DOCSLIB.ORG

Laser Physics I

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Laser Physics I Laser Physics I PH481/581-VTA (Mirov) Spontaneous and Stimulated Transitions Lectures 1-2 Fall 2017 C. Davis, “Lasers and Electro-optics” 6 A laser is an oscillator of optical frequencies that concentrates light energy in spatial, spectral and temporal domains. Excited state LOSER – Truthful Acronym- Light Oscillation by Stimulated Emission of Radiation. Inappropriate!!! LASER - Light Amplification by Stimulated Emission of Radiation Stimulated emission - Stimulated emission Ground state occurs when a traveling photon interacts with an exited atom. During the interaction, the atom will become de-excited and release a photon of the same frequency and 100% Mirror 75 % Mirror direction of the incident photon. Gain medium Lasers have 3 parts: 1. Gain medium – a place for stimulated emmision to occur (crystal, gas, etc.) 2. Positive feedback – means for oscillation (mirrors, diffraction grating, etc.) 3. Source of energy – an incoming energy source which keeps more atoms in the excited state than in the ground state. First Solid State Ruby Laser (Dr. Ted Maiman, Hughes Aircraft 1960) A laser is an oscillator that operates at optical frequencies. These frequencies of operation lie within a spectral region that extends from the very far infrared to the vacuum ultraviolet (VUV) or soft-X-ray region. At the lowest frequencies at which they operate, lasers overlap with the frequency coverage of masers (mm scale). Ti:S/Cr:LiSAF Co:MgF2 Cr:Zn/CdSe Fe:ZnSe/ CdZnTe Athmospheric transmission 0.2 0.5 1 2 5 10 20 µm Cr:YAG Tm:laser Molecular frequencies UV –Middle infrared part of electromagnetic spectrum and tuning ranges of the most common solid state lasers 9 HISTORY A laser is an oscillator of optical frequencies that concentrates light energy in spatial, spectral and temporal domains. In 1917 Albert Einstein, in his paper On the Quantum Theory of Radiation, laid the foundation for the invention of the laser and its predecessor, the maser, by introducing the concepts of probability coefficients (later to be termed 'Einstein coefficients') for the absorption, spontaneous emission, and stimulated emission of electromagnetic radiation. A little bit of history 1917 Albert Einstein. Basic physics of light emission and absorption by atoms and molecules 1928 Rudolph Walther Landenburg confirmed the existence of stimulated emission and negative absorption. 1939, Valentin Fabrikant predicted the actual use of stimulated emission in gas discharges to amplify light. Observation and patenting of negative absorption in 1944. 1954 James Gordon, Herbert Zeigel and Charles Townes proposed and developed maser, a microwave amplifier using stimulated emission. 1954 Aleksandr Prokhorov and Nikolai Basov independently proposed and developed maser. 1960 Theodore H. Maiman –first Ruby laser. 1964, Nikolai Basov, Charles Townes, and Aleksandr Prokhorov received the Nobel Prize for "fundamental work in the field of quantum electronics, which has led to the construction of oscillators and amplifiers based 11 on the maser-laser principle. Academician T. Basiev ZrO2 Lebedev Physics Institute Academician A. Prokhorov explains how laser works Academician V. Osiko inventor of CubicCubic Zirconia Zirconia Gems Gems Light and Electromagnetic Waves Light is one form of electromagnetic radiation. Electromagnetic radiation, which transports energy from point to point at the velocity of light, can be described in terms of both wave and particle "pictures" or "models." This is the famous "wave-particle" duality of all fields or particles in our model of the Universe. In the electromagnetic-wave picture, waves are