EE 485 Introduction to Photonics Photon Optics and Photon Statistics
|
|
- Betty Ellis
- 5 years ago
- Views:
Transcription
1 Itroductio to Photoics Photo Optics ad Photo Statistics
2 Historical Origi Photo-electric Effect (Eistei, 905) Clea metal V stop Differet metals, same slope Light I Slope h/q ν c/λ Curret flows for λ < λ 0, for ay itesity of light pply stoppig potetial Higher voltage required for shorter λ The slopes are idepedet of light itesity, but curret is proportioal to light itesity. h ν qv + W E ph hν Eergy of light (Kietic eergy of the electro) + (Work fuctio) Eergy of quatum of light (Smallest eergy uit): Photo Lih Y. Li
3 Photo Eergy E hν ω h h / π 34 Joule Sec : Plak s costat λ ( µ m).4 E (ev) Lih Y. Li 3
4 Photo Positio Heiseberg s Ucertaity Priciple ( z) ( p) 4 Photo positio caot be determied exactly. It eeds to be determied with probability. p ( r) d I( r) d Example: () Photo positio probability i a Gaussia beam. () Trasmissio of a sigle photo through a beam-splitter. () () Lih Y. Li 4
5 Plae wave Photo mometum Photo Mometum E( r, t) exp( jk r)exp( jπνt) eˆ p k p k h λ Radiatio Pressure p h λ Force: Pressure: p t Force rea h λ t N h λ Example: Photo-mometum recoil versus thermal velocity. Lih Y. Li 5
6 Optical Tweezer Forces arisig from mometum chage of the light F P t a I (a-b) q p Out (c-d) p q b p P B Q 3. µm Movig a DN-tethered bead with a optical tweezer (5 mw) ( q pp Q c C Resultat gradiet force D d E.g., λ 064 m, P 00 mw, diameter of polystyree sphere 5 µm F 3.8 x 0 - N. shki, et al., Observatio of radiatio pressure trappig of particles by alteratig laser beams, Phys. Rev. Lett., V. 54, p , µm sphere ( Lih Y. Li 6
7 7 Lih Y. Li Photo Polarizatio Liearly Polarized Photos ( ) ( ) y x y y x x y x y x t j jkz t t j jkz t + ω + ω +, ) )exp( ˆ')exp( ˆ' ( ), ( ) )exp( ˆ)exp( ˆ ( ), ( ' ' ' ' y x r E y x r E Photo polarized alog x-directio Example: Trasmissio of a liearly-polarized photo through a polarizer
8 Quatum Commuicatio Secured Iformatio Trasmissio with Sigle Photos Qubit: α 0>+β > lice Bob Codig Ecryptio (Determie α ad β) Eve Without the key give by lice, obtais the wrog result with high probability, ad destroys the qubit. With the key give by lice, obtais the same result as lice s. Polarizatio codig lice: : 0> : > Bob: Measure with or basis Lih Y. Li 8
9 Photo Polarizatio Circularly Polarized Photos ad Photo Spi E( r, t) eˆ R ( eˆ + eˆ ) R (ˆ x + R jyˆ) L L exp( eˆ L jkz)exp( jπνt) (ˆ x Example: () liearly-polarized photo trasmittig through a circular polarizer. () right-circularly-polarized photo trasmittig through a liear polarizer. jyˆ) Photo Spi Photo has itrisic agular mometum. Photo spi: S ± For right-circularly-polarized photos, S is parallel to k. For left-circularly-polarized photos, S is ati-parallel to k. Liearly-polarized photos have a equal probability of exhibitig parallel ad ati-parallel spi. Lih Y. Li 9
10 Photo Iterferece ssume the mirrors ad beam-splitters are perfectly flat ad lossless. Path legth differece is d. Probability of fidig the photo at the detector? If we do t fid the photo at the detector, where is it? Lih Y. Li 0
11 Photo Time Heiseberg s Ucertaity Priciple also implies t E The probability of observig a photo at (r, t) withi a icremetal area of d ad durig the icremetal time iterval dt followig time t: p( r, t) ddt I( r, t) ddt U ( r, t) ddt Lih Y. Li
12 Mea Photo Flux Desity photos sec area Moochromatic light of frequecy ν ad itesity I(r) Photo flux desity I ( r) ϕ( r) hν Quasi-moochromatic light of cetral-frequecy Photo flux desity ϕ( r) I ( r) hν ν Lih Y. Li
