DOCSLIB.ORG

Optical Pumping of Rubidium

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Optical Pumping of Rubidium Optical Pumping of Rubidium Adam Egbert,1, a) Will Wiegand,1 and Hannah Sheppard2 1)University of San Diego 2)University of San Diego (Dated: 26 September 2015) In this experiment, we explored the how optical pumping can be used to access the quantum numbers associated with Zeeman splitting inside of Rubidium-85 and Rubidium-87 atoms. Optical pumping is a process where electrons are driven into specific energy levels whose transitions can be easily detected. We were able to determine the g-factors associated with each Rb and use these factors to find values of nuclear spin (I). The quadratic Zeeman effect was also observed in this experiment. I. INTRODUCTION L and S. Quantizing these values as multiples of ~, yields J = L ± S: (1) Understanding nuclear and electronic quantum num- bers that characterize angular momentum of an atom 2 The lone valence electron in Rb is designated by S1=2, is a fundamental part of quantum mechanics. Optical so the ground state must have L=0 and S = 1/2 giving a pumping allows us to raise electrons to specific states, value of 1/2 for J. Using the selection rule that governs but the basic states are not all there is to see in the realm transitions of angular momentum, ∆L can only shift one of optical pumping. This experiment demonstrates that whole integer up or down. Knowing that J cannot be states which appear to be degenerate are able to be split negative, the atom reaches its first excited state at L=1 further when Rb atoms are exposed to a magnetic field. and S=1/2 so J can equal 1/2 or 3/2. L, S and J describe Due to the Zeeman Effect, as an external magnetic field energy levels under no perturbation and contain degener- increases, the energy levels separate allowing for simple ate states which can be observed under a magnetic field observation. Due to the selection rules common to quan- thanks to the Zeeman Effect. tum mechanics, the allowable transitions between states of an electron are limited. Based on relative absorbance of photons passing through that atoms and strength of B. Energy Level Splitting the B-field applied, we can determine the magnitude of the splitting between the previously degenerate states. Besides the electrons momentum, the angular momen- This paper will first begin by explaining theory dis- tum of the nucleus also has a spin state, I. The combi- cussing spin states and optical pumping. The following nation of the electrons momentum as well as the nuclear section will cover the apparatus and set up used, as well angular momentum yields the total angular momentum, as the procedure involved with optical pumping. The F. F is calculated by the coupling relation paper will be concluded by analyzed data with results as well as error analysis. F = I ± J: (2) One goal of this experiment is to empirically determine I for both isotopes of Rb. Due to difference in the nucleus II. THEORY of Rb isotopes, values of I are not the same for the dif- ferent isotopes. The difference between energy levels of A. Atomic Structure F are incredibly small relative to the difference between the ground state and first excited state leading to what Optical pumping requires a basic understanding of is first seen as degeneracy of the states. the energy level structure because of the absorption and The degeneracy just described can be eliminated when emission of photons within the atom happens at quan- the atom is exposed to a magnetic field and the F en- tized energy levels. Rubidium was used in our experiment ergy states are spilt into further sub levels and labelled because it only contains one election in its outer-most va- with a new quantum number, M, representing the Zee- lence shell, so it is a close representation of a hydrogen man states. The difference between the Zeeman states atom. Taking Rb to be similar to H, we know of three increases linearly with and increasing B-field if the B- important quantities representing its energy: the orbital field is relatively small. In accordance to perturbation angular momentum L, the spin angular momentum S, theory, the perturbation due to the magnetic field on the and the total angular momentum J, the combination of nuclear magnetic moments through the Hamiltonian H = AI~ · J~ + gf µJ J~ · gI µN I~ · B;~ (3) where µJ is the total electronic magnetic dipole mo- a)Physics Department, University of San Diego. ment and µI is the nuclear magnetic dipole moment. The 2 first zone is where the B-field is low and we have a linear relationship between the B-field and energy. Then a sec- ond zone appears for larger B-fields and a quadratic term comes into play. At very high B-fields all states return to normal linearity. FIG. 1. 