DOCSLIB.ORG

Precision Measurements with Rydberg States of Rubidium

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Precision Measurements with Rydberg States of Rubidium Precision Measurements with Rydberg States of Rubidium by Andira Ramos A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) in The University of Michigan 2019 Doctoral Committee: Professor Georg Raithel, Chair Professor Timothy Chupp Professor Duncan Steel Associate Professor Kai Sun Dr. Nicolaas Johannes Van Druten, University of Amsterdam. Andira Ramos [email protected] ORCID iD: 0000-0002-0086-8446 c Andira Ramos 2019 To my wonderful parents. ii ACKNOWLEDGEMENTS Graduate school has not been easy and I am extremely grateful to all the people in my life who have been there to help me through this journey. First, I want to thank my advisor, Georg Raithel, whose endless enthusiasm for physics is contagious. Georg, I truly appreciate the time you spent to answer questions, run calculations and listen to ideas, I know you were always very busy and yet somehow made sure to find time for meetings. You were always patient, understanding and supportive, I am happy to have had you as my research advisor. Getting to work with current and past members of the Raithel group has also been amazing. Thanks to Jamie MacLennan, Ryan Cardman, Michael Viray, Lu Ma and Xiaoxuan Han. Jamie, your support knows no limits and it is a big reason why I have made it this far. Thank you for staying in the lab until the morning hours to keep me company while I ran experiments, thank you for editing applications, emails, and even this thesis (you are hired for life), thank you for the many surprise treats that so often cheered me up when the experiment was not cooperating. Most importantly, thank you for your friendship, it really means a lot. Ryan, thank you for being so willing to take over the experiment with such short notice before I left to Amsterdam, you did a wonderful job while I was gone. I really enjoyed running experiments with you and getting the chance to brainstorm together, you always impressed me with your clear grasp of physics theory and I know you have a bright future as a researcher. Michael, thank you for the work you do for the group and the graduate students in the department in general, you are great at creating and maintaining community. iii I also had a great time trying out all possible juices in Rio de Janeiro, hiking in California and singing along to your playlist on our way to MCAW in Illinois, you are a great travel partner, thank you for the great memories. Lu, I love your endless curiosity, you always ask interesting questions and force me to think in more detail about physics, I hope you never lose that. Xiaoxuan, even though you joined the group recently, it already feels like you have always been with us. Thank you for your warm smiles and conversations on our bus rides home, they were always good pick-me ups. Thanks to David Anderson, Luis Felipe Goncalves, Nithiwadee \Pound" Thaicharoen, Stephanie Miller, Yun-Jhih Chen and Kaitlin Moore for sharing their knowledge with me when I was starting out in the lab. Special thanks to Kaitlin, who took me under her wing when I first joined the group and did a beautiful job designing the vacuum chamber for the Rydberg constant measurement experiment. Thanks to Stephen DiIorio and Eric Peterson for helping me with the design and construction of the coils in the system. To my Amsterdam family, Julius de Hond, Carla Sanna, David Davtyan, Maarten Soudijn, Severin Charpignon, Nataly Cisternas San Martin, Klaasjan van Druten, Ben van Linden van den Heuvell and Robert Spreeuw, I am beyond grateful for your hospitality. I could not have asked for a better experience abroad. Julius, thank you for patiently showing me the Celsius experimental setup, for sharing many snack breaks with me and keeping me company when the roof of the physics building blew away. You are an amazing scientist and I know you will do great things. Carla, finding your happy notes in the mornings was always a great way to start the day. You always bring happiness into a room with you. Thank you for all of the delicious Italian sweets, for the workouts and for even opening the doors of your home when needed, you are amazing. David, working with you was a lot of fun, you were always straight to the point and full of humor. Klaasjan, thank you for your constant words of encouragement and your guidance with the research project. You were always iv very kind and made me feel welcomed from the very beginning. You all made the Netherlands feel like home, thank you. Besides my research advisors, I was also very lucky to find a mentor in Dr. Chris- tine Aidala. Thank you, Christine, for offering ice cream and listening to my worries during difficult times in my first year. You helped me feel like