13 Mea Photo Flux ad Mea Number of Photos photos sec Mea Photo Flux Φ P P ϕ( r) d hν I( r) d: Optical power (watts) Mea Number of Photos Time-varyig light E T 0 T 0 E Φ T hν E P T : Optical eergy (joule) Φ( t) dt P( t) dt : E hν Optical eergy (joule) Lih Y. Li 3
14 Radomess of Photo Flux Eve if the optical power is costat, the time of arrival of a sigle photo is govered by probabilistic laws. Lih Y. Li 4
15 Photo Statistics for Coheret Light Probability Mea photo umber It s possible to detect differet umber of photos at differet time itervals. Probability of detectig photos is a Poisso distributio: p( ) exp( )! Lih Y. Li 5
16 Photo Statistics for Coheret Light Mea, Variace, ad SNR Mea: 0 p( ) σ Variace: 0 ( ) p( ) For Poisso distributio, σ Sigal-to-oise ratio: SNR (mea) Variace σ For Poisso distributio, SNR Lih Y. Li 6
17 7 Lih Y. Li Photo Statistics for Icoheret Light Probability follows Boltzma distributio T k E E P B exp ) ( J/k B k : Boltzma costat B B T k h T k h p ν ν exp exp ) ( exp ν T k h B p + + ) ( + σ SNR < + No matter how large the optical power is.
Experimental Fact: E = nhf
CHAPTR 3 The xperimetal Basis of Quatum PHYS-3301 Lecture 4 Sep. 6, 2018 3.1 Discovery of the X Ray ad the lectro 3.2 Determiatio of lectro Charge 3.3 Lie Spectra 3.4 Quatizatio 3.5 Blackbody Radiatio
More informationEE485 Introduction to Photonics
Pattern formed by fluorescence of quantum dots EE485 Introduction to Photonics Photon and Laser Basics 1. Photon properties 2. Laser basics 3. Characteristics of laser beams Reading: Pedrotti 3, Sec. 1.2,
More informationPHYS-3301 Lecture 10. Wave Packet Envelope Wave Properties of Matter and Quantum Mechanics I CHAPTER 5. Announcement. Sep.
Aoucemet Course webpage http://www.phys.ttu.edu/~slee/3301/ PHYS-3301 Lecture 10 HW3 (due 10/4) Chapter 5 4, 8, 11, 15, 22, 27, 36, 40, 42 Sep. 27, 2018 Exam 1 (10/4) Chapters 3, 4, & 5 CHAPTER 5 Wave
More informationAIT. Blackbody Radiation IAAT
3 1 Blackbody Radiatio Itroductio 3 2 First radiatio process to look at: radiatio i thermal equilibrium with itself: blackbody radiatio Assumptios: 1. Photos are Bosos, i.e., more tha oe photo per phase
More information17 Phonons and conduction electrons in solids (Hiroshi Matsuoka)
7 Phoos ad coductio electros i solids Hiroshi Matsuoa I this chapter we will discuss a miimal microscopic model for phoos i a solid ad a miimal microscopic model for coductio electros i a simple metal.
More informationPreliminary Examination - Day 1 Thursday, May 12, 2016
UNL - Departmet of Physics ad Astroomy Prelimiary Examiatio - Day Thursday, May, 6 This test covers the topics of Quatum Mechaics (Topic ) ad Electrodyamics (Topic ). Each topic has 4 A questios ad 4 B
More information3/21/2017. Commuting and Non-commuting Operators Chapter 17. A a
Commutig ad No-commutig Operators Chapter 17 Postulate 3. I ay measuremet of the observable associated with a operator A the oly values that will ever be observed are the eige values, a, which satisfy
More informationAndrei Tokmakoff, MIT Department of Chemistry, 5/19/
drei Tokmakoff, MT Departmet of Chemistry, 5/9/5 4-9 Rate of bsorptio ad Stimulated Emissio The rate of absorptio iduced by the field is E k " (" (" $% ˆ µ # (" &" k k (4. The rate is clearly depedet o
More informationOptics. n n. sin. 1. law of rectilinear propagation 2. law of reflection = 3. law of refraction
Optics What is light? Visible electromagetic radiatio Geometrical optics (model) Light-ray: extremely thi parallel light beam Usig this model, the explaatio of several optical pheomea ca be give as the
More informationDevelopment of QM. What do we know from classical physics? 1. Energy can take any continuous value.