1 a diagram depicting the possible energy state transitions for Rb magnetic moment of the nucleus is much smaller, due to its large size, than the magnetic moment of the electron, it can be ignored. The magnetic energy can be calculated by E = gJ µf MB; (4) where gjis the Lande g-factor and evaluated as gj = 1+(J(J +1)+S(S +1)−L(L+1))=2J(J +1): (5) If we do consider the interaction with the nucleus we obtain a new g-factor given by FIG. 2. 1 a diagram depicting the possible energy state transitions for gf = gj((F (F +1)+J(J +1)−I(I +1))=2F (F +1)): (6) Rb in a magnetic field when spin is 3/2. The x-axis represents an increasing magnetic field and the y-axis is a Incorporating the new g-factor the interaction energy is unit-less representation of energy states given by W = gf µ0MB; (7) C. Relevant Optics where µ0 is the Bohr Magneton.This result allows us to determine g by plotting energy levels against B-field f Photons are absorbed by electrons in the rubidium strength to obtain a slope of g µ M. Knowing g al- f 0 f atoms which raise the electrons to a particular energy lows Equation (6) to be solved for I because we already level based frequency of the photons. The electron can know F and J. This model only works under small mag- then spontaneously emit a photon of a particular wave- netic fields; the effect begins to change as magnetic field length to reach a lower energy state. The energy of the is significantly increased. photon absorbed does not have to equal the energy of What we obtain after raising the B field a significant the photon emitted, but the energy levels still follow the amount is the Quadratic Zeeman Effect where the differ- relevant selection rules. The most important one to our ences in Zeeman level change quadratically rather than experiment is ∆M = 0; ± 1. By circularly polarizing the linearly. The splitting is calculated by the Briet-Rabi photons, we limit the possible transitions of states to the equation: one previously listed. However, there is a limit in which W (F; M) = −(∆W=2(2I + 1)) − (µI =I)BM ± ∆M cannot be lower than -1, so eventually we pump (∆W=2)[1 + (4M=(2I + 1))x + x2]1=2; (8) the entire population into this higher M state. With all atoms in this higher state, no more photons can be ab- where sorbed making the atoms inaccessible to other photons disrupting the thermal equilibrium of the system. When x = (gJ − gI )(µ0B=∆W ) (9) the atoms experience no B-field (the zero-field transmis- sion), the thermal equilibrium is then reset and the Rb and atoms can absorb photons again. This results in a loss of intensity at a detector until they are fully pumped up gI = −µI =IµI: (10) once again. A plot of this equation is seen in Fig. (2.1). Upon in- Introducing a RF signal at a specific frequency allows spection we see there are 3 zones within the figure: the transitions from the M=2 state to lower states which 3 gives the electrons a break from their highly excited state. B. Procedure Again, this is observed by a decrease in photon absorp- tion at the detector. Most importantly the frequency 1. Low Field Splitting at which the phenomena occurs is proportional to the strength of the B-field allowing us to determine the en- ergy states the electrons are occupying. It is also impor- tant to note, the differences in atomic structure leads to a different energy gap between the two isotopes allowing the observation of the quantum numbers for each isotope. III. APPARATUS AND PROCEDURE A. Apparatus We used a TeachSpin optical pumping apparatus for all parts of our experiment. The set up has an RF discharge lamp, interference filter, linear polarizer, quarter wave plate, rubidium absorption cell and optical detector in FIG. 4. 1 that order as seen in figure (). The RF discharge lamp Frequency vs. Magnetic Field for Rb isotopes. The slopes was the source of all our RF waves that pass through a were used to determine the I values. focusing lens to get the maximum amount of light into the absorption cell. Following the lens is the interference First we had to determine the strength of the B-field filter which only allows the wavelengths of light through that remained from the earth's magnetic field because that we want to study. The polarizers act together to the vertical field from the Helmholtz coils leaves one axial produce circularly polarized light which limits transitions component.