characterized by their frequency , wavelength , and the velocity of light c, which are inter-related by c = . A propagating electromagnetic wave is characterized by a number of field vectors, which vary in time and space. These include the electric field E (volts/m), the magnetic field H (amps/m), the displacement vector D (coulombs/m2), and the magnetic flux density B (tesla). For a complete description the polarization state of the wave must also be specified. Linearly polarized waves have fixed directions for their field vectors, which do not re-orient themselves as the wave propagates. Circularly or elliptically polarized waves have field vectors that trace out circular, or elliptical, helical paths as the wave travels along. 13 Particle Picture of Light ln the particle picture, electromagnetic energy is carried from point to point as quantized packets of energy called photons. The energy of a photon of frequency is h , where h is Planck's constant, namely 6.626 x10-34 J s. Photons have zero mass, and travel at the velocity of light, but carry both linear and angular momentum. The linear momentum of a photon of wavelength is p = h /, and the angular momentum depends on the equivalent polarization state of the corresponding wave. Circularly polarized photons have angular momentum h /(2 ) = Our everyday experience of "light" generally encompasses only the small part of the electromagnetic spectrum to which the human eye is sensitive, a wavelength range running roughly from 400 nm to 700 nm. The full electromagnetic spectrum, going from low to high frequencies, is divided into radiowaves (0-1 GHz), microwaves (1-300 GHz), infrared waves (of wavelength = 0.7-1000 m; 300 GHz to 430 THz), visible light (= 400- 700 nm), ultraviolet light (= 10-400 nm), X-rays (= 0.1-10 nm), and - rays (< 0.1 nm). 14 Some basic electromagnetic theory 15 16 The polarization state of an electromagnetic wave 17 18 19 20 21 22 23 Bands in crystalline solids 24 Bands in crystalline solids 25 Basic laser structure 26 Amplifier of optical frequencies 27 Spontaneous Emission 28 29 The lineshape function, g() 30 Lineshape function. Example Hz s 31 32 Stimulated Emission 33 The relation between energy density and intensity 34 35 36 37 38 Intensity of a Beam of Electromagnetic Radiation in Terms of Photon Flux 39 Thermal Radiation 40 Blackbody Radiation Incident radiation is completely absorpbed after successive reflections. The radiation emitted by the hole will have a blackbody spectrum 41 Blackbody Radiation – experimental results 1899 first accurate measurements by Lummer and Pringsheim Spectral radiancy ܴ ் ሺߥ ሻ : The spectral distribution of blackbody radiation. ்ܴሺߥሻ݀ߥ represents the emitted energy from a unit area per unit time between ߥ and ߥ൅݀ߥ from a unit area of the surface at absolute temperature T. The total energy emitted per unit time per unit area is called Radiancy RRvdv TT0 Figure of spectral distribution of blackbody radiation 42 The spectral radiancy of blackbody radiation shows that: (1) little power radiation at very low frequency (2) the power radiation increases rapidly as ν increases from very small value. (3) the power radiation is most intense at certain v max for particular temperature. (4)vv max , RvT drops slowly, but continuously as ν increases, and Rv T 0. (5)vmax increases linearly with increasing temperature. (6) the total radiation for all ν ( radiancy RRvdv ) TT0 increases more rapidly than linearly with increasing temperature. 