DOCSLIB.ORG

Spontaneous Emission Stimulated Emission E E E E Before After

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Spontaneous Emission Stimulated Emission E E E E Before After LECTURE 8 How a Laser Works Laser is an acroynm that stands for Light Ampli cation by Stimulated Emission of Radiation. A maser is the corresp onding system for microwaves. To understand how a laser works, consider an atom with 2 energy levels and one electron. Let's call this a two level system. Let E be the energy of the ground state and E be the energy of 1 2 the excited state. Supp ose the electron is in the lower energy state. If the atom absorbs a photon of frequency = E E =h, the electron makes a transition to the excited 2 1 state. From there it can decaybacktothelower state by emitting a photon of frequency = E E =h. There are 2 typ es of emission pro cesses. In stimulated emission, 2 1 an incident photon of frequency stimulates the atom to make a transition from the higher state to the lower energy state and emit another photon of frequency that is in phase with the rst photon. The second photon is in phase b ecause the rst photon causes the electron charge of the atom to oscillate in phase with it and this oscillation causes the second photon to b e in phase with the rst. So one photon comes in and two photons leave. In sp ontaneous emission the excited atom sp ontaneously decays to the lower energy state and emits a photon of frequency . One can regard this as emission stimulated by zero pointvacuum uctuations of the electromagnetic eld. Before After E 2 E 1 Stimulated Emission E 2 E 1 Spontaneous Emission Now supp ose we start with an inverted p opulation of atoms which are each in their excited state. This can b e accomplished by optically pumping the atoms into their excited state with incident radiation. Now an incident photon of frequency = E E =h, 2 1 which may have b een pro duced by sp ontaneous emission, stimulates one of the excited atoms to emit a photon in phase with it. These two photons of frequency then pro duce stimulated emission from other excited atoms. If we put the system in a cavity with re ecting walls at the ends, the photons bounce back and forth, gaining more and more cohorts via stimulated emission. If one of the walls is slightly transparent, rather than b eing totally re ecting, part of this coherent mono chromatic b eam escap es as a laser beam. Mono chromatic means the photons are all of one frequency and coherent means that the photons are all in phase. The fact that the photons are in phase means that the amplitudes of the electromagnetic waves add constructively, and this enhances the intensity and energy density concentration of the b eam. In fact a laser with less power than a typical light bulb can burn a hole in a metal plate. In contrast, white light is incoherent and nonmono chromatic b ecause there is no correlation in the times that the atoms make transitions. Let's make this more quantitative. Consider a set of twolevel systems atoms in the presence of electromagnetic radiation. Let N be the number of photons of frequency . Let there be n atoms in energy state E and n atoms in energy state E , where 1 1 2 2 E >E and =E E =h. The rate of absorption of photons is prop ortional to the 2 1 2 1 numb er of photons of frequency and to the concentration of atoms in state 1 whichcan absorb photons: ! dN = Bn N 1 1 dt absorption where B is a constant of prop ortionality that dep ends on the prop erties of states 1 and 2. The minus sign indicates that the photon density decreases due to absorption by the atoms. The rate of stimulated emission is prop ortional to the number of photons of frequency and to the concentration of atoms in state 2 which can be induced to emit photons of frequency : ! dN =+Bn N 2 2 dt stimulated emission The plus sign indicates that emission increases the number of photons. Sp ontaneous emission can o ccur even when there are no photons and the corresp onding rate is ! dN = An 3 2 dt sp ontaneous emission So the total rate of change of the number of photons is the sum of all these pro cesses. ! dN = B n n N + An 4 2 1 2 dt total This is an example of a rate equation. It tells us the rate of change of a p opulation due to emission and absorption. A and B are called the Einstein co ecients. 