Load more

Recommended publications
  • Optical Pumping of Stored Atomic Ions (*)
    Ann. Phys. Fr. 10 (1985) 737-748 DhCEMBRE 1985, PAGE 131 Optical pumping of stored atomic ions (*) D. J. Wineland, W. M. Itano, J. C. Bergquist, J. J. Bollinger and J. D. Prestage Time and Frequency Division, National Bureau of Standards, Boulder, Colorado 80303, U.S.A. Resume. - Ce texte discute les expkriences de pompage optique sur des ions atomiques confints dans des pikges tlectromagnttiques. Du fait de la faible relaxation et des dtplacements d'energie trbs petits des ions confine$ on peut obtenir une trb haute rtsolution et une tres grande prkision dans les exptriences de pompage optique associt a la double rtsonance. Dans la ligne de l'idee de Kastler de (( lumino-rtfrigtration H (1950), l'tnergie cinttique des niveaux des ions confines peut Ctre pompke optiquement. Cette technique, appelee refroidissement laser, rtduit sensiblement les dtplacements de frtquence Doppler dans les spectres. Abstract. - Optical pumping experiments on atomic ions which are stored in ekG tromagnetic (( traps )) are discussed. Weak relaxation and extremely small energy shifts of the stored ions lead to very high resolution and accuracy in optical pumping- double resonance experiments. In the same spirit of Kastler's proposal for (( lumino refrigeration )) (1950), the kinetic energy levels of stored ions can be optically pumped. This technique, which has been called laser cooling significantly reduces Doppler frequency shifts in the spectra. 1. Introduction. For more than thirty years, the technique of optical pumping, as originally proposed by Alfred Kastler [I], has provided information about atomic structure, atom-atom interactions, and the interaction of atoms with external radiation. This technique continues today as one of the primary methods used in atomic physics.
    [Show full text]
  • H20 Maser Observations in W3 (OH): a Comparison of Two Epochs
    DePaul University Via Sapientiae College of Science and Health Theses and Dissertations College of Science and Health Summer 7-13-2012 H20 Maser Observations in W3 (OH): A comparison of Two Epochs Steven Merriman DePaul University, [email protected] Follow this and additional works at: https://via.library.depaul.edu/csh_etd Part of the Physics Commons Recommended Citation Merriman, Steven, "H20 Maser Observations in W3 (OH): A comparison of Two Epochs" (2012). College of Science and Health Theses and Dissertations. 31. https://via.library.depaul.edu/csh_etd/31 This Thesis is brought to you for free and open access by the College of Science and Health at Via Sapientiae. It has been accepted for inclusion in College of Science and Health Theses and Dissertations by an authorized administrator of Via Sapientiae. For more information, please contact [email protected]. DEPAUL UNIVERSITY H2O Maser Observations in W3(OH): A Comparison of Two Epochs by Steven Merriman A thesis submitted in partial fulfillment for the degree of Master of Science in the Department of Physics College of Science and Health July 2012 Declaration of Authorship I, Steven Merriman, declare that this thesis titled, `H2O Maser Observations in W3OH: A Comparison of Two Epochs' and the work presented in it are my own. I confirm that: This work was done wholly while in candidature for a masters degree at Depaul University. Where I have consulted the published work of others, this is always clearly attributed. Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work.