43 Stefan’s and Wien’s Laws 44 Stars as black bodies 45 Classical theory of cavity radiation. Rayleigh-Jeans calculations R-J took as a blackbody the cavity shown in the figure and calculated the energy density inside. The energy density T v is defined as the energy contained in a unit volume of the cavity at temperature T in the frequency interval vvdv to , and is related to the spectral radiancy by the relationship: c Rv v TT4 Rayleigh and Jeans (1900): (1) standing wave with nodes at the metallic surface (2) geometrical arguments count the number of standing waves (3) average total energy depends only on the temperature 46 Rayleigh-Jeans calculations For simplicity, we assume a metallic cubic cavity filled with electromagnetic radiation. The incident and reflected waves combine to form standing waves. one-dimensional cavity: one-dimensional electromagnetic standing wave 2 x Ext(,) E sin( )sin(2 t ) 0 for all time t, nodes at 2x / n , n 0,1,2,3....... x 0 x a 2a n 2a / n nc / 2a standing wave N ( )d : the number of allowed standing wave between ν and ν+dν n (2a / c ) dn (2a / c )d N ( )d 2 dn (4a / c )d two polarization states d (2a / c )( d ) d (2a / c ) 47 0 n Rayleigh-Jeans calculations Three dimensional cavity: we follow the same procedure counting the number of points within a shell of radius r and thickness dr r (2a / c) dr (2a / c)d the volume of concentric shell r r dr 2a 2a 2a 4r 2dr 4 ( )2 v 2 ( )d 4 ( )3 2d c c c 1 8a 3 8V N ( )d 2 4r 2dr 2d 2d 8 c 3 c 3 48 Rayleigh-Jeans calculations: classical kinetic theory the final stage will be to evaluate the average energy contained on each standing wave of frequency v apply classical statistical physics and the law of equipartition energy: For a system of gas molecules in thermal equilibrium at temperature T, the average kinetic energy of a molecules per degree of freedom is kT/2, k 1.38 10 23 joule / oK is Boltzmann constant. average total energy of each standing wave : 2 KT / 2 KT the energy density between ν and ν+dν: 8 2 ( )d kTd Rayleigh-Jeans blackbody radiation T c 3 ultraviolet catastrophe Thermal radiation and Planck’s postulate The real problem in classical derivation of the radiancy spectrum is in the kT assumption. Planck’s theory of cavity radiation Planck’s assumption: ( T , ) and kT, 0 0 the origin of equipartition law kT . Boltzmann distribution P( )
Load more

Recommended publications
  • Physics 305, Fall 2008 Problem Set 8 Due Thursday, December 3
    Physics 305, Fall 2008 Problem Set 8 due Thursday, December 3 1. Einstein A and B coefficients (25 pts): This problem is to make sure that you have read and understood Griffiths 9.3.1. Consider a system that consists of atoms with two energy levels E1 and E2 and a thermal gas of photons. There are N1 atoms with energy E1, N2 atoms with energy E2 and the energy density of photons with frequency ! = (E2 − E1)=~ is W (!). In thermal equilbrium at temperature T , W is given by the Planck distribution: ~!3 1 W (!) = 2 3 : π c exp(~!=kBT ) − 1 According to Einstein, this formula can be understood by assuming the following rules for the interaction between the atoms and the photons • Atoms with energy E1 can absorb a photon and make a transition to the excited state with energy E2; the probability per unit time for this transition to take place is proportional to W (!), and therefore given by Pabs = B12W (!) for some constant B12. • Atoms with energy E2 can make a transition to the lower energy state via stimulated emission of a photon. The probability per unit time for this to happen is Pstim = B21W (!) for some constant B21. • Atoms with energy E2 can also fall back into the lower energy state via spontaneous emission. The probability per unit time for spontaneous emission is independent of W (!). Let's call this probability Pspont = A21 : A21, B21, and B12 are known as Einstein coefficients. a. Write a differential equation for the time dependence of the occupation numbers N1 and N2.