I belonged in the program and for that I will be forever grateful. To my wonderful husband, Daniel, thank you for the many leaps of faith you have taken with me, from moving away from your family to quitting your job and moving to another continent, having you there with me through this journey has made it so much brighter. Thank you for your constant support, love and kindness, you have no idea how much energy you give me to keep on moving forward. I love you. Thank you to my family who throughout these years has always been sending me love and warnings about winter storms. Spatially to my dear parents, Marisol and Rolando, who left two countries, family, friends and careers behind so that I could have better opportunities. I am deeply grateful for all the sacrifices you have made for me and I am always striving to make you proud. Thank you for your boundless love and support, you make me feel like I can do anything I set my mind to. I would like to acknowledge support from the National Science Foundation (NSF) Graduate Research Fellowship Program (GRFP) under Grant No. DGE 1256260 and the University of Michigan Rackham Merit Fellowship (RMF) and Rackham Pre- doctoral Fellowship for fully funding my graduate school years. Moreover, I would like to acknowledge the NSF Graduate Research Opportunity Worldwide (GROW) program for granting me the funds to collaborate with the group of Dr. van Druten, Dr. Spreeuw and Dr. van Linden vanden Heuvell at the University of Amsterdam in the Netherlands. This work was supported by NSF Grant No. PHY1506093, and NASA Grant No.NNH13ZTT002N NRA. Lastly, I want to thank my committee, Duncan Steel, Tim Chupp, Kai Sun and v Klaasjan van Druten for their helpful revisions of this document. vi TABLE OF CONTENTS DEDICATION :::::::::::::::::::::::::::::::::: ii ACKNOWLEDGEMENTS :::::::::::::::::::::::::: iii LIST OF FIGURES ::::::::::::::::::::::::::::::: x LIST OF TABLES :::::::::::::::::::::::::::::::: xviii ABSTRACT ::::::::::::::::::::::::::::::::::: xxi CHAPTER I. Introduction ..............................1 1.1 Rydberg Atoms . .2 1.2 Rydberg Constant . .5 1.2.1 The Proton Radius Puzzle . .6 1.2.2 Measuring R1 with Circular States . .8 1.3 Thesis Outline . 10 II. Theoretical Background ....................... 12 2.1 Mathematical Formalism for Circular States . 12 2.1.1 Parabolic Coordinates . 14 2.1.2 Relation between Spherical and Parabolic States . 15 2.2 Energy Corrections . 15 2.2.1 Quantum Defects . 16 2.2.2 Fine Structure Correction . 20 2.2.3 Quantum Electrodynamic Corrections . 23 2.2.4 Hyperfine Structure Correction . 24 2.2.5 Stark Shift . 27 2.2.6 Zeeman Shift . 28 2.2.7 Blackbody Effects . 31 2.2.8 Ponderomotive Optical Lattice . 35 vii 2.2.9 Doppler Effect with POL Spectroscopy . 40 III. Experimental Setup .......................... 46 3.1 Ultra-High Vacuum System . 46 3.2 Cooling of 85Rb.......................... 50 3.2.1 Cooling Lasers . 50 3.2.2 Magneto-Optical Trap . 53 3.2.3 Optical Molasses . 57 3.3 Three-photon Rydberg Excitation . 59 3.4 Circularization of Rydberg Atoms . 61 3.5 Detection Method . 62 3.6 Electric-field Zeroing . 64 3.6.1 Stark Maps and Calibration . 65 3.6.2 Electrodes . 67 3.7 Magnetic-field Zeroing . 71 3.7.1 Magnetic Field Zeroing with Microwave Spectroscopy 72 3.7.2 Magnetic Field Calibration . 74 IV. Precision Measurement of nS1=2 Rubidium-85 Hyperfine Struc- ture Splittings ............................. 77 4.1 Procedure . 78 4.2 Results . 79 4.3 Uncertainty Budget . 81 4.4 Discussion . 84 V. A Study of Systematic Uncertainties in the R1 Measurement 85 5.1 Lattice-induced Shift . 86 5.2 Quantum Defect Correction . 87 5.3 Stark and Zeeman Corrections . 88 5.4 Blackbody Radiation Correction . 89 5.5 Other sources of uncertainty . 90 5.6 Conclusion . 92 VI. Discussion and Outlook ....................... 94 6.1 Future Work . 95 6.2 Solving the Proton Radius Puzzle . 95 6.3 Rydberg Constant Measurement in Microgravity . 96 APPENDIX :::::::::::::::::::::::::::::::::::: 98 A.1 Introduction . 99 A.2 Atom-Chip Experimental Setup . 101 viii A.3 1D Optical Lattice Implementation . 102 A.4 Future Work: Spatially Probing Lattice Sites . 106 BIBLIOGRAPHY :::::::::::::::::::::::::::::::: 108 ix LIST OF FIGURES Figure 1.1 Proton radius (top) and Rydberg constant (bottom) values obtained using different approaches. The error bars for the proton radius ob- tained with muonic hydrogen spectroscopy are not visible in the scale on the top. .7 1.2 Sketch of the probability density j j2 of the Rydberg electron in a circular state. Near the Rb+ core, j j2 = 0. (figure not to scale). .9 2.1 Rydberg electron probability distributions for different parabolic quan- tum numbers. Top left: n1 = n2 = 0; ml = 4; top right: n1 = 0; n2 = 1; ml = 3; bottom left: n1 = 2; n2 = 0; ml = 2; bottom right: n1 = n2 = 1; ml = 2 (all have n = 5).