2 Let us consider the steady state where the system is in equilibrium. This is not the case for a laser, but let's lo ok at it anyway. In steady state the number of photons do es not change with time, so ! dN =0 5 dt total or B n n N + An =0 6 2 1 2 Solving for N , we obtain A N = 7 n 1 1 B n 2 In equilibrium the ratio of the p opulations of the excited and lower states is given bythe Boltzmann probability distribution n 2 E E 2 1 = e 8 n 1 or n 1 E E 2 1 = e 9 n 2 Plugging this into 7 yields A 10 N = E E 2 1 B e 1 On the other hand, we already know what the distribution is for photons in equilibrium. It's just the Planck distribution that wederived when we discussed black b o dy radiation 1 1 = 11 N = h E E 2 1 e 1 e 1 Comparing 10 and 11 yields A = B 12 Thus the co ecient in the sp ontaneous emission rate is exactly the same as in the induced emission rate; the total emission rate is ! dN = Bn N +1 13 2 dt total emission Note that the form of the emission rate was deduced without knowing the actual value of B ;onlydetailedbalancing arguments were used. Detailed balancing is simply the idea that in equilibrium the amount of energy absorb ed and emitted must b e equal. Now let's consider the case of the laser. This is not an equilibrium situation. The ratio of the emission and absorption of photons is given by dN A + BN n dt 2 emission = 14 dN BN n 1 dt absorption 3 In equilibrium dN dt emission =1 15 dN dt absorption but in a laser we have p opulation inversion n >n and 2 1 dN n dt 2 emission 16 dN n 1 dt absorption So when the p opulation is inverted, the rate of emission is greater than the rate of absorption. This means that the applied radiation of frequency =E E =h will b e 2 1 ampli ed in intensity b ecause of stimulated emission with much more radiation emerging than entering. Of course, such a pro cess will reduce the p opulation of the upp er state until equilibrium is established. In order to sustain the pro cess, p opulation inversion must be maintained. One common way to do this is via optical pumping. As an example let's consider a solid state laser that op erates with a ruby crystal in which some of the Al atoms in the Al O molecules are replaced by Cr atoms. These 2 3 \impurity" chromium atoms account for the laser action. The energy level scheme of chromium has 3 energy levels E <E <E . 2 3 E 1 3 Spontaneous Emission E 2 Pumping Stimulated Radiation Emission E 1 The energy di erence E E corresp onds to a wavelength of ab out 5500 A. Optical 3 1 pumping o ccurs in the following way. Pumping radiation with a wavelength 5500 A is sent in and absorb ed by Cr atoms which make a transition from their ground state 8 to the level with energy E . This is a short lived state lifetime is ab out 10 seconds 3 which decays sp ontaneously to the intermediate excited state which is long lived ab out 3 3 10 seconds. The net result of the optical pumping is to invert the p opulation such that n > n . So when a Cr atom makes a transition from state 2 to state 1, 2 1 it emits a photon of wavelength 6943 A which will stimulate transitions in other Cr atoms. Because n >n , emission dominates over absorption and an intensi ed coherent 2 1 mono chromatic b eam results. The ruby laser consists of a cylindrical ro d with parallel, 4 optically at re ecting ends, one of which is only partly re ecting. The laser b eam exits through this partially re ecting end. The emitted photons that do not travel along the axis escap e through the sides b efore they are able to cause much stimlated emission. But those photons that move exactly in the direction of the axis are re ected several times, and they are capable of stimulating emission rep eatedly. Thus the numb er of photons is built up rapidly, those escaping from the partially re ecting end giving a unidirectional beam of great intensity and sharply de ned wavelength. There are many kinds of lasers{gas lasers, liquid lasers, semiconductor lasers, and solid state lasers made from crystals. These cover a wide range of the electromagnetic sp ectrum. Lasers have a wide range of uses including medical physics, biophysics, com- munications, and data storage CD players. For example, semiconductor lasers that are the size of a grain of sand are used to send signals down optic b ers.