Developmet of QM 1-1 What do we kow from classical physics? 1. Eergy ca take ay cotiuous value.. Electromagetic radiatio is a electric field oscillatig perpedicular to the directio of propagatio. 3. Ay
More informationRounding Answers. => Z=12.03±0.15 cm
Roudig Aswers The ucertaity should be rouded off to oe or two sigificat figures. If the leadig figure i the ucertaity is 1, we use two sigificat figures, otherwise we use oe sigificat figure. The aswer
More informationIntrinsic Carrier Concentration
Itrisic Carrier Cocetratio I. Defiitio Itrisic semicoductor: A semicoductor material with o dopats. It electrical characteristics such as cocetratio of charge carriers, deped oly o pure crystal. II. To
More informationLecture 9: Diffusion, Electrostatics review, and Capacitors. Context
EECS 5 Sprig 4, Lecture 9 Lecture 9: Diffusio, Electrostatics review, ad Capacitors EECS 5 Sprig 4, Lecture 9 Cotext I the last lecture, we looked at the carriers i a eutral semicoductor, ad drift currets
More informationPhys 102 Lecture 25 The quantum mechanical model of light
Phys 102 Lecture 25 The quatum mechaical model of light 1 Recall last time Problems with classical physics Stability of atoms Atomic spectra Photoelectric effect Quatum model of the atom Bohr model oly
More informationFormation of A Supergain Array and Its Application in Radar
Formatio of A Supergai Array ad ts Applicatio i Radar Tra Cao Quye, Do Trug Kie ad Bach Gia Duog. Research Ceter for Electroic ad Telecommuicatios, College of Techology (Coltech, Vietam atioal Uiversity,
More informationAtomic Physics 4. Name: Date: 1. The de Broglie wavelength associated with a car moving with a speed of 20 m s 1 is of the order of. A m.
Name: Date: Atomic Pysics 4 1. Te de Broglie wavelegt associated wit a car movig wit a speed of 0 m s 1 is of te order of A. 10 38 m. B. 10 4 m. C. 10 4 m. D. 10 38 m.. Te diagram below sows tree eergy
More informationRecent Experimental Results in ADITYA Tokamak
Recet Experimetal Results i ADITYA Tokamak R. Jha ad the ADITYA Team Istitute for Plasma Research, Bhat, Gadhiagar-382 428, INDIA e-mail:rjha@ipr.res.i Abstract. Recet studies o measuremets of edge turbulece
More informationPHYS-3301 Lecture 7. CHAPTER 4 Structure of the Atom. Rutherford Scattering. Sep. 18, 2018
CHAPTER 4 Structure of the Atom PHYS-3301 Lecture 7 4.1 The Atomic Models of Thomso ad Rutherford 4.2 Rutherford Scatterig 4.3 The Classic Atomic Model 4.4 The Bohr Model of the Hydroge Atom 4.5 Successes
More informationWave Phenomena Physics 15c
Wave Pheomea Physics 5c Lecture Fourier Aalysis (H&L Sectios 3. 4) (Georgi Chapter ) Admiistravia! Midterm average 68! You did well i geeral! May got the easy parts wrog, e.g. Problem (a) ad 3(a)! erm
More informationPHYS-3301 Lecture 9. CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I. 5.3: Electron Scattering. Bohr s Quantization Condition
CHAPTER 5 Wave Properties of Matter ad Quatum Mecaics I PHYS-3301 Lecture 9 Sep. 5, 018 5.1 X-Ray Scatterig 5. De Broglie Waves 5.3 Electro Scatterig 5.4 Wave Motio 5.5 Waves or Particles? 5.6 Ucertaity
More informationHilbert Space Methods Used in a First Course in Quantum Mechanics
Hilbert Space Methods Used i a First Course i Quatum Mechaics Victor Poliger Physics/Mathematics Bellevue College 03/07/3-04//3 Outlie The Ifiite Square Well: A Follow-Up Timelie of basic evets Statistical
More informationSECTION 2 Electrostatics
SECTION Electrostatics This sectio, based o Chapter of Griffiths, covers effects of electric fields ad forces i static (timeidepedet) situatios. The topics are: Electric field Gauss s Law Electric potetial
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science. BACKGROUND EXAM September 30, 2004.