    [Show full text]
  • Inis: Terminology Charts
    IAEA-INIS-13A(Rev.0) XA0400071 INIS: TERMINOLOGY CHARTS agree INTERNATIONAL ATOMIC ENERGY AGENCY, VIENNA, AUGUST 1970 INISs TERMINOLOGY CHARTS TABLE OF CONTENTS FOREWORD ... ......... *.* 1 PREFACE 2 INTRODUCTION ... .... *a ... oo 3 LIST OF SUBJECT FIELDS REPRESENTED BY THE CHARTS ........ 5 GENERAL DESCRIPTOR INDEX ................ 9*999.9o.ooo .... 7 FOREWORD This document is one in a series of publications known as the INIS Reference Series. It is to be used in conjunction with the indexing manual 1) and the thesaurus 2) for the preparation of INIS input by national and regional centrea. The thesaurus and terminology charts in their first edition (Rev.0) were produced as the result of an agreement between the International Atomic Energy Agency (IAEA) and the European Atomic Energy Community (Euratom). Except for minor changesq the terminology and the interrela- tionships btween rms are those of the December 1969 edition of the Euratom Thesaurus 3) In all matters of subject indexing and ontrol, the IAEA followed the recommendations of Euratom for these charts. Credit and responsibility for the present version of these charts must go to Euratom. Suggestions for improvement from all interested parties. particularly those that are contributing to or utilizing the INIS magnetic-tape services are welcomed. These should be addressed to: The Thesaurus Speoialist/INIS Section Division of Scientific and Tohnioal Information International Atomic Energy Agency P.O. Box 590 A-1011 Vienna, Austria International Atomic Energy Agency Division of Sientific and Technical Information INIS Section June 1970 1) IAEA-INIS-12 (INIS: Manual for Indexing) 2) IAEA-INIS-13 (INIS: Thesaurus) 3) EURATOM Thesaurusq, Euratom Nuclear Documentation System.
    [Show full text]
  • Fundamentals of Radiative Transfer
    RADIATIVE PROCESSE S IN ASTROPHYSICS GEORGE B. RYBICKI, ALAN P. LIGHTMAN Copyright 0 2004 WY-VCHVerlag GmbH L Co. KCaA FUNDAMENTALS OF RADIATIVE TRANSFER 1.1 THE ELECTROMAGNETIC SPECTRUM; ELEMENTARY PROPERTIES OF RADIATION Electromagnetic radiation can be decomposed into a spectrum of con- stituent components by a prism, grating, or other devices, as was dis- covered quite early (Newton, 1672, with visible light). The spectrum corresponds to waves of various wavelengths and frequencies, related by Xv=c, where v is the frequency of the wave, h is its wavelength, and c-3.00~10" cm s-I is the free space velocity of light. (For waves not traveling in a vacuum, c is replaced by the appropriate velocity of the wave in the medium.) We can divide the spectrum up into various regions, as is done in Figure 1.1. For convenience we have given the energy E = hv and temperature T= E/k associated with each wavelength. Here h is Planck's constant = 6.625 X erg s, and k is Boltzmann's constant = 1.38 X erg K-I. This chart will prove to be quite useful in converting units or in getting a quick view of the relevant magnitude of quantities in a given portion of the spectrum. The boundaries between different regions are somewhat arbitrary, but conform to accepted usage. 1 2 Fundamentals of Radiatiw Transfer -6 -5 -4 -3 -2 -1 0 1 2 1 I 1 I I I I 1 1 log A (cm) Wavelength I I I I I log Y IHr) Frequency 0 -1 -2 -3 -4 -5 -6 I I I I I I I log Elev) Energy 43 21 0-1 I I 1 I I I log T("K)Temperature Y ray X-ray UV Visible IR Radio Figum 1.1 The electromagnetic spctnun.