    [Show full text]
  • Quantum Mechanics of Atoms and Molecules Lectures, the University of Manchester 2005
    Quantum Mechanics of Atoms and Molecules Lectures, The University of Manchester 2005 Dr. T. Brandes April 29, 2005 CONTENTS I. Short Historical Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 I.1 Atoms and Molecules as a Concept . 1 I.2 Discovery of Atoms . 1 I.3 Theory of Atoms: Quantum Mechanics . 2 II. Some Revision, Fine-Structure of Atomic Spectra : : : : : : : : : : : : : : : : : : : : : 3 II.1 Hydrogen Atom (non-relativistic) . 3 II.2 A `Mini-Molecule': Perturbation Theory vs Non-Perturbative Bonding . 6 II.3 Hydrogen Atom: Fine Structure . 9 III. Introduction into Many-Particle Systems : : : : : : : : : : : : : : : : : : : : : : : : : 14 III.1 Indistinguishable Particles . 14 III.2 2-Fermion Systems . 18 III.3 Two-electron Atoms and Ions . 23 IV. The Hartree-Fock Method : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 24 IV.1 The Hartree Equations, Atoms, and the Periodic Table . 24 IV.2 Hamiltonian for N Fermions . 26 IV.3 Hartree-Fock Equations . 28 V. Molecules : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 35 V.1 Introduction . 35 V.2 The Born-Oppenheimer Approximation . 36 + V.3 The Hydrogen Molecule Ion H2 . 39 V.4 Hartree-Fock for Molecules . 45 VI. Time-Dependent Fields : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 48 VI.1 Time-Dependence in Quantum Mechanics . 48 VI.2 Time-dependent Hamiltonians . 50 VI.3 Time-Dependent Perturbation Theory . 53 VII.Interaction with Light : : : : : : : : : : : : : : : : : : : : : : :
    [Show full text]
  • Optical Pumping: a Possible Approach Towards a Sige Quantum Cascade Laser
    Institut de Physique de l’ Universit´ede Neuchˆatel Optical Pumping: A Possible Approach towards a SiGe Quantum Cascade Laser E3 40 30 E2 E1 20 10 Lasing Signal (meV) 0 210 215 220 Energy (meV) THESE pr´esent´ee`ala Facult´edes Sciences de l’Universit´ede Neuchˆatel pour obtenir le grade de docteur `essciences par Maxi Scheinert Soutenue le 8 octobre 2007 En pr´esence du directeur de th`ese Prof. J´erˆome Faist et des rapporteurs Prof. Detlev Gr¨utzmacher , Prof. Peter Hamm, Prof. Philipp Aebi, Dr. Hans Sigg and Dr. Soichiro Tsujino Keywords • Semiconductor heterostructures • Intersubband Transitions • Quantum cascade laser • Si - SiGe • Optical pumping Mots-Cl´es • H´et´erostructures semiconductrices • Transitions intersousbande • Laser `acascade quantique • Si - SiGe • Pompage optique i Abstract Since the first Quantum Cascade Laser (QCL) was realized in 1994 in the AlInAs/InGaAs material system, it has attracted a wide interest as infrared light source. Main applications can be found in spectroscopy for gas-sensing, in the data transmission and telecommuni- cation as free space optical data link as well as for infrared monitoring. This type of light source differs in fundamental ways from semiconductor diode laser, because the radiative transition is based on intersubband transitions which take place between confined states in quantum wells. As the lasing transition is independent from the nature of the band gap, it opens the possibility to a tuneable, infrared light source based on silicon and silicon compatible materials such as germanium. As silicon is the material of choice for electronic components, a SiGe based QCL would allow to extend the functionality of silicon into optoelectronics.
    [Show full text]
  • Optical Pumping
    Optical Pumping MIT Department of Physics (Dated: February 17, 2011) Measurement of the Zeeman splittings of the ground state of the natural rubidium isotopes; measurement of the relaxation time of the magnetization of rubidium vapor; and measurement of the local geomagnetic field by the rubidium magnetometer. Rubidium vapor in a weak (∼.01- 10 gauss) magnetic field controlled with Helmholtz coils is pumped with circularly polarized D1 light from a rubidium rf discharge lamp. The degree of magnetization of the vapor is inferred from a differential measurement of its opacity to the pumping radiation. In the first part of the experiment the energy separation between the magnetic substates of the ground-state hyperfine levels is determined as a function of the magnetic field from measurements of the frequencies of rf photons that cause depolarization and consequent greater opacity of the vapor. The magnetic moments of the ground states of the 85Rb and 87Rb isotopes are derived from the data and compared with the vector model for addition of electronic and nuclear angular momenta. In the second part of the experiment the direction of magnetization is alternated between nearly parallel and nearly antiparallel to the optic axis, and the effects of the speed of reversal on the amplitude of the opacity signal are observed and compared with a computer model. The time constant of the pumping action is measured as a function of the intensity of the pumping light, and the results are compared with a theory of competing rate processes - pumping versus collisional depolarization. I. PREPARATORY PROBLEMS II. INTRODUCTION 1. With reference to Figure 1 of this guide, estimate A.