Load more

Recommended publications
  • Calculation of Rydberg Interaction Potentials
    Tutorial Calculation of Rydberg interaction potentials Sebastian Weber,1, ∗ Christoph Tresp,2, 3 Henri Menke,4 Alban Urvoy,2, 5 Ofer Firstenberg,6 Hans Peter B¨uchler,1 and Sebastian Hofferberth2, 3, † 1Institute for Theoretical Physics III and Center for Integrated Quantum Science and Technology, Universit¨atStuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany 25. Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universit¨at Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany 3Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark 4Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany 5Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 6Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel (Dated: June 7, 2017) The strong interaction between individual Rydberg atoms provides a powerful tool exploited in an ever-growing range of applications in quantum information science, quantum simulation, and ultracold chemistry. One hallmark of the Rydberg interaction is that both its strength and angular dependence can be fine-tuned with great flexibility by choosing appropriate Rydberg states and applying external electric and magnetic fields. More and more experiments are probing this interaction at short atomic distances or with such high precision that perturbative calculations as well as restrictions to the leading dipole-dipole interaction term are no longer sufficient. In this tutorial, we review all relevant aspects of the full calculation of Rydberg interaction potentials. We discuss the derivation of the interaction Hamiltonian from the electrostatic multipole expansion, numerical and analytical methods for calculating the required electric multipole moments, and the inclusion of electromagnetic fields with arbitrary direction.
    [Show full text]
  • RSC Spectroscopy and Dynamics Group Meeting 2020
    RSC Spectroscopy and Dynamics Group Meeting 2020 University of Warwick 6th – 8th January 2020 We would like to extend our thanks to the RSC and all of our sponsors for their generous support of this year’s Spectroscopy and Dynamics Group meeting. Please show your support for our sponsors by visiting their trade stands during the coffee breaks and Tuesday’s poster session. Programme All presentation sessions will take place in Meeting Room 2 inside the Radcliffe Conference Centre. Monday 6th January 16:00 - 18:00 Arrival and Registration 18:00 - 19:00 Dinner Dining Room Session 1 Chair: Caroline Dessent 19:00 - 19:05 Welcome Vas Stavros (Warwick) 19:05 - 19:50 Invited tutorial talk Helen Fielding (UCL) 19:50 - 20:35 Invited tutorial talk Tom Penfold (Newcastle) 20:35 - 21:35 SDG AGM Meeting Room 2 Tuesday 7th January 07:00 - 08:30 Breakfast Dining Room* Session 2 Chair: Michael Staniforth 09:00 - 09:45 Invited talk David Osborn (Sandia NL) 09:45 - 10:05 Contributed talk David Kemp (Nottingham) 10:05 - 10:25 Contributed talk Klaudia Gawlas (UCL) 10:25 - 10:45 Contributed talk Preeti Manjari Mishra (RIKEN) 10:45 - 11:15 Tea/Coffee Lounge Session 3 Chair: Jutta Toscano 11:15 - 12:00 Invited talk Sonia Melandri (Bologna) 12:00 - 12:20 Contributed talk Maria Elena Castellani (Durham) 12:20 - 12:40 Contributed talk Javier S. Marti (Imperial) 12:40 - 13:00 Contributed talk Conor Rankine (Newcastle) 13:00 - 14:15 Lunch Dining Room Session 4 Chair: Nat das Neves Rodrigues 14:15 - 14:35 Contributed talk Jacob Berenbeim (York) 14:35 - 14:55 Contributed
    [Show full text]
  • Dynamics of Rydberg Atom Lattices in the Presence of Noise and Dissipation
    Dynamics of Rydberg atom lattices in the presence of noise and dissipation D zur Erlangung des akademischen Grades Doctor rerum naturalium (Dr. rer. nat.) vorgelegt der Fakultät Mathematik und Naturwissenschaften der Technischen Universität Dresden von Wildan Abdussalam M.Sc. Eingereicht am 19.1.2017 Verteidigt am 07.08.2017 Eingereicht am 19.1.2017 Verteidigt am 07.08.2017 1. Gutachter: Prof. Dr. Jan Michael Rost 2. Gutachter: Prof. Dr. Walter Strunz To my family and teachers Abstract The work presented in this dissertation concerns dynamics of Rydberg atom lattices in the presence of noise and dissipation. Rydberg atoms possess a number of exaggerated properties, such as a strong van der Waals interaction. The interplay of that interaction, coherent driving and decoherence leads to intriguing non-equilibrium phenomena. Here, we study the non-equilibrium physics of driven atom lattices in the pres- ence of decoherence caused by either laser phase noise or strong decay. In the Vrst case, we compare between global and local noise and explore their eUect on the number of ex- citations and the full counting statistics. We Vnd that both types of noise give rise to a characteristic distribution of the Rydberg excitation number. The main method employed is the Langevin equation but for the sake of eXciency in certain regimes, we use a Marko- vian master equation and Monte Carlo rate equations, respectively. In the second case, we consider dissipative systems with more general power- law interactions. We determine the phase diagram in the steady state and analyse its generation dynamics using Monte Carlo rate equations.
    [Show full text]
  • Spectroscopy of Cold Rubidium Rydberg Atoms for Applications in Quantum Information
    Spectroscopy of cold rubidium Rydberg atoms for applications in quantum information I.I. Ryabtsev, I.I. Beterov, D.B.Tretyakov, V.M. Entin, E.A. Yakshina Rzhanov Institute of Semiconductor Physics SB RAS, 630090 Novosibirsk, Russia Novosibirsk State University, 630090 Novosibirsk, Russia E-mail: [email protected] Abstract Atoms in highly excited (Rydberg) states have a number of unique properties which make them attractive for applications in quantum information. These are large dipole moments, lifetimes and polarizabilities, as well as strong long-range interactions between Rydberg atoms. Experimental methods of laser cooling and precision spectroscopy enable the trapping and manipulation of single Rydberg atoms and applying them for practical implementation of quantum gates over qubits of a quantum computer based on single neutral atoms in optical traps. In this paper, we give a review of the experimental and theoretical work performed by the authors at the Rzhanov Institute of Semiconductor Physics SB RAS and Novosibirsk State University on laser and microwave spectroscopy of cold Rb Rydberg atoms in a magneto-optical trap and on their possible applications in quantum information. We also give a brief review of studies done by other groups in this area. PACS numbers: 03.67.Lx, 32.70.Jz, 32.80.-t, 32.80.Ee, 32.80.Rm Key words: Rydberg atoms, laser cooling, spectroscopy, quantum information, qubits Journal reference: Physics − Uspekhi 59 (2) 196-208 (2016) DOI: 10.3367/UFNe.0186.201602k.0206 Translated from the original Russian text: Uspekhi Fizicheskikh Nauk 186 (2) 206-219 (2016) DOI: 10.3367/UFNr.0186.201602k.0206 Received 9 November 2015, revised 9 December 2015 2 1.
    [Show full text]
  • Ultrafast Dynamics of Neutral Superexcited Oxygen: a Direct Measurement of the Competition Between Autoionization and Predissociation
    Ultrafast dynamics of neutral superexcited Oxygen: A direct measurement of the competition between autoionization and predissociation Henry Timmers,∗ Niranjan Shivaram, and Arvinder Sandhuy Department of Physics, University of Arizona, Tucson, AZ, 85721 USA. Using ultrafast extreme ultraviolet pulses, we performed a direct measurement of the relaxation 4 − dynamics of neutral superexcited states corresponding to the nlσg(c Σu ) Rydberg series of O2. An XUV attosecond pulse train was used to create a temporally localized Rydberg wavepacket and the ensuing electronic and nuclear dynamics were probed using a time-delayed femtosecond near- infrared pulse. We investigated the competing predissociation and autoionization mechanisms in superexcited molecules and found that autoionization is dominant for the low n Rydberg states. We measured an autoionization lifetime of 92±6 fs and 180±10 fs for (5s; 4d)σg and (6s; 5d)σg Rydberg state groups respectively. We also determine that the disputed neutral dissociation lifetime for the ν = 0 vibrational level of the Rydberg series is 1100 ± 100 fs. A pervasive theme in ultrafast science is the charac- terization and control of energy distributions in elemen- tary molecular processes. Ultrashort light pulses are used Energy to excite and probe electronic and nuclear wavepackets, Neutral whose evolution is fundamental to understanding many Dissociation Autoionization physical and chemical phenomena [1]. However, until Potential recently, time-resolved studies of wavepacket dynamics using light pulses in the infrared (IR), visible, and ultra- violet (UV) regime had predominantly been limited to Internuclear Distance low-lying excited states and femtosecond timescales [2]. Advances in photon technologies, specifically in the ( )+ field of laser high-harmonic generation (HHG)[3, 4], have opened new avenues in the time-resolved studies of molec- FIG.
    [Show full text]
  • Rydberg Molecules and Circular Rydberg States in Cold Atom Clouds
    Rydberg molecules and circular Rydberg states in cold atom clouds by David Alexander Anderson A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Applied Physics) in The University of Michigan 2015 Doctoral Committee: Professor Georg A. Raithel, Chair Professor Luming Duan Professor Alex Kuzmich Thomas Pohl, Max Plank Institute for Physics Associate Professor Vanessa Sih ⃝c David A. Anderson 2015 All Rights Reserved For my family ii ACKNOWLEDGEMENTS First I have to thank my advisor Georg Raithel for his continued support, patience, and encouragement during the completion of this dissertation and throughout my time working in the Raithel group. Without his insights, direction, and deep understanding of the subject matter, none of it would have been possible. His enthusiasm for research and insatiable curiosity have been an inspiration in the years I have been fortunate to have spent under his wing. Thank you Georg for giving me the opportunity to learn from you. Over the years I have had the pleasure of working with many former and current members of the Raithel group from whom I have learned a great deal. Many thanks to Sarah Anderson, Yun-Jhih Chen, Lu´ıs Felipe Gon¸calves, Cornelius Hempel, Jamie MacLennan, Stephanie Miller, Kaitlin Moore, Eric Paradis, Erik Power, Andira Ramos, Rachel Sapiro, Andrew Schwarzkopf, Nithiwadee Thaicharoen (Pound), Mallory Traxler, and Kelly Younge, for making my time in the Raithel group such an enjoyable experience. Thank you to my committee members, Georg Raithel, Thomas Pohl, Vanessa Sih, Alex Kuzmich, and Luming Duan, for your support and willingness to serve on my committee.
    [Show full text]
  • Recent Advances in Rydberg Physics Using Two-Electron Atoms Abstract
    Recent advances in Rydberg Physics using two-electron atoms F. B. Dunning,1 T.C. Killian,1 S. Yoshida,2 and J. Burgd¨orfer2 1Department of Physics and Astronomy and the Rice Quantum Institute, Rice University, Houston, TX 77005-1892, USA 2Institute for Theoretical Physics, Vienna University of Technology, Vienna, Austria, EU Abstract In this brief review, the opportunities that the alkaline-earth elements afford to study new aspects of Rydberg physics are discussed. For example, the bosonic alkaline-earth isotopes have zero nuclear spin which eliminates many of the complexities present in alkali Rydberg studies permitting simpler and more direct comparison between theory and experiment. The presence of two valence electrons allows the production of singlet and triplet Rydberg states that can exhibit a variety of attractive or repulsive interactions. The availability of weak intercombination lines is advantageous for laser cooling and for applications such as Rydberg dressing. Excitation of one electron to a Rydberg state leaves behind an optically-active core ion allowing, for high-L states, the optical imaging of Rydberg atoms and their (spatial) manipulation using light scattering. The second valence electron also opens up the possibility of engineering long-lived doubly-excited states such as planetary atoms. Recent advances in both theory and experiment are highlighted together with a number of possible directions for the future. 1 Rydberg atoms provide an excellent vehicle with which to study strongly-interacting quantum systems due to their long-range interactions. Such interactions can give rise to a number of interesting effects including dipole blockade in which multiple Rydberg excita- tions within some blockade sphere are inhibited due to the level shifts induced by the first Rydberg atom created.
    [Show full text]
  • Level Shifts of Rubidium Rydberg States Due to Binary Interactions
    PHYSICAL REVIEW A 75, 032712 ͑2007͒ Level shifts of rubidium Rydberg states due to binary interactions A. Reinhard, T. Cubel Liebisch, B. Knuffman, and G. Raithel FOCUS Center and Michigan Center for Theoretical Physics, Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA ͑Received 16 August 2006; published 14 March 2007; corrected 19 March 2007͒ We use perturbation theory to directly calculate the van der Waals and dipole-dipole energy shifts of pairs of interacting Rb Rydberg atoms for different quantum numbers n, ᐉ, j, and mj, taking into account a large number of perturbing states. Our results can be used to identify good experimental parameters and illuminate important considerations for applications of the “Rydberg-excitation blockade.” We also use the results of the calculation to explain features of previous experimental data on the Rydberg-excitation blockade. To explore control methods for the blockade, we discuss energy shifts due to atom-atom interaction in an external electric field. DOI: 10.1103/PhysRevA.75.032712 PACS number͑s͒: 34.20.Cf, 31.15.Md, 34.60.ϩz, 03.67.Ϫa I. INTRODUCTION external electric field has also been reported ͓15͔. The Ryd- berg blockade has been modeled using many-body quantum Due to their large sizes and polarizabilities, Rydberg at- simulations ͓16,17͔, and the application of the blockade to oms excited from ensembles of laser-cooled ground state at- quantum phase gates ͓18,19͔ has been analyzed. Additional oms interact strongly via resonant dipole-dipole or off- work has been done to characterize Rydberg-atom interac- resonant van der Waals interactions.
    [Show full text]
  • Rydberg States of Atoms and Molecules. Basic Group Theoretical and Topological Analysis
    Physics Reports 341 (2001) 173}264 Symmetry, invariants, topology. III Rydberg states of atoms and molecules. Basic group theoretical and topological analysis L. Michel! , B.I. ZhilinskimH " * !Institut des Hautes E! tudes Scientixques, 91440 Bures-sur-Yvette, France "Universite& du Littoral, BP 5526, 59379 Dunkerque Ce& dex, France Contents 1. Introduction 175 3.2. Qualitative description of e!ective 1.1. Dynamical symmetry of Rydberg states 178 Hamiltonians invariant with respect to 2. Groups and their actions appropriate for the continuous subgroups of O(3) 205 Rydberg problem 179 3.3. Qualitative description of e!ective 2.1. Structure of O(4) 179 Hamiltonians invariant with respect to 2.2. The adjoint representation of O(4); induced "nite subgroups of O(3) 210 R" ; action on S S 182 4. Manifestation of qualitative e!ects in physical 2.3. Action of O(3), SO(3), O(3)?T, systems. Hydrogen atom in magnetic and ? ? R SO(3) T, and SO(3) TQ on ; their electric "eld 213 strata, orbits and invariants 185 4.1. Di!erent "eld con"gurations and their 2.4. Invariants of the one-dimensional Lie symmetry 213 subgroups of O(3) acting on R 188 4.2. Quadratic Zeeman e!ect in hydrogen 2.5. One-dimensional Lie subgroups of atom 215 O(3)?T and their invariants 191 4.3. Hydrogen atom in parallel electric and 2.6. Orbits, strata and orbit spaces of the one- magnetic "elds 217 dimensional Lie subgroups of O(3) acting 4.4. Hydrogen atom in orthogonal electric and on R 192 magnetic "elds 223 2.7.
