Optical Pumping: a Possible Approach Towards a Sige Quantum Cascade Laser
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Accomplishments in Nanotechnology
U.S. Department of Commerce Carlos M. Gutierrez, Secretaiy Technology Administration Robert Cresanti, Under Secretaiy of Commerce for Technology National Institute ofStandards and Technolog}' William Jeffrey, Director Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment used are necessarily the best available for the purpose. National Institute of Standards and Technology Special Publication 1052 Natl. Inst. Stand. Technol. Spec. Publ. 1052, 186 pages (August 2006) CODEN: NSPUE2 NIST Special Publication 1052 Accomplishments in Nanoteciinology Compiled and Edited by: Michael T. Postek, Assistant to the Director for Nanotechnology, Manufacturing Engineering Laboratory Joseph Kopanski, Program Office and David Wollman, Electronics and Electrical Engineering Laboratory U. S. Department of Commerce Technology Administration National Institute of Standards and Technology Gaithersburg, MD 20899 August 2006 National Institute of Standards and Teclinology • Technology Administration • U.S. Department of Commerce Acknowledgments Thanks go to the NIST technical staff for providing the information outlined on this report. Each of the investigators is identified with their contribution. Contact information can be obtained by going to: http ://www. nist.gov Acknowledged as well, -
Federico Capasso “Physics by Design: Engineering Our Way out of the Thz Gap” Peter H
6 IEEE TRANSACTIONS ON TERAHERTZ SCIENCE AND TECHNOLOGY, VOL. 3, NO. 1, JANUARY 2013 Terahertz Pioneer: Federico Capasso “Physics by Design: Engineering Our Way Out of the THz Gap” Peter H. Siegel, Fellow, IEEE EDERICO CAPASSO1credits his father, an economist F and business man, for nourishing his early interest in science, and his mother for making sure he stuck it out, despite some tough moments. However, he confesses his real attraction to science came from a well read children’s book—Our Friend the Atom [1], which he received at the age of 7, and recalls fondly to this day. I read it myself, but it did not do me nearly as much good as it seems to have done for Federico! Capasso grew up in Rome, Italy, and appropriately studied Latin and Greek in his pre-university days. He recalls that his father wisely insisted that he and his sister become fluent in English at an early age, noting that this would be a more im- portant opportunity builder in later years. In the 1950s and early 1960s, Capasso remembers that for his family of friends at least, physics was the king of sciences in Italy. There was a strong push into nuclear energy, and Italy had a revered first son in En- rico Fermi. When Capasso enrolled at University of Rome in FREDERICO CAPASSO 1969, it was with the intent of becoming a nuclear physicist. The first two years were extremely difficult. University of exams, lack of grade inflation and rigorous course load, had Rome had very high standards—there were at least three faculty Capasso rethinking his career choice after two years. -
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. -
Electronic Supplementary Information: Low Ensemble Disorder in Quantum Well Tube Nanowires
Electronic Supplementary Material (ESI) for Nanoscale. This journal is © The Royal Society of Chemistry 2015 Electronic Supplementary Information: Low Ensemble Disorder in Quantum Well Tube Nanowires Christopher L. Davies,∗a Patrick Parkinson,b Nian Jiang,c Jessica L. Boland,a Sonia Conesa-Boj,a H. Hoe Tan,c Chennupati Jagadish,c Laura M. Herz,a and Michael B. Johnston.a‡ (a) 3.950 nm (b) GaAs-QW 2.026 nm 2.181 nm 4.0 nm 3.962 nm 50 nm 20 nm GaAs-core Fig. S1 TEM image of top of B50 sample Fig. S2 TEM image of bottom of B50 sample S1 TEM Figure S1(a) corresponds to a low magnification bright field TEM image of a representative cross-section of the sample B50. The thickness of the GaAs QW has been measured in different regions. S2 1D Finite Square Well Model The variations in thickness are found to be around 4 nm and 2 For a semiconductor the Fermi-Dirac distribution for electrons in nm in the edges and in the facets, respectively, confirming the the conduction band and holes in the valence band is given by, disorder in the GaAs QW. In the HR-TEM image performed in 1 one of the edges of the nanowire cross section, figure S1(b), the f = ; (1) e,h exp((E − Ec,v) ) + 1 variation in the QW thickness (marked by white dashed lines) f b between the edge and the facets is clearly visible. c,v where b = 1=kBT, T is the electron temperature and Ef is the Figures S2 and S3 are additional TEM images of sample B50 Fermi energies of the electrons and holes. -