    [Show full text]
  • Optical Pumping 1
    Optical Pumping 1 OPTICAL PUMPING OF RUBIDIUM VAPOR Introduction The process of optical pumping is a beautiful example of the interaction between light and matter. In the Advanced Lab experiment, you use circularly polarized light to pump a particular level in rubidium vapor. Then, using magnetic fields and radio-frequency excitations, you manipulate the population of the pumped state in a manner similar to that used in the Spin Echo experiment. You will determine the energy separation between the magnetic substates (Zeeman levels) in rubidium as well as determine the Bohr magneton and observe two-photon transitions. Although the experiment is relatively simple to perform, you will need to understand a fair amount of atomic physics and experimental technique to appreciate the signals you witness. A simple example of optical pumping Let’s imagine a nearly trivial atom: no nuclear spin and only one electron. For concreteness, you can think of the 4He+ ion, which is similar to a Hydrogen atom, but without the nuclear spin of the proton. Its ground state is 1S1=2 (n = 1,S = 1=2,L = 0, J = 1=2). Photon absorption can excite it to the 2P1=2 (n = 2,S = 1=2,L = 1, J = 1=2) state. If you place it in a magnetic field, the energy levels become split as indicated in Figure 1. In effect, each original level really consists of two levels with the same energy; when you apply a field, the “spin up” state becomes higher in energy, the “spin down” lower. The spin energy splitting is exaggerated on the figure.
    [Show full text]
  • Spin Coherence and Optical Properties of Alkali-Metal Atoms in Solid Parahydrogen
    Spin coherence and optical properties of alkali-metal atoms in solid parahydrogen Sunil Upadhyay,1 Ugne Dargyte,1 Vsevolod D. Dergachev,2 Robert P. Prater,1 Sergey A. Varganov,2 Timur V. Tscherbul,1 David Patterson,3 and Jonathan D. Weinstein1, ∗ 1Department of Physics, University of Nevada, Reno NV 89557, USA 2Department of Chemistry, University of Nevada, Reno NV 89557, USA 3Broida Hall, University of California, Santa Barbara, Santa Barbara, California 93106, USA We present a joint experimental and theoretical study of spin coherence properties of 39K, 85Rb, 87Rb, and 133Cs atoms trapped in a solid parahydrogen matrix. We use optical pumping to prepare the spin states of the implanted atoms and circular dichroism to measure their spin states. Optical pumping signals show order-of-magnitude differences depending on both matrix growth conditions ∗ and atomic species. We measure the ensemble transverse relaxation times (T2) of the spin states ∗ of the alkali-metal atoms. Different alkali species exhibit dramatically different T2 times, ranging 87 2 39 from sub-microsecond coherence times for high mF states of Rb, to ∼ 10 microseconds for K. ∗ These are the longest ensemble T2 times reported for an electron spin system at high densities 16 −3 (n & 10 cm ). To interpret these observations, we develop a theory of inhomogenous broadening of hyperfine transitions of 2S atoms in weakly-interacting solid matrices. Our calculated ensemble transverse relaxation times agree well with experiment, and suggest ways to longer coherence times in future work. I. INTRODUCTION In this work, we compare the optical pumping prop- ∗ erties and ensemble transverse spin relaxation time (T2) Addressable solid-state electron spin systems are of in- for potassium, rubidium, and cesium in solid H2.
    [Show full text]
  • Quantum State Detection of a Superconducting Flux Qubit Using A
    PHYSICAL REVIEW B 71, 184506 ͑2005͒ Quantum state detection of a superconducting flux qubit using a dc-SQUID in the inductive mode A. Lupașcu, C. J. P. M. Harmans, and J. E. Mooij Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands ͑Received 27 October 2004; revised manuscript received 14 February 2005; published 13 May 2005͒ We present a readout method for superconducting flux qubits. The qubit quantum flux state can be measured by determining the Josephson inductance of an inductively coupled dc superconducting quantum interference device ͑dc-SQUID͒. We determine the response function of the dc-SQUID and its back-action on the qubit during measurement. Due to driving, the qubit energy relaxation rate depends on the spectral density of the measurement circuit noise at sum and difference frequencies of the qubit Larmor frequency and SQUID driving frequency. The qubit dephasing rate is proportional to the spectral density of circuit noise at the SQUID driving frequency. These features of the back-action are qualitatively different from the case when the SQUID is used in the usual switching mode. For a particular type of readout circuit with feasible parameters we find that single shot readout of a superconducting flux qubit is possible. DOI: 10.1103/PhysRevB.71.184506 PACS number͑s͒: 03.67.Lx, 03.65.Yz, 85.25.Cp, 85.25.Dq I. INTRODUCTION A natural candidate for the measurement of the state of a flux qubit is a dc superconducting quantum interference de- An information processor based on a quantum mechanical ͑ ͒ system can be used to solve certain problems significantly vice dc-SQUID .
    [Show full text]
  • Quantum Mechanics Department of Physics and Astronomy University of New Mexico
    Preliminary Examination: Quantum Mechanics Department of Physics and Astronomy University of New Mexico Fall 2004 Instructions: • The exam consists two parts: 5 short answers (6 points each) and your pick of 2 out 3 long answer problems (35 points each). • Where possible, show all work, partial credit will be given. • Personal notes on two sides of a 8X11 page are allowed. • Total time: 3 hours Good luck! Short Answers: S1. Consider a free particle moving in 1D. Shown are two different wave packets in position space whose wave functions are real. Which corresponds to a higher average energy? Explain your answer. (a) (b) ψ(x) ψ(x) ψ(x) ψ(x) ψ = 0 ψ(x) S2. Consider an atom consisting of a muon (heavy electron with mass m ≈ 200m ) µ e bound to a proton. Ignore the spin of these particles. What are the bound state energy eigenvalues? What are the quantum numbers that are necessary to completely specify an energy eigenstate? Write out the values of these quantum numbers for the first excited state. sr sr H asr sr S3. Two particles of spins 1 and 2 interact via a potential ′ = 1 ⋅ 2 . a) Which of the following quantities are conserved: sr sr sr 2 sr 2 sr sr sr sr 2 1 , 2 , 1 , 2 , = 1 + 2 , ? b) If s1 = 5 and s2 = 1, what are the possible values of the total angular momentum quantum number s? S4. The energy levels En of a symmetric potential well V(x) are denoted below. V(x) E4 E3 E2 E1 E0 x=-b x=-a x=a x=b (a) How many bound states are there? (b) Sketch the wave functions for the first three levels (n=0,1,2).
    [Show full text]
  • Molecular Column Density Calculation
    Molecular Column Density Calculation Jeffrey G. Mangum National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA [email protected] and Yancy L. Shirley Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA [email protected] May 29, 2013 Received ; accepted – 2 – ABSTRACT We tell you how to calculate molecular column density. Subject headings: ISM: molecules – 3 – Contents 1 Introduction 5 2 Radiative and Collisional Excitation of Molecules 5 3 Radiative Transfer 8 3.1 The Physical Meaning of Excitation Temperature . 11 4 Column Density 11 5 Degeneracies 14 5.1 Rotational Degeneracy (gJ)........................... 14 5.2 K Degeneracy (gK)................................ 14 5.3 Nuclear Spin Degeneracy (gI ).......................... 15 5.3.1 H2CO and C3H2 ............................. 16 5.3.2 NH3 and CH3CN............................. 16 5.3.3 c–C3H and SO2 .............................. 18 6 Rotational Partition Functions (Qrot) 18 6.1 Linear Molecule Rotational Partition Function . 19 6.2 Symmetric and Asymmetric Rotor Molecule Rotational Partition Function . 21 2 7 Dipole Moment Matrix Elements (|µjk| ) and Line Strengths (S) 24 – 4 – 8 Linear and Symmetric Rotor Line Strengths 26 8.1 (J, K) → (J − 1, K) Transitions . 28 8.2 (J, K) → (J, K) Transitions . 29 9 Symmetry Considerations for Asymmetric Rotor Molecules 29 10 Hyperfine Structure and Relative Intensities 30 11 Approximations to the Column Density Equation 32 11.1 Rayleigh-Jeans Approximation . 32 11.2 Optically Thin Approximation . 34 11.3 Optically Thick Approximation . 34 12 Molecular Column Density Calculation Examples 35 12.1 C18O........................................ 35 12.2 C17O........................................ 37 + 12.3 N2H ....................................... 42 12.4 NH3 .......................................