    [Show full text]
  • Acknowledgements Acknowl
    1277 Acknowledgements Acknowl. A.1 The Properties of Light by Helen Wächter, Markus W. Sigrist by Richard Haglund The authors thank a number of coworkers for their The author thanks Prof. Emil Wolf for helpful discus- valuable input, notably R. Bartlome, Dr. C. Fischer, sions, and gratefully acknowledges the financial support D. Marinov, Dr. J. Rey, M. Stahel, and Dr. D. Vogler. of a Senior Scientist Award from the Alexander von The financial support by the Swiss National Science Humboldt Foundation and of the Medical Free-Electron Foundation and ETH Zurich for the isotopomer studies Laser program of the Department of Defense (Con- is gratefully acknowledged. tract F49620-01-1-0429) during the preparation of this chapter. by Jürgen Helmcke In writing the chapter on frequency-stabilized lasers, A.4 Nonlinear Optics the author has greatly benefited from fruitful coopera- by Aleksei Zheltikov, Anne L’Huillier, Ferenc Krausz tion and helpful discussions with his colleagues at PTB, We acknowledge the support of the European Com- in particular with Drs. Fritz Riehle, Harald Schnatz, munity’s Human Potential Programme under contract Uwe Sterr, and Harald Telle. Special thanks belong to HPRN-CT-2000-00133 (ATTO) and the Swedish Sci- Dr. Fritz Riehle for his careful and critical reading of the ence Council. manuscript. Part of the work discussed in this chapter was supported by the Deutsche Forschungsgemeinschaft A.5 Optical Materials and Their Properties (DFG) under SFB 407. by Klaus Bonrad The author of Sect. 5.9.2 is grateful to Dr. Thomas C.12 Femtosecond Laser Pulses: Däubler, Dr. Dirk Hertel, and Dr.
    [Show full text]
  • 1 LASERS LASER Is the Acronym for Light Amplification by Stimulated
    1 LASERS LASER is the acronym for Light Amplification by Stimulated Emission of Radiation. Laser is a light source but quite different from conventional light sources. In conventional light sources different atoms emit radiations at different times and in different directions and there is no phase relationship between them Light from an incandescent lamp is an example of incoherent radiation and it is spread over a continuous range of wavelengths The characteristics of laser light : i) The light is coherent which means that waves all exactly in phase with one another It is possible to observe interference effects from two independent lasers ii) The light is monochromatic ( same frequency ) in the visible region of the electromagnetic spectrum. The spread in wavelength () is extremely small. Ordinary incandescent light is spread over a continuous range iii) The beam is very narrow, highly directional and does not diverge . The directionality of the laser beam is expressed in terms of divergence = ( r2 --r1)/ ( D2 --D1) where r2 and r1 are the radii of laser beam spots at distances D2 and D1, respectively. iv)The laser beam is extremely intense. The intensity of laser beam is expressed by number of photons coming out from the laser per second per unit area. It is about 1022 to 1034 photons /sec/sq cm Lasers are based on the concept of amplification of light by stimulated emission of radiation by matter. Einstein predicted this possibility of stimulated emission in 1917 but the first laser was built bt T.A.Maiman in 1960. To explain the working principle of a laser, let us consider the interaction of photons with atoms.
    [Show full text]
  • Astronomy 700: Radiation. 1 Basic Radiation Properties
    Astronomy 700: Radiation. 1 Basic Radiation Properties 1.1 Basic definitions Fundamental importance to Astronomy: Almost exclusive carrier of information Radiation: Energy transport by electromagnetic fields Other forms of energy transport: cosmic rays • stochastic transport (micro: conduction, macro: convection) • gravitational waves • bulk transport (organized flows) • plasma waves • ... • Transport time variability (see section of E&M) → 1.1.1 The spectrum The most natural description of electromagnetic radiation is through Fourier decomposition into waves: f(~r, t) f(~k,ν) (1.1) ↔ where E is some variable describing the radiation field. Question: Why is this so natural? As we will shortly see, electromagnetic radiation naturally decomposes into waves with wave- length λ and frequency ν 1 Often, it is convenient to write the wave vector ~k =2πk/λˆ and angular frequency ω =2πν. In vacuum, group and phase velocity of those waves are equal: 10 1 λν = ∂ω/∂k c 2.99792... 10 cms− (1.2) ≡ ≡ × Fourier decomposition allows us to describe the local spectrum of the radiation at a fixed point in space as the Fourier transform ∞ f f(ν)= dtei2πνtf(t) (1.3) F ≡ Z−∞ and the inverse Fourier transform 1 ∞ i2πνt − f f(t)= dνe− f(ν) (1.4) F ≡ Z−∞ Without going into any details on Lebesque integration, it is worth pointing out the following identity: The inverse Fourier transform of a delta function in frequency is ∞ 1 i2πνt i2πν0t − δ(ν ν )= dνe− δ(ν ν )= e− (1.5) F − 0 − 0 Z−∞ i2πν0 t Thus, the Fourier transform of e− is ∞ i2πν0t i2π(ν ν0)t e− = dte − = δ(ν ν ) (1.6) F − 0 Z−∞ as one would expect for a decomposition into a spectrum of different exponentials.
