can be used to perform quantum state manipulations in a controlled way. The rough procedure is described in the following. With trapped ions quantum states can be generated and quantum information processed. This requires ionization and trapping with lasers. Different prop- erties of ground or excited states can be used to generate certain quantum states.
    [Show full text]
  • Hydrogen Atom. We find a Heirarchy of Symmetries and Symmetry Groups
    14 Hydrogenic Atoms Contents 14.1 Introduction 251 14.2 Two Important Principals of Physics 252 14.3 The Wave Equations 253 14.4 Quantization Conditions 254 14.5 Geometric Symmetry SO(3) 257 14.6 Dynamical Symmetry SO(4) 261 14.7 Relation With Dynamics in Four Dimensions 264 14.8 DeSitter Symmetry SO(4, 1) 266 14.9 Conformal Symmetry SO(4, 2) 270 14.9.1 Schwinger Representation 270 14.9.2 Dynamical Mappings 271 14.9.3 Lie Algebra of Physical Operators 274 14.10 Spin Angular Momentum 275 14.11 Spectrum Generating Group 277 14.11.1 Bound States 278 14.11.2 Scattering States 279 14.11.3 Quantum Defect 280 14.12 Conclusion 281 14.13 Problems 282 Many physical systems exhibit symmetry. When a symmetry exists it is possible to use Group theory to simplify both the treatment and the un- derstanding of the problem. Central two-body forces, such as the gravita- tional and Coulomb interactions, give rise to systems exhibiting spherical symmetry (two particles) or broken spherical symmetry (planetary sys- tems). In this Chapter we see how spherical symmetry has been used to probe the details of the hydrogen atom. We find a heirarchy of symmetries and symmetry groups. At the most obvious level is the geometric symme- try group, SO(3), which describes invariance under rotations. At a less obvious level is the dynamical symmetry group, SO(4), which accounts for the degeneracy of the levels in the hydrogen atom with the same principal quantum number. At an even higher level are the spectrum generating groups, SO(4, 1) and SO(4, 2), which do not maintain energy degeneracy 250 14.1 Introduction 251 at all, but rather map any bound (scattering) state of the hydrogen atom into linear combinations of all bound (scattering) states.
    [Show full text]
  • Laser and Microwave Spectroscopy of Even-Parity Rydberg States of Neutral Ytterbium and Multichannel Quantum Defect Theory Analysis
    Laser and microwave spectroscopy of even-parity Rydberg states of neutral ytterbium and Multichannel Quantum Defect Theory analysis H. Lehec, A. Zuliani, W. Maineult, E. Luc-Koenig, P. Pillet and P. Cheinet∗ Laboratoire Aim´eCotton, CNRS, Univ. Paris-Sud, ENS Cachan, Universit´eParis-Saclay, B^at. 505, 91405 Orsay, France F. Niyaz and T. F. Gallaghery Department of Physics, University of Virginia, Charlottesville, Virginia 22904 (Dated: May 28, 2018) 1 3;1 Abstract. New measurements of high-lying even parity 6sns S0 and 6snd D2 levels of neutral 174Yb are presented in this paper. Spectroscopy is performed by a two-step laser excitation from the 14 2 1 ground state 4f 6s S0, and the Rydberg levels are detected by using the field ionization method. Additional two-photon microwave spectroscopy is used to improve the relative energy accuracy where possible. The spectroscopic measurements are complemented by a multichannel quantum defect theory (MQDT) analysis for the J=0 and the two-coupled J=2 even parity series. We compare our results with the previous analysis of Aymar et al [1] and analyze the observed differences. From −1 the new MQDT models, a revised value for the first ionization limit I6s = 50443:07041(25) cm is proposed. I. INTRODUCTION be similar to the imaging in [16, 17] but without the need to ionize the Rydberg cloud. On one-electron Ry- The Rydberg levels of Yb are a focus of attention for dberg atoms, other imaging [18, 19] or trapping [20{22] two reasons. First, two (valence) electron atoms are at- techniques have been implemented, relying on complex tractive for optical clocks based on the neutral atoms schemes or compromises.
    [Show full text]
  • Quantum Defect Measurements for High Angular Momentum Rydberg States of Potassium
    Colby College Digital Commons @ Colby Honors Theses Student Research 2020 Quantum Defect Measurements for High Angular Momentum Rydberg States of Potassium Abraham Hill Colby College Follow this and additional works at: https://digitalcommons.colby.edu/honorstheses Part of the Atomic, Molecular and Optical Physics Commons Colby College theses are protected by copyright. They may be viewed or downloaded from this site for the purposes of research and scholarship. Reproduction or distribution for commercial purposes is prohibited without written permission of the author. Recommended Citation Hill, Abraham, "Quantum Defect Measurements for High Angular Momentum Rydberg States of Potassium" (2020). Honors Theses. Paper 989. https://digitalcommons.colby.edu/honorstheses/989 This Honors Thesis (Open Access) is brought to you for free and open access by the Student Research at Digital Commons @ Colby. It has been accepted for inclusion in Honors Theses by an authorized administrator of Digital Commons @ Colby. Quantum Defect Measurements for High Angular Momentum Rydberg States of Potassium Abraham Hill A thesis presented to the faculty of the Department of Physics and Astronomy at Colby College Department of Physics and Astronomy Colby College Waterville, ME May, 2020 Abstract We report measurements of the quantum defect for the f-, g-, and h-states of potassium with principal quantum number n between 26 and 29. Ground state potassium atoms in a magneto-optical trap are excited from the 4s state to the 5p state, then from the 5p state to the ndj state using lasers at 405nm and 980nm, respectively. We then measure the millimeter wave frequencies of the ndj to nl transitions.