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Departmet of Electrical Egieerig ad Computer Sciece 6.34 Discrete Time Sigal Processig Fall 24 BACKGROUND EXAM September 3, 24. Full Name: Note: This exam is closed
More informationEE / EEE SAMPLE STUDY MATERIAL. GATE, IES & PSUs Signal System. Electrical Engineering. Postal Correspondence Course
Sigal-EE Postal Correspodece Course 1 SAMPLE STUDY MATERIAL Electrical Egieerig EE / EEE Postal Correspodece Course GATE, IES & PSUs Sigal System Sigal-EE Postal Correspodece Course CONTENTS 1. SIGNAL
More informationUniversity of Washington Department of Chemistry Chemistry 453 Winter Quarter 2015
Uiversity of Wasigto Departmet of Cemistry Cemistry 453 Witer Quarter 15 Lecture 14. /11/15 Recommeded Text Readig: Atkis DePaula: 9.1, 9., 9.3 A. Te Equipartitio Priciple & Eergy Quatizatio Te Equipartio
More informationReview of Discrete-time Signals. ELEC 635 Prof. Siripong Potisuk
Review of Discrete-time Sigals ELEC 635 Prof. Siripog Potisuk 1 Discrete-time Sigals Discrete-time, cotiuous-valued amplitude (sampled-data sigal) Discrete-time, discrete-valued amplitude (digital sigal)
More informationBohr s Atomic Model Quantum Mechanical Model
September 7, 0 - Summary - Itroductio to Atomic Theory Bohr s Atomic Model Quatum Mechaical Model 3- Some Defiitio 3- Projects Temperature Pressure Website Subject Areas Plasma is a Mixture of electros,
More informationStatistical Noise Models and Diagnostics
L. Yaroslavsky: Advaced Image Processig Lab: A Tutorial, EUSIPCO2 LECTURE 2 Statistical oise Models ad Diagostics 2. Statistical models of radom iterfereces: (i) Additive sigal idepedet oise model: r =
More informationLecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting
Lecture 6 Chi Square Distributio (χ ) ad Least Squares Fittig Chi Square Distributio (χ ) Suppose: We have a set of measuremets {x 1, x, x }. We kow the true value of each x i (x t1, x t, x t ). We would
More informationName Solutions to Test 2 October 14, 2015
Name Solutios to Test October 4, 05 This test cosists of three parts. Please ote that i parts II ad III, you ca skip oe questio of those offered. The equatios below may be helpful with some problems. Costats
More informationLinear Regression Models
Liear Regressio Models Dr. Joh Mellor-Crummey Departmet of Computer Sciece Rice Uiversity johmc@cs.rice.edu COMP 528 Lecture 9 15 February 2005 Goals for Today Uderstad how to Use scatter diagrams to ispect
More informationECE 564/645 - Digital Communication Systems (Spring 2014) Final Exam Friday, May 2nd, 8:00-10:00am, Marston 220
ECE 564/645 - Digital Commuicatio Systems (Sprig 014) Fial Exam Friday, May d, 8:00-10:00am, Marsto 0 Overview The exam cosists of four (or five) problems for 100 (or 10) poits. The poits for each part
More information8. IRREVERSIBLE AND RANDOM PROCESSES Concepts and Definitions
8. IRREVERSIBLE ND RNDOM PROCESSES 8.1. Cocepts ad Defiitios I codesed phases, itermolecular iteractios ad collective motios act to modify the state of a molecule i a time-depedet fashio. Liquids, polymers,
More informationComputing Confidence Intervals for Sample Data
Computig Cofidece Itervals for Sample Data Topics Use of Statistics Sources of errors Accuracy, precisio, resolutio A mathematical model of errors Cofidece itervals For meas For variaces For proportios
More informationSemiconductors a brief introduction
Semicoductors a brief itroductio Bad structure from atom to crystal Fermi level carrier cocetratio Dopig Readig: (Sedra/Smith 7 th editio) 1.7-1.9 Trasport (drift-diffusio) Hyperphysics (lik o course homepage)
More informationLecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting
Lecture 6 Chi Square Distributio (χ ) ad Least Squares Fittig Chi Square Distributio (χ ) Suppose: We have a set of measuremets {x 1, x, x }. We kow the true value of each x i (x t1, x t, x t ). We would
More informationInformation Theory and Coding
Sol. Iformatio Theory ad Codig. The capacity of a bad-limited additive white Gaussia (AWGN) chael is give by C = Wlog 2 ( + σ 2 W ) bits per secod(bps), where W is the chael badwidth, is the average power