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. -
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. -
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. -
Optical Physics of Quantum Wells
Optical Physics of Quantum Wells David A. B. Miller Rm. 4B-401, AT&T Bell Laboratories Holmdel, NJ07733-3030 USA 1 Introduction Quantum wells are thin layered semiconductor structures in which we can observe and control many quantum mechanical effects. They derive most of their special properties from the quantum confinement of charge carriers (electrons and "holes") in thin layers (e.g 40 atomic layers thick) of one semiconductor "well" material sandwiched between other semiconductor "barrier" layers. They can be made to a high degree of precision by modern epitaxial crystal growth techniques. Many of the physical effects in quantum well structures can be seen at room temperature and can be exploited in real devices. From a scientific point of view, they are also an interesting "laboratory" in which we can explore various quantum mechanical effects, many of which cannot easily be investigated in the usual laboratory setting. For example, we can work with "excitons" as a close quantum mechanical analog for atoms, confining them in distances smaller than their natural size, and applying effectively gigantic electric fields to them, both classes of experiments that are difficult to perform on atoms themselves. We can also carefully tailor "coupled" quantum wells to show quantum mechanical beating phenomena that we can measure and control to a degree that is difficult with molecules. In this article, we will introduce quantum wells, and will concentrate on some of the physical effects that are seen in optical experiments. Quantum wells also have many interesting properties for electrical transport, though we will not discuss those here. -
Schrödinger Equation: (Time Independent) Hψ = Eψ This Is a Differential Eigenvalue Equation
Physics and Material Science of Semiconductor Nanostructures PHYS 570P Prof. Oana Malis Email: [email protected] Lecture 9 Review of quantum mechanics, statistical physics, and solid state Band structure of materials Semiconductor band structure Semiconductor nanostructures Ref. Davies Chapter 1 Quantum Mechanics (QM) • The Schrödinger Equation: (time independent) Hψ = Eψ This is a differential eigenvalue equation. H Hamiltonian operator for the system (energy operator) E Energy eigenvalue, ψ wavefunction Particles are QM waves! |ψ|2 probability density; ψ is a function of ALL coordinates of ALL particles in the problem! One Page Elementary Quantum Mechanics & Solid State Physics Review • Quantum Mechanics of a Free Electron: 2 – The energies are continuous: E = (k) /(2mo) (1d, 2d, or 3d) – The wavefunctions are traveling waves: ikx ikr ψk(x) = A e (1d) ψk(r) = A e (2d or 3d) • Solid State Physics: Quantum Mechanics of an Electron in a Periodic Potential in an infinite crystal : – The energy bands are (approximately) continuous: E= Enk – At the bottom of the conduction band or the top of the valence band, in the effective mass approximation, the bands can be written: 2 Enk (k) /(2m*) – The wavefunctions are Bloch Functions = traveling waves: ikr Ψnk(r) = e unk(r); unk(r) = unk(r+R) QM Review: The 1d (infinite) Potential Well (“particle in a box”) In all QM texts!! Consider the case of a particle in a 1-D potential well, with width L e infinite barriers V(x) = 0 for 0 x L V(x) = for x<0, x>L Schrödinger equation Inside the well -
Stationary States in a Potential Well- H.C