    [Show full text]
  • Introduction to Biomolecular Electron Paramagnetic Resonance Theory
    Introduction to Biomolecular Electron Paramagnetic Resonance Theory E. C. Duin Content Chapter 1 - Basic EPR Theory 1.1 Introduction 1-1 1.2 The Zeeman Effect 1-1 1.3 Spin-Orbit Interaction 1-3 1.4 g-Factor 1-4 1.5 Line Shape 1-6 1.6 Quantum Mechanical Description 1-12 1.7 Hyperfine and Superhyperfine Interaction, the Effect of Nuclear Spin 1-13 1.8 Spin Multiplicity and Kramers’ Systems 1-24 1.9 Non-Kramers’ Systems 1-32 1.10 Characterization of Metalloproteins 1-33 1.11 Spin-Spin Interaction 1-35 1.12 High-Frequency EPR Spectroscopy 1-40 1.13 g-Strain 1-42 1.14 ENDOR, ESEEM, and HYSCORE 1-43 1.15 Selected Reading 1-51 Chapter 2 - Practical Aspects 2.1 The EPR Spectrometer 2-1 2.2 Important EPR Spectrometer Parameters 2-3 2.3 Sample Temperature and Microwave Power 2-9 2.4 Integration of Signals and Determination of the Signal Intensity 2-15 2.5 Redox Titrations 2-19 2.6 Freeze-quench Experiments 2-22 2.7 EPR of Whole Cells and Organelles 2-25 2.8 Selected Reading 2-28 Chapter 3 - Simulations of EPR Spectra 3.1 Simulation Software 3-1 3.2 Simulations 3-3 3.3 Work Sheets 3-17 i Chapter 4: Selected samples 4.1 Organic Radicals in Solution 4-1 4.2 Single Metal Ions in Proteins 4-2 4.3 Multi-Metal Systems in Proteins 4-7 4.4 Iron-Sulfur Clusters 4-8 4.5 Inorganic Complexes 4-17 4.6 Solid Particles 4-18 Appendix A: Rhombograms Appendix B: Metalloenzymes Found in Methanogens Appendix C: Solutions for Chapter 3 ii iii 1.
    [Show full text]
  • Optical Pumping on Rubidium
    Optical Pumping on Rubidium E. Lance (Dated: March 27, 2011) By means of optical pumping the values of gf and nuclear spin for Rubidium were determined. 85 87 85 For Rb gf was found to be .35. For Rb gf was found to be .50. The nuclear spin for Rb was found to be 2.35 with a theoretical value of 2.5, for Rb87 the nuclear spin was found to be 1.5 with a theoretical value of 1.5. Quadratic Zeeman effect resonances were observed around magnetic fields of 6.98 gauss and RF of 4.064 MHz. I. INTRODUCTION Rabi equation: Optical pumping refers to the redistribution of oc- cupied energy states, in thermal equilibrium, inside an ∆W µ ∆W 4M 1=2 W (F; M) = − − j BM± 1+ x+x2 : atom. The redistribution is achieved by polarizing inci- 2(2I + 1) I 2 2I + 1 dent light, therefor, pumping electrons to less absorbent (4) energy states. By confining electrons in less absorbent A plot of Breit-Rabi equation is shown in figure 2, this energy states we can then study the relationship between plot shows how when the magnetic field becomes large, magnetic fields and Zeeman splitting. the energy splittings stop behaving in a linear fashion and a quadratic Zeeman effect can be seen. II. THEORY We will be dealing with Rubidium atoms which can, essentially, be conceived as a hydrogen like single elec- tron atoms. The single valence electron in Rubidium can be described by a total angular momentum vector J which couples the orbital angular momentum L with the spin orbital angular momentum S.
    [Show full text]