More informationSample Size Determination (Two or More Samples)
Sample Sie Determiatio (Two or More Samples) STATGRAPHICS Rev. 963 Summary... Data Iput... Aalysis Summary... 5 Power Curve... 5 Calculatios... 6 Summary This procedure determies a suitable sample sie
More informationFree Space Optical Wireless Communications under Turbulence Channel Effect
IOSR Joural of Electroics ad Commuicatio Egieerig (IOSR-JECE) e-issn: 78-834,p- ISSN: 78-8735.Volume 9, Issue 3, Ver. III (May - Ju. 014), PP 01-08 Free Space Optical Wireless Commuicatios uder Turbulece
More informationLecture #5: Begin Quantum Mechanics: Free Particle and Particle in a 1D Box
561 Fall 013 Lecture #5 page 1 Last time: Lecture #5: Begi Quatum Mechaics: Free Particle ad Particle i a 1D Box u 1 u 1-D Wave equatio = x v t * u(x,t): displacemets as fuctio of x,t * d -order: solutio
More informationTopic 10: Introduction to Estimation
Topic 0: Itroductio to Estimatio Jue, 0 Itroductio I the simplest possible terms, the goal of estimatio theory is to aswer the questio: What is that umber? What is the legth, the reactio rate, the fractio
More informationQuiz #3 Practice Problem Set
Name: Studet Number: ELEC 3908 Physical Electroics Quiz #3 Practice Problem Set? Miutes March 11, 2016 - No aids excet a o-rogrammable calculator - ll questios must be aswered - ll questios have equal
More informationStat 421-SP2012 Interval Estimation Section
Stat 41-SP01 Iterval Estimatio Sectio 11.1-11. We ow uderstad (Chapter 10) how to fid poit estimators of a ukow parameter. o However, a poit estimate does ot provide ay iformatio about the ucertaity (possible
More informationMATH 320: Probability and Statistics 9. Estimation and Testing of Parameters. Readings: Pruim, Chapter 4
MATH 30: Probability ad Statistics 9. Estimatio ad Testig of Parameters Estimatio ad Testig of Parameters We have bee dealig situatios i which we have full kowledge of the distributio of a radom variable.
More informationENGI 4421 Confidence Intervals (Two Samples) Page 12-01
ENGI 44 Cofidece Itervals (Two Samples) Page -0 Two Sample Cofidece Iterval for a Differece i Populatio Meas [Navidi sectios 5.4-5.7; Devore chapter 9] From the cetral limit theorem, we kow that, for sufficietly
More informationFizeau s Experiment with Moving Water. New Explanation. Gennady Sokolov, Vitali Sokolov
Fizeau s Experimet with Movig Water New Explaatio Geady Sokolov, itali Sokolov Email: sokolov@vitalipropertiescom The iterferece experimet with movig water carried out by Fizeau i 85 is oe of the mai cofirmatios
More informationExpectation and Variance of a random variable
Chapter 11 Expectatio ad Variace of a radom variable The aim of this lecture is to defie ad itroduce mathematical Expectatio ad variace of a fuctio of discrete & cotiuous radom variables ad the distributio
More informationPhysics Supplement to my class. Kinetic Theory
Physics Supplemet to my class Leaers should ote that I have used symbols for geometrical figures ad abbreviatios through out the documet. Kietic Theory 1 Most Probable, Mea ad RMS Speed of Gas Molecules
More informationTIME-CORRELATION FUNCTIONS
p. 8 TIME-CORRELATION FUNCTIONS Time-correlatio fuctios are a effective way of represetig the dyamics of a system. They provide a statistical descriptio of the time-evolutio of a variable for a esemble
More informationFinal Review. Fall 2013 Prof. Yao Xie, H. Milton Stewart School of Industrial Systems & Engineering Georgia Tech
Fial Review Fall 2013 Prof. Yao Xie, yao.xie@isye.gatech.edu H. Milto Stewart School of Idustrial Systems & Egieerig Georgia Tech 1 Radom samplig model radom samples populatio radom samples: x 1,..., x
More informationCSIR-UGC-NET/JRF Jue 0 CSIR-UGC NET/JRF JUNE - 0 PHYSICAL SCIENCES BOOKLET - [A] PART - B. A particle of uit mass moves i a potetial V x b ax, where a ad b are positive costats. x The agular frequecy of
More informationOffice: JILA A709; Phone ;
Office: JILA A709; Phoe 303-49-7841; email: weberjm@jila.colorado.edu Problem Set 5 To be retured before the ed of class o Wedesday, September 3, 015 (give to me i perso or slide uder office door). 1.