    [Show full text]
  • Fundamentals of Spectroscopy for Optical Remote Sensing Course
    Fundamentals of Spectroscopy for Optical Remote Sensing Course Outline 2013 (Draft) Part I. Introduction to Quantum Physics Chapter 1. Quantum Concepts and Experimental Facts 1.1. Blackbody Radiation and Planck’s Radiation Law [Textbook “Laser Spectroscopy” Sections 2.1 – 2.4, Corney’s book Section 1.1] 1.2. Photoelectric Effect and Quantized Energy [Textbook Section 4.5.4, Corney’s book Section 1.2] 1.3. Compton Effect and Quantized Momentum 1.4. Hydrogen Spectra and Discrete Energy Levels [Textbook Section 4.1, Corney’s book Section 1.3] 1.5. Bohr’s Model [Corney’s book Sections 1.4-1.8] Chapter 2. Wave-Particle Duality [Dirac’s The Principles of Quantum Mechanics, and Cohen-Tannoudji’s Quantum Mechanics, vol. I and II] 2.1. Wave Behavior of Light 2.2. Single Photon Experiment 2.3. Wave-Particle Duality of Light 2.4. Wave-Particle Duality of Material Particles 2.5. de Broglie Relationship Chapter 3. Basics of Quantum Mechanics (Postulates, Principles, and Mathematic Formalism) [Cohen-Tannoudji’s Quantum Mechanics, vol. I and II] 3.1. Postulates of Quantum Mechanics 3.2. Principle of Superposition of States 3.3. Principle of Motion – Schrödinger Equation 3.4. Principle of Uncertainty – Indeterminacy 3.5. Dirac Notation and Representations 3.6. Solutions to Eigenvalue Equation and Schrödinger Equation Part II. Fundamentals of Atomic Spectroscopy Chapter 4. Introduction to Atomic Structure and Atomic Spectra Chapter 5. Atomic Structure 5.1. Atomic Structure Overview 5.2. Atomic Structure for Hydrogen Atom and Hydrogen-like Ions 1. Hydrogen energy eigenvalues and eigenstate in Coulomb Potential 2.
    [Show full text]
  • Chapter 4 the Quantum Theory of Light
    Chapter 4 The quantum theory of light In this chapter we study the quantum theory of interactions between light and matter. Historically the understanding how light is created and absorbed by atoms was central for development of quantum theory, starting with Planck’s revolutionary idea of energy quanta in the description of black body radiation. Today a more complete description is given by the theory of quantum electrodynamics (QED), which is a part of a more general relativistic quantum field theory (the standard model) that describe the physics of the elementary particles. Even so the the non- relativistic theory of photons and atoms has continued to be important, and has been developed further, in directions that are referred to as quantum optics. We will study here the basics of the non-relativistic description of interactions between photons and atoms, in particular with respect to the processes of spontaneous and stimulated emission. As a particular application we study a simple model of a laser as a source of coherent light. 4.1 Classical electromagnetism The Maxwell theory of electromagnetism is the basis for the classical as well as the quantum description of radiation. With some modifications due to gauge invariance and to the fact that this is a field theory (with an infinite number of degrees of freedom) the quantum theory can be derived from classical theory by the standard route of canonical quantization. In this approach the natural choice of generalized coordinates correspond to the field amplitudes. In this section we make a summary of the classical theory and show how a Lagrangian and Hamiltonian formulation of electromagnetic fields interacting with point charges can be given.
    [Show full text]
  • Numerical Study of the Dynamics of Laser Lineshape and Linewidth M
    Vol. 130 (2016) ACTA PHYSICA POLONICA A No. 3 Numerical Study of the Dynamics of Laser Lineshape and Linewidth M. Eskef∗ Department of Physics, Atomic Energy Commission of Syria, P.O. Box 6091, Damascus, Syria (Received January 28, 2015; revised version May 31, 2016; in final form July 27, 2016) A rate equations model for lasers with homogeneously broadened gain is written and solved in both time and frequency domains. The model is applied to study the dynamics of laser lineshape and linewidth using the example of He–Ne laser oscillating at λ = 632:8 nm. Saturation of the frequency spectrum is found to take much longer time compared to the saturation time of the overall power. The saturated lineshape proves to be Lorentzian, whereas the unsaturated line profile is found to have a Gaussian peak and a Lorentzian tail. Above threshold, our numerical results for the linewidth are in good agreement with the Schawlow–Townes formula. Below threshold, however, the linewidth is found to have an upper limit defined by the spectral width of the pure cavity. Our model provides a unique and powerful tool for studying the dynamics of the frequency spectrum for different kinds of laser systems, and is also applicable for investigating lineshape and linewidth of pulsed lasers. DOI: 10.12693/APhysPolA.130.710 PACS/topics: 42.55.Ah, 42.55.Lt 1. Introduction give no information about the dynamics of lineshape and Laser lineshape and linewidth play a key role in the- linewidth. Second, their way of calculating lineshape and oretical studies related to the fields of resonance ion- linewidth leads through the implicit assumption that the ization spectroscopy (RIS) [1, 2], laser isotope separa- laser field can be represented by a complex amplitude tion [3], as well as resonance ionization mass spectrome- oscillating at the resonance frequency of the pure cav- try (RIMS) [4].
    [Show full text]
  • Stimulated Emission from a Single Excited Atom in a Waveguide
    week ending PRL 108, 143602 (2012) PHYSICAL REVIEW LETTERS 6 APRIL 2012 Stimulated Emission from a Single Excited Atom in a Waveguide Eden Rephaeli1,* and Shanhui Fan2,† 1Department of Applied Physics, Stanford University, Stanford, California 94305, USA 2Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA (Received 6 September 2011; published 3 April 2012) We study stimulated emission from an excited two-level atom coupled to a waveguide containing an incident single-photon pulse. We show that the strong photon correlation, as induced by the atom, plays a very important role in stimulated emission. Additionally, the temporal duration of the incident photon pulse is shown to have a marked effect on stimulated emission and atomic lifetime. DOI: 10.1103/PhysRevLett.108.143602 PACS numbers: 42.50.Ct, 42.50.Gy, 78.45.+h Introduction.—Stimulated emission, first formulated by In recent years, there has been much advancement in Einstein in 1917 [1], is the fundamental physical mecha- the capacity to deterministically generate single photons nism underlying the operation of lasers [2] and optical [25,26] and to control the shape of the single-photon pulse amplifiers [3,4], both of which are of paramount impor- [27,28]. In both waveguide and free space, a single photon, tance in modern technology. In recent years, stimulated by necessity, must exist as a pulse [29]. Therefore, our emission has been studied in a variety of novel systems, study of stimulated emission at the single-photon level including a surface plasmon nanosystem [5], a single mole- reveals important dynamic characteristics of stimulated cule transistor [6], and superconducting transmission lines emission.