Load more

Recommended publications
  • Amplified and Directional Spontaneous Emission from Arbitrary Composite
    PHYSICAL REVIEW B 93, 125415 (2016) Amplified and directional spontaneous emission from arbitrary composite bodies: A self-consistent treatment of Purcell effect below threshold Weiliang Jin,1 Chinmay Khandekar,1 Adi Pick,2 Athanasios G. Polimeridis,3 and Alejandro W. Rodriguez1 1Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA 2Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 3Skolkovo Institute of Science and Technology, Moscow, Russia (Received 19 October 2015; revised manuscript received 22 December 2015; published 9 March 2016) We study amplified spontaneous emission (ASE) from wavelength-scale composite bodies—complicated arrangements of active and passive media—demonstrating highly directional and tunable radiation patterns, depending strongly on pump conditions, materials, and object shapes. For instance, we show that under large enough gain, PT symmetric dielectric spheres radiate mostly along either active or passive regions, depending on the gain distribution. Our predictions are based on a recently proposed fluctuating-volume-current formulation of electromagnetic radiation that can handle inhomogeneities in the dielectric and fluctuation statistics of active media, e.g., arising from the presence of nonuniform pump or material properties, which we exploit to demonstrate an approach to modeling ASE in regimes where Purcell effect (PE) has a significant impact on the gain, leading to spatial dispersion and/or changes in power requirements. The nonlinear feedback of PE on the active medium, captured by the Maxwell-Bloch equations but often ignored in linear formulations of ASE, is introduced into our linear framework by a self-consistent renormalization of the (dressed) gain parameters, requiring the solution of a large system of nonlinear equations involving many linear scattering calculations.
    [Show full text]
  • Experimental Detection of Photons Emitted During Inhibited Spontaneous Emission
    Invited Paper Experimental detection of photons emitted during inhibited spontaneous emission David Branning*a, Alan L. Migdallb, Paul G. Kwiatc aDepartment of Physics, Trinity College, 300 Summit St., Hartford, CT 06106; bOptical Technology Division, NIST, Gaithersburg, MD, 20899-8441; cDepartment of Physics, University of Illinois,1110 W. Green St., Urbana, IL 61801 ABSTRACT We present an experimental realization of a “sudden mirror replacement” thought experiment, in which a mirror that is inhibiting spontaneous emission is quickly replaced by a photodetector. The question is, can photons be counted immediately, or only after a retardation time that allows the emitter to couple to the changed modes of the cavity, and for light to propagate to the detector? Our results, obtained with a parametric downconverter, are consistent with the cavity QED prediction that photons can be counted immediately, and are in conflict with the retardation time prediction. Keywords: inhibited spontaneous emission, cavity QED, parametric downconversion, quantum interference 1. INTRODUCTION When an excited atom is placed near a mirror, it is allowed to radiate only into the set of electromagnetic modes that satisfy the boundary conditions imposed by the mirror. The result is enhancement or suppression of the spontaneous emission rate, depending on the structure of the allowed modes. In particular, if the atom is placed between two mirrors separated by a distance smaller than the shortest emission wavelength, it will not radiate into the cavity [1-3]. This phenomenon, known as inhibited spontaneous emission, seems paradoxical; for if the atom is prohibited from emitting a photon, then how can it “know” that the cavity is there? One explanation is that the vacuum fluctuations which produce spontaneous emission cannot exist in the cavity, because the modes themselves do not exist [1].
    [Show full text]
  • The Concept of the Photon—Revisited
    The concept of the photon—revisited Ashok Muthukrishnan,1 Marlan O. Scully,1,2 and M. Suhail Zubairy1,3 1Institute for Quantum Studies and Department of Physics, Texas A&M University, College Station, TX 77843 2Departments of Chemistry and Aerospace and Mechanical Engineering, Princeton University, Princeton, NJ 08544 3Department of Electronics, Quaid-i-Azam University, Islamabad, Pakistan The photon concept is one of the most debated issues in the history of physical science. Some thirty years ago, we published an article in Physics Today entitled “The Concept of the Photon,”1 in which we described the “photon” as a classical electromagnetic field plus the fluctuations associated with the vacuum. However, subsequent developments required us to envision the photon as an intrinsically quantum mechanical entity, whose basic physics is much deeper than can be explained by the simple ‘classical wave plus vacuum fluctuations’ picture. These ideas and the extensions of our conceptual understanding are discussed in detail in our recent quantum optics book.2 In this article we revisit the photon concept based on examples from these sources and more. © 2003 Optical Society of America OCIS codes: 270.0270, 260.0260. he “photon” is a quintessentially twentieth-century con- on are vacuum fluctuations (as in our earlier article1), and as- Tcept, intimately tied to the birth of quantum mechanics pects of many-particle correlations (as in our recent book2). and quantum electrodynamics. However, the root of the idea Examples of the first are spontaneous emission, Lamb shift, may be said to be much older, as old as the historical debate and the scattering of atoms off the vacuum field at the en- on the nature of light itself – whether it is a wave or a particle trance to a micromaser.
    [Show full text]
  • PAM Dirac and the Discovery of Quantum Mechanics
    P.A.M. Dirac and the Discovery of Quantum Mechanics Kurt Gottfried∗ Laboratory for Elementary Particle Physics Cornell University, Ithaca New York 14853 Dirac’s contributions to the discovery of non-relativist quantum mechanics and quantum elec- trodynamics, prior to his discovery of the relativistic wave equation, are described. 1 Introduction Dirac’s most famous contributions to science, the Dirac equation and the prediction of anti-matter, are known to all physicists. But as I have learned, many today are unaware of how crucial Dirac’s earlier contributions were – that he played a key role in the discovery and development of non- relativistic quantum mechanics, and that the formulation of quantum electrodynamics is almost entirely due to him. I therefore restrict myself here to his work prior to his discovery of the Dirac equation in 1928.1 Dirac was one of the great theoretical physicist of all times. Among the founders of ‘mod- ern’ theoretical physics, his stature is comparable to that of Bohr and Heisenberg, and surpassed only by Einstein. Dirac had an astounding physical intuition combined with the ability to invent new mathematics to create new physics. His greatest papers are, for long stretches, argued with inexorable logic, but at crucial points there are critical, illogical jumps. Among the inventors of quantum mechanics, only deBroglie, Heisenberg, Schr¨odinger and Dirac wrote breakthrough papers that have such brilliantly successful long jumps. Dirac was also a great stylist. In my view his book arXiv:1006.4610v1 [physics.hist-ph] 23 Jun 2010 The Principles of Quantum Mechanics belongs to the great literature of the 20th Century; it has an austere tone that reminds me of Kafka.2 When we speak or write quantum mechanics we use a language that owes a great deal to Dirac.
    [Show full text]
  • 4.4. Spontaneous Emission
    4-19 4.4. SPONTANEOUS EMISSION What doesn’t come naturally out of semi-classical treatments is spontaneous emission—transitions when the field isn’t present. To treat it properly requires a quantum mechanical treatment of the field, where energy is conserved, such that annihilation of a quantum leads to creation of a photon with the same energy. We need to treat the particles and photons both as quantized objects. You can deduce the rates for spontaneous emission from statistical arguments (Einstein). For a sample with a large number of molecules, we will consider transitions between two states m and n with EEmn> . The Boltzmann distribution gives us the number of molecules in each state. −ωmn /kT NNmn/ = e (4.71) For the system to be at equilibrium, the time-averaged transitions up Wmn must equal those down Wnm . In the presence of a field, we would want to write for an ensemble ? NBUmnm()ωω mn= NBU nmn () mn (4.72) but clearly this can’t hold for finite temperature, where NNmn< , so there must be another type of emission independent of the field. So we write WWnm= mn (4.73) NAm() nm+= BU nm()ωω mn NBU n mn() mn Andrei Tokmakoff, MIT Department of Chemistry, 5/19/2005 4-20 If we substitute the Boltzmann equation into this and use Bmn= B nm , we can solve for Anm : ωmn /kT ABUnm=− nm(ω mn )( e 1) (4.74) For the energy density we will use Planck’s blackbody radiation distribution: ω3 1 U ()ω = (4.75) π 23c ωmn /kT −1 e U ω Nω Uω is the energy density per photon of frequency ω.