    [Show full text]
  • Arxiv:1902.10803V1 [Physics.Atom-Ph] 27 Feb 2019 Tions Between Rydberg Atoms and Neutral Systems
    1934 Edoardo Amaldi and Emilio Segr´e1 observed that Rydberg atoms could be excited even when immersed in a dense gas of other atoms (\perturbers"), although at an energy shifted from that of an isolated Rydberg Trilobites, butterflies, and other atom [3]. Curiously, depending on the species of per- turber, these line shifts could be either blue or red exotic specimens of long-range detuned from the atomic line. This behavior quali- Rydberg molecules tatively contradicted the classical model, which treats the surrounding gas of polarizable atoms as a dielectric material and predicts only a red shift. Fermi resolved Matthew T Eiles1;2 this mystery by developing a quantum scattering the- 1Department of Physics and Astronomy, Purdue University, ory which introduced foundational concepts like the West Lafayette, Indiana, 47907, USA. scattering length and zero-range pseudopotential [4]. 2 Max-Planck-Institut f¨urPhysik komplexer Systeme, His model recognized that a ground state atom's po- N¨othnitzerStr. 38, 01187 Dresden, Germany larization potential extends over only a fraction of the E-mail: [email protected] Rydberg electron's enormous de Broglie wavelength, and thus it only adds a scattering phase shift to the Abstract. This Ph.D. tutorial discusses ultra-long-range Rydberg wave function2. The resulting energy shift is Rydberg molecules, the exotic bound states of a Rydberg atom and one or more ground state atoms immersed in the Rydberg equivalent to that provided by a delta function poten- electron's wave function. This novel chemical bond is distinct tial located at the perturber and proportional to the from an ionic or covalent bond, and is accomplished by a very electron-atom scattering length.
    [Show full text]
  • Quantum Nonequilibrium Physics with Rydberg Atoms
    Quantum Nonequilibrium Physics with Rydberg Atoms Thesis by Tony E. Lee In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2012 (Defended May 2, 2012) c 2012 Tony E. Lee All Rights Reserved ii Acknowledgements I would like to thank my advisor, Michael Cross, for his mentorship. I learned from him how to ask basic questions when doing research, as well as how to articulate the results in a paper or talk. I appreciate that I could always drop by to ask questions about any kind of physics. I also appreciate the freedom I had to work on some admittedly random problems. Next, I would like to thank Gil Refael for teaching me a lot of new physics and broadening my horizons. In addition, I want to thank Hartmut H¨affner,to whom I owe my knowledge of quantum optics. Thanks also to Harvey Newman for his support during college. I would also like to acknowledge the people that I have had the pleasure of dis- cussing physics with: Oleg Kogan, Milo Lin, Heywood Tam, Olexei Motrunich, De- banjan Chowdhury, Hsin-Hua Lai, Kun Woo Kim, Liyan Qiao, Shankar Iyer, Chang- Yu Hou, Ron Lifshitz, Alexey Gorshkov, Jens Honer, Mark Rudner, Rob Clark, Nikos Daniilidis, and Sankar Narayanan. Thanks to Loly Ekmekjian for her help. Thanks also to Kevin Park, whom I hold responsible for introducing me to Caltech. I am grateful to my parents and brother for encouraging and supporting my ed- ucation. Finally, I want to thank Patty for her support over the past few years.
    [Show full text]
  • Rydberg Atoms
    Rydberg atoms Tobias Thiele References • T. Gallagher: Rydberg atoms Content • Part 1: Rydberg atoms • Part 2: A typical beam experiment Introduction – What is „Rydberg“? • Rydberg atoms are (any) atoms in state with high principal quantum number n. Introduction – What is „Rydberg“? • Rydberg atoms are (any) atoms in state with high principal quantum number n. • Rydberg atoms are (any) atoms with exaggerated properties Introduction – What is „Rydberg“? • Rydberg atoms are (any) atoms in state with high principal quantum number n. • Rydberg atoms are (any) atoms with exaggerated properties equivalent! Introduction – How was it found? • In 1885: Balmer series: – Visible absorption wavelengths of H: bn2 n2 4 – Other series discovered by Lyman, Brackett, Paschen, ... – Summarized by Johannes Rydberg: Introduction – How was it found? • In 1885: Balmer series: – Visible absorption wavelengths of H: bn2 n2 4 – Other series discovered by Lyman, Brackett, Paschen, ... – Summarized by Johannes Rydberg: Introduction – How was it found? • In 1885: Balmer series: – Visible absorption wavelengths of H: bn2 n2 4 – Other series discovered by Lyman, Brackett, Paschen, ... Ry – Summarized by Johannes Rydberg: ~ ~ n2 Introduction – Generalization • In 1885: Balmer series: – Visible absorption wavelengths of H: bn2 n2 4 – Other series discovered by Lyman, Brackett, Paschen, ... ~ ~ Ry – Quantum Defect was found for other atoms: 2 (n l ) Introduction – Rydberg formula? • Energy follows Rydberg formula: hRy E E 2 (n l ) Introduction – Rydberg
    [Show full text]