    [Show full text]
  • Sitzungsberichte Der Leibniz-Sozietät, Jahrgang 2003, Band 61
    SITZUNGSBERICHTE DER LEIBNIZ-SOZIETÄT Band 61 • Jahrgang 2003 trafo Verlag Berlin ISSN 0947-5850 ISBN 3-89626-462-1 Inhalt Heinz Kautzleben Hans-Jürgen Treder, die kosmische Physik und die Geo- und Kosmoswissenschaften >>> Herbert Hörz Kosmische Rätsel in philosophischer Sicht >>> Karl-Heinz Schmidt Die Lokale Galaxiengruppe >>> Helmut Moritz Epicycles in Modern Physics >>> Armin Uhlmann Raum-Zeit und Quantenphysik >>> Rainer Schimming Über Gravitationsfeldgleichungen 4. Ordnung >>> Werner Holzmüller Energietransfer und Komplementarität im kosmischen Geschehen >>> Klaus Strobach Mach'sches Prinzip und die Natur von Trägheit und Zeit >>> Fritz Gackstatter Separation von Raum und Zeit beim eingeschränkten Dreikörperproblem mit Anwendung bei den Resonanzphänomenen im Saturnring und Planetoidengürtel >>> Gerald Ulrich Fallende Katzen >>> Rainer Burghardt New Embedding of the Schwarzschild Geometry. Exterior Solution >>> Holger Filling und Ralf Koneckis Die Goldpunkte auf der frühbronzezeitlichen Himmelsscheibe von Nebra >>> Joachim Auth Hans-Jürgen Treder und die Humboldt-Universität zu Berlin >>> Thomas Schalk Hans-Jürgen Treder und die Förderung des wissenschaftlichen Nachwuchses >>> Wilfried Schröder Hans-Jürgen Treder und die kosmische Physik >>> Dieter B. Herrmann Quantitative Methoden in der Astronomiegeschichte >>> Gottfried Anger und Helmut Moritz Inverse Problems and Uncertainties in Science and Medicine >>> Ernst Buschmann Geodäsie: die Raum+Zeit-Disziplin im Bereich des Planeten Erde >>> Hans Scheurich Quantengravitation auf der Grundlage eines stringkollektiven Fermionmodells >>> Hans Scheurich Ein mathematisches Modell der Subjektivität >>> Hans-Jürgen Treder Anstelle eines Schlußwortes >>> Leibniz-Sozietät/Sitzungsberichte 61(2003)5, 5–16 Heinz Kautzleben Hans-Jürgen Treder, die kosmische Physik und die Geo- und Kosmoswissenschaften Laudatio auf Hans-Jürgen Treder anläßlich des Festkolloquiums am 02.10.2003 Das Kolloquium ist ein Geburtstagsgeschenk der Leibniz-Sozietät an ihr Mit- glied Hans-Jürgen Treder.
    [Show full text]
  • Arxiv:2006.10084V3 [Quant-Ph] 7 Mar 2021
    Quantum time dilation in atomic spectra Piotr T. Grochowski ,1, ∗ Alexander R. H. Smith ,2, 3, y Andrzej Dragan ,4, 5, z and Kacper Dębski 4, x 1Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland 2Department of Physics, Saint Anselm College, Manchester, New Hampshire 03102, USA 3Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA 4Institute of Theoretical Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland 5Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore (Dated: March 9, 2021) Quantum time dilation occurs when a clock moves in a superposition of relativistic momentum wave packets. The lifetime of an excited hydrogen-like atom can be used as a clock, which we use to demonstrate how quantum time dilation manifests in a spontaneous emission process. The resulting emission rate differs when compared to the emission rate of an atom prepared in a mixture of momentum wave packets at order v2=c2. This effect is accompanied by a quantum correction to the Doppler shift due to the coherence between momentum wave packets. This quantum Doppler shift affects the spectral line shape at order v=c. However, its effect on the decay rate is suppressed when compared to the effect of quantum time dilation. We argue that spectroscopic experiments offer a technologically feasible platform to explore the effects of quantum time dilation. I. INTRODUCTION The purpose of the present work is to provide evi- dence in support of the conjecture that quantum time The quintessential feature of quantum mechanics is dilation is universal.
    [Show full text]