    [Show full text]
  • Detailed Description of Spontaneous Emission
    1 Detailed description of spontaneous emission M. V. Guryev Author is not affiliated with any institution. Home address: Shipilovskaya st., 62-1-172, 115682-RU, Moscow, Russian Federation E-mail: [email protected] The wave side of wave-photon duality, describing light as an electromagnetic field (EMF), is used in this article. EMF of spontaneous light emission (SE) of laser ex- cited atom is calculated from first principles for the first time. This calculation is done using simple method of atomic quantum electrodynamics. EMF of SE is calcu- lated also for three types of polyatomic light sources excited by laser. It is shown that light radiated by such sources can be coherent, which explains recent experi- ments on SE of laser excited atoms. Small sources of SE can be superradiant, which also conforms to experiment. Thus SE is shown not to be a random event itself. Random properties of natural light are simply explained as a result of thermal exci- tation randomness without additional hypotheses. EMF of SE is described by simple complex functions, but not real ones. Key words: classical optics; spontaneous emission; coherence; superradiance; small sources. 1. Introduction Spontaneous emission (SE) of an excited atom is the simplest example of a process, where atom interaction with electromagnetic field (EMF) takes place. The first theory of SE was formulated by Dirac in 1927 and further by Weiskopff in 1930. The modern version of this theory see, e. g., [1, 2]. This theory describes photon emission and is now accepted as a basic one. The main result of this theory is the well known formula for the probability of photon emission event.
    [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]
  • RELATIVISTIC THEORY of SPONTANEOUS EMISSION Dipole Calculations
    INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS RELATIVISTTC THEORY OF SPONTANEOUS EMISSION A.O. Barut and INTERNATIONAL ATOMIC ENERGY Y.I. Salamin AGENCY UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION 1987 MIRAMARE-TRIESTE IC/87/S ABSTRACT We derive a formula for the relativistic decay rates in atoms in a formula- International Atomic Energy Agency tion of Quantum Electrodynamics based upon the electron's self energy. Relativis- and tic Coulomb wavefunctions are used, the full spin calculation is carried out and the United Nations Educational Scientific and Cultural Organization dipole approximation is not employed. The formula has the correct nonreiativistic limit and is used here for calculating the decay rates in Hydrogen and Muonium for the transitions IP —^ lSi and 2Si —* lSi. The results for Hydrogen are: INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS T(2P -> 15A) = 6.2649 x 108a~l and T{2Si. -• lSi) = 2.4946 x lO"6*"1. Our result for the 2P —* lSi transition rate is in perfect agreement with the best non- reiativistic calculations as well as with the results obtained from the best known radiative decay lifetime measurements. As for the Hydrogen 2S^ —> IS^ decay rate, the result obtained here is also in good agreement with the best known magnetic RELATIVISTIC THEORY OF SPONTANEOUS EMISSION dipole calculations. For Muonium we get: T{2P -> IS^) = 6.2382 x lO8^"1 and 15^) = 2.3997 x lO"6*"1. A.O. Barut ** and Y.I. Salamin ** International Centre for Theoretical Physics, Trieste, Italy. MIRAMARE - TRIESTE June 1987 * To be submitted for publication. ** On leave of absence from: Physics Department, University of Colorado, Boulder, CO BO3O9, USA.
    [Show full text]
  • On Misinterpretation of the Casimir Effect As a Result of the Decrease In
    “Bose minus Einstein” and other examples of misattribution V. Hushwater a) 70 St. Botolph St, apt. 401, Boston, MA 02116 Following the paper of J.D. Jackson on a false attribution of discoveries, equations, and methods [Am. J. Phys. 76, 704-719 (2008)] I consider examples, in which some of independent discoverers are forgotten, and in other cases discoveries and effects are attributed to people who did not discover them at all. I also discuss in brief why that happens and how physics community can avoid this. I. INTRODUCTION In an interesting paper1 J.D. Jackson gave a few examples on a false attribution of discoveries, equations, and methods to people who had not done them first. Following that paper I consider below examples, in which some of independent discoverers are forgotten, and in other cases discoveries and effects are attributed to people who did not discover them at all! I conclude by discussing in brief why that happens and how physics community can avoid this. II. EXAMPLES WHEN SOME OF INDEPENDENT DISCOVERERS ARE FORGOTTEN A. Landau levels The energy levels of a nonrelativistic charged particle in homogeneous magnetic field were determined by L. Landau in 1930. Now they are called Landau levels. But he has predecessors: in 1928 V. Fock solved a problem of an oscillator in external magnetic field and I. Rabi solved a problem of a Dirac electron in external magnetic field. Also, J. Frenkel’ and M. Bronstein solved in 1930 the Schrödinger eq. of a nonrelativistic charged particle in homogeneous magnetic field independently from L. Landau, see a paper of V.L.
    [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]