More informationLecture 5. Random variable and distribution of probability
Itroductio to theory of probability ad statistics Lecture 5. Radom variable ad distributio of probability prof. dr hab.iż. Katarzya Zarzewsa Katedra Eletroii, AGH e-mail: za@agh.edu.pl http://home.agh.edu.pl/~za
More informationRandom Variables, Sampling and Estimation
Chapter 1 Radom Variables, Samplig ad Estimatio 1.1 Itroductio This chapter will cover the most importat basic statistical theory you eed i order to uderstad the ecoometric material that will be comig
More informationWave Motion
Wave Motio Wave ad Wave motio: Wave is a carrier of eergy Wave is a form of disturbace which travels through a material medium due to the repeated periodic motio of the particles of the medium about their
More informationRepetition: Refractive Index
Repetitio: Refractive Idex (ω) κ(ω) 1 0 ω 0 ω 0 The real part of the refractive idex correspods to refractive idex, as it appears i Sellius law of refractio. The imagiary part correspods to the absorptio
More informationLecture 2: Poisson Sta*s*cs Probability Density Func*ons Expecta*on and Variance Es*mators
Lecture 2: Poisso Sta*s*cs Probability Desity Fuc*os Expecta*o ad Variace Es*mators Biomial Distribu*o: P (k successes i attempts) =! k!( k)! p k s( p s ) k prob of each success Poisso Distributio Note
More informationPH 425 Quantum Measurement and Spin Winter SPINS Lab 1
PH 425 Quatum Measuremet ad Spi Witer 23 SPIS Lab Measure the spi projectio S z alog the z-axis This is the experimet that is ready to go whe you start the program, as show below Each atom is measured
More informationSOLUTIONS: ECE 606 Homework Week 7 Mark Lundstrom Purdue University (revised 3/27/13) e E i E T
SOUIONS: ECE 606 Homework Week 7 Mark udstrom Purdue Uiversity (revised 3/27/13) 1) Cosider a - type semicoductor for which the oly states i the badgap are door levels (i.e. ( E = E D ). Begi with the
More informationPHYC - 505: Statistical Mechanics Homework Assignment 4 Solutions
PHYC - 55: Statistical Mechaics Homewor Assigmet 4 Solutios Due February 5, 14 1. Cosider a ifiite classical chai of idetical masses coupled by earest eighbor sprigs with idetical sprig costats. a Write
More informationNATIONAL UNIVERSITY OF SINGAPORE
NATIONAL UNIVERSITY OF SINGAPORE PC4 Physics II (Semester I: AY 008-09, 6 November) Time Allowed: Hours INSTRUCTIONS TO CANDIDATES This examiatio paper comprises EIGHT (8) prited pages with FIVE (5) short
More informationModule 4. Signal Representation and Baseband Processing. Version 2 ECE IIT, Kharagpur
Module 4 Sigal Represetatio ad Basebad Processig ersio ECE IIT, Kharagpur Lesso 17 Noise ersio ECE IIT, Kharagpur After readig this lesso, you will lear about Basic features of Short Noise; Thermal (Johso)
More informationCoherent control of Rydberg atoms
Coheret cotrol of Rydberg atoms Haruka Maeda Departmet of Phys. & Math., Aoyama Gakui Uiversity Why Rydberg atom? Multilevel ladder system What ca we study with Rydberg atom? Microwave multiphoto ioizatio
More informationQuantum Annealing for Heisenberg Spin Chains
LA-UR # - Quatum Aealig for Heiseberg Spi Chais G.P. Berma, V.N. Gorshkov,, ad V.I.Tsifriovich Theoretical Divisio, Los Alamos Natioal Laboratory, Los Alamos, NM Istitute of Physics, Natioal Academy of
More informationis completely general whenever you have waves from two sources interfering. 2
MAKNG SENSE OF THE EQUATON SHEET terferece & Diffrctio NTERFERENCE r1 r d si. Equtio for pth legth differece. r1 r is completely geerl. Use si oly whe the two sources re fr wy from the observtio poit.