FUNDAMENTALS OF PHYSICS - Vol. II - Stationary States In A Potential Well- H.C. Rosu and J.L. Moran-Lopez STATIONARY STATES IN A POTENTIAL WELL H.C. Rosu and J.L. Moran-Lopez Instituto Potosino de Investigación Científica y Tecnológica, SLP, México Keywords: Stationary states, Bohr’s atomic model, Schrödinger equation, Rutherford’s planetary model, Frank-Hertz experiment, Infinite square well potential, Quantum harmonic oscillator, Wilson-Sommerfeld theory, Hydrogen atom Contents 1. Introduction 2. Stationary Orbits in Old Quantum Mechanics 2.1. Quantized Planetary Atomic Model 2.2. Bohr’s Hypotheses and Quantized Circular Orbits 2.3. From Quantized Circles to Elliptical Orbits 2.4. Experimental Proof of the Existence of Atomic Stationary States 3. Stationary States in Wave Mechanics 4. The Infinite Square Well: The Stationary States Most Resembling the Standing Waves on a String 3.1. The Schrödinger Equation 3.2. The Dynamical Phase 3.3. The Schrödinger Wave Stationarity 3.4. Stationary Schrödinger States and Classical Orbits 3.5. Stationary States as Sturm-Liouville Eigenfunctions 5. 1D Parabolic Well: The Stationary States of the Quantum Harmonic Oscillator 5.1. The Solution of the Schrödinger Equation 5.2. The Normalization Constant 5.3. Final Formulas for the HO Stationary States 5.4. The Algebraic Approach: Creation and Annihilation Operators 5.5. HO Spectrum Obtained from Wilson-Sommerfeld Quantization Condition 6. The 3D Coulomb Well: The Stationary States of the Hydrogen Atom 6.1. The Separation of Variables in Spherical Coordinates 6.2. The Angular Separation Constants as Quantum Numbers 6.3. Polar andUNESCO Azimuthal Solutions Set Together – EOLSS 6.4. -
New Developments in Gaas-Based Quantum Cascade Lasers
New Developments in GaAs-based Quantum Cascade Lasers Chris Neil Atkins PhD Thesis October 2013 Department of Physics and Astronomy Abstract This thesis presents a study of the design and optimisation of gallium-arsenide-based quantum cascade lasers (QCLs). Traditionally, the optical and electrical performance of these devices has been inferior in comparison to QCLs that are based on the InP material system, due mainly to the limitations imposed on performance by the intrinsic material properties of GaAs. In an attempt to improve the performance of GaAs QCLs, indium-gallium-phosphide and indium-aluminium-phosphide have been used as the waveguide cladding layers in several new QCL designs. These two materials combine low waveguide losses with a high confinement of the laser optical mode, and are easily integrated into typical GaAs QCL structures. Devices containing a double-phonon relaxation active region design have been combined with an InAlP waveguide, with the result being that the lowest threshold currents yet observed for a GaAs-based QCL have been observed - 2.1kA/cm2 and 4.0kA/cm2 at 240K and 300K respectively. Accompanying these low threshold currents however, were large operating voltages approaching 30V at room-temperature and 60V at 80K. These voltages were responsible for a high rate of device failure due to overheating. In an attempt to address this situation, two transitional layer (TL) designs were applied at the QCL GaAs/InAlP interfaces in order to aid electron flow at these points. The addition of the TLs resulted in a lowering of operating voltage by ~12V and 30V at 300K and 240K respectively, however threshold current density increased to 5.1kA/cm2 and 2.7kA/cm2 at the same temperatures. -
Infinite (And Finite) Square Well Potentials Announcements: Homework Set #8 Is Posted This Afternoon and Due on Wednesday
Infinite (and finite) square well potentials Announcements: Homework set #8 is posted this afternoon and due on Wednesday. Note I received an email from a student that problem 5c had a typo and should say exp(-iEt/ hbar). I corrected the homework set this morning. Second Midterm is Thursday, Nov. 7 – 7:30 – 9:00 pm in this room. http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 1 Some wave function rules ψ(x) and dψ(x)/dx must be continuous These requirements are used to match boundary conditions. |ψ(x)|2 must be properly normalized This is necessary to be able to interpret |ψ(x)|2 as the probability density This is required to be able to normalize ψ(x) http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 2 Infinite square well (particle in a box) solution After applying boundary conditions we found and which gives us an energy of Things to notice: Energies are quantized. Energy Minimum energy E1 is not zero. 16E1 n=4 Consistent with uncertainty principle. x is between 0 and a so Δx~a/2. Since ΔxΔp≥ħ/2, must be uncertainty 9E1 n=3 in p. But if E=0 then p=0 so Δp=0, violating the uncertainty principle. 4E1 n=2 When a is large, energy levels get E n=1 closer so energy becomes more like 1 V=0 a x continuum (like classical result). 0 http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 3 Finishing the infinite square well We need to normalize ψ(x).