    [Show full text]
  • Interacting Cold Rydberg Atoms: a Toy Many-Body System
    Bohr, 1913-2013, S´eminairePoincar´eXVII (2013) 125 { 144 S´eminairePoincar´e Interacting Cold Rydberg Atoms: a Toy Many-Body System Antoine Browaeys and Thierry Lahaye Institut d'Optique Laboratoire Charles Fabry 2 av. A. Fresnel 91127 Palaiseau cedex, France Abstract. This article presents recent experiments where cold atoms excited to Rydberg states interact with each other. It describes the basic properties of Rydberg atoms and their interactions, with the emphasis on the Rydberg blockade mechanism. The paper details a few experimental demonstrations us- ing two individual atoms or atomic ensembles, as well as applications of this \toy many-body system" to quantum information processing using photons. 1 Introduction One of the great challenges in physics is to understand how complexity emerges from the simple underlying physical laws that govern the interactions between con- stituents of matter, like atoms or molecules. Interactions between particles are for the most part well-understood, and the equations of quantum mechanics governing an ensemble of interacting particles are known. However, due to the exponential scaling of the size of the Hilbert space with the number of particles, they are too difficult to be solved beyond a few tens of particles: this is called the many-body problem. One idea to progress is to build in the laboratory some simple toy systems that are ruled by known but unsolved equations and to measure the properties of these systems. In doing so, one can validate or infirm theoretical approaches or models. Furthermore, by developing and harnessing quantum systems, one can envision technological developments. Presently, this quantum engineering has two main applications: quantum information processing and quantum metrology.
    [Show full text]
  • Low-Dielectric-Constant Polyimide Aerogel
    University of Birmingham Identification of a new electron-transfer relaxation pathway in photoexcited pyrrole dimers Neville, Simon P.; Kirkby, Oliver M.; Kaltsoyannis, Nikolas; Worth, Graham A.; Fielding, Helen H. DOI: 10.1038/ncomms11357 License: Creative Commons: Attribution (CC BY) Document Version Publisher's PDF, also known as Version of record Citation for published version (Harvard): Neville, SP, Kirkby, OM, Kaltsoyannis, N, Worth, GA & Fielding, HH 2016, 'Identification of a new electron- transfer relaxation pathway in photoexcited pyrrole dimers', Nature Communications, vol. 7, 11357. https://doi.org/10.1038/ncomms11357 Link to publication on Research at Birmingham portal Publisher Rights Statement: Neville, S., Kirkby, O., Kaltsoyannis, N. et al. Identification of a new electron-transfer relaxation pathway in photoexcited pyrrole dimers. Nat Commun 7, 11357 (2016). https://doi.org/10.1038/ncomms11357 General rights Unless a licence is specified above, all rights (including copyright and moral rights) in this document are retained by the authors and/or the copyright holders. The express permission of the copyright holder must be obtained for any use of this material other than for purposes permitted by law. •Users may freely distribute the URL that is used to identify this publication. •Users may download and/or print one copy of the publication from the University of Birmingham research portal for the purpose of private study or non-commercial research. •User may use extracts from the document in line with the concept of ‘fair dealing’ under the Copyright, Designs and Patents Act 1988 (?) •Users may not further distribute the material nor use it for the purposes of commercial gain.
    [Show full text]
  • $ C 6 $ Coefficients for Interacting Rydberg Atoms and Alkali-Metal
    C6 coefficients for interacting Rydberg atoms and alkali-metal dimers Vanessa Olaya,1 Jes´usP´erez-R´ıos,2 and Felipe Herrera1, 3, ∗ 1Department of Physics, Universidad de Santiago de Chile, Av. Ecuador 3493, Santiago, Chile. 2Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany 3Millennium Institute for Research in Optics MIRO, Chile. (Dated: December 4, 2019) We study the van der Waals interaction between Rydberg alkali-metal atoms with fine structure 2 1 + (n Lj ; L ≤ 2) and heteronuclear alkali-metal dimers in the ground rovibrational state (X Σ ; v = 0, J = 0). We compute the associated C6 dispersion coefficients of atom-molecule pairs involving 133Cs and 85Rb atoms interacting with KRb, LiCs, LiRb, and RbCs molecules. The obtained dispersion coefficients can be accurately fitted to a state-dependent polynomial O(n7) over the range of principal quantum numbers 40 ≤ n ≤ 150. For all atom-molecule pairs considered, 2 2 6 2 Rydberg states n Sj and n Pj result in attractive 1=R potentials. In contrast, n Dj states can give rise to repulsive potentials for specific atom-molecule pairs. The interaction energy at the LeRoy −5 distance approximately scales as n for n > 40. For intermediate values of n . 40, both repulsive and attractive interaction energies in the order of 10 − 100 µK can be achieved with specific atomic and molecular species. The accuracy of the reported C6 coefficients is limited by the quality of the atomic quantum defects, with relative errors ∆C6=C6 estimated to be no greater than 1% on average.
    [Show full text]