More informationTrue Nature of Potential Energy of a Hydrogen Atom
True Nature of Potetial Eergy of a Hydroge Atom Koshu Suto Key words: Bohr Radius, Potetial Eergy, Rest Mass Eergy, Classical Electro Radius PACS codes: 365Sq, 365-w, 33+p Abstract I cosiderig the potetial
More informationChapter 2 Motion and Recombination of Electrons and Holes
Chapter 2 Motio ad Recombiatio of Electros ad Holes 2.1 Thermal Eergy ad Thermal Velocity Average electro or hole kietic eergy 3 2 kt 1 2 2 mv th v th 3kT m eff 3 23 1.38 10 JK 0.26 9.1 10 1 31 300 kg
More informationCS/ECE 715 Spring 2004 Homework 5 (Due date: March 16)
CS/ECE 75 Sprig 004 Homework 5 (Due date: March 6) Problem 0 (For fu). M/G/ Queue with Radom-Sized Batch Arrivals. Cosider the M/G/ system with the differece that customers are arrivig i batches accordig
More informationPhysics 201 Final Exam December
Physics 01 Fial Exam December 14 017 Name (please prit): This test is admiistered uder the rules ad regulatios of the hoor system of the College of William & Mary. Sigature: Fial score: Problem 1 (5 poits)
More informationLecture 6. Semiconductor physics IV. The Semiconductor in Equilibrium
Lecture 6 Semicoductor physics IV The Semicoductor i Equilibrium Equilibrium, or thermal equilibrium No exteral forces such as voltages, electric fields. Magetic fields, or temperature gradiets are actig
More informationApproximations and more PMFs and PDFs
Approximatios ad more PMFs ad PDFs Saad Meimeh 1 Approximatio of biomial with Poisso Cosider the biomial distributio ( b(k,,p = p k (1 p k, k λ: k Assume that is large, ad p is small, but p λ at the limit.
More informationInformation Theory Model for Radiation
Joural of Applied Mathematics ad Physics, 26, 4, 6-66 Published Olie August 26 i SciRes. http://www.scirp.org/joural/jamp http://dx.doi.org/.426/jamp.26.487 Iformatio Theory Model for Radiatio Philipp
More informationChapter 6 Principles of Data Reduction
Chapter 6 for BST 695: Special Topics i Statistical Theory. Kui Zhag, 0 Chapter 6 Priciples of Data Reductio Sectio 6. Itroductio Goal: To summarize or reduce the data X, X,, X to get iformatio about a
More informationProbability, Expectation Value and Uncertainty
Chapter 1 Probability, Expectatio Value ad Ucertaity We have see that the physically observable properties of a quatum system are represeted by Hermitea operators (also referred to as observables ) such
More informationFYS Vår 2016 (Kondenserte fasers fysikk)
FYS3410 - Vår 2016 (Kodeserte fasers fysikk) http://www.uio.o/studier/emer/matat/fys/fys3410/v16/idex.html Pesum: Itroductio to Solid State Physics by Charles Kittel (Chapters 1-9 ad 17, 18, 20) Adrej
More informationTime-Domain Representations of LTI Systems
2.1 Itroductio Objectives: 1. Impulse resposes of LTI systems 2. Liear costat-coefficiets differetial or differece equatios of LTI systems 3. Bloc diagram represetatios of LTI systems 4. State-variable
More informationDirection of Arrival Estimation Method in Underdetermined Condition Zhang Youzhi a, Li Weibo b, Wang Hanli c
4th Iteratioal Coferece o Advaced Materials ad Iformatio Techology Processig (AMITP 06) Directio of Arrival Estimatio Method i Uderdetermied Coditio Zhag Youzhi a, Li eibo b, ag Hali c Naval Aeroautical
More informationVibrational Spectroscopy 1
Applied Spectroscopy Vibratioal Spectroscopy Recommeded Readig: Bawell ad McCash Chapter 3 Atkis Physical Chemistry Chapter 6 Itroductio What is it? Vibratioal spectroscopy detects trasitios betwee the
More informationLast time: Moments of the Poisson distribution from its generating function. Example: Using telescope to measure intensity of an object
6.3 Stochastic Estimatio ad Cotrol, Fall 004 Lecture 7 Last time: Momets of the Poisso distributio from its geeratig fuctio. Gs () e dg µ e ds dg µ ( s) µ ( s) µ ( s) µ e ds dg X µ ds X s dg dg + ds ds
More informationRandom Signals and Noise Winter Semester 2017 Problem Set 12 Wiener Filter Continuation
Radom Sigals ad Noise Witer Semester 7 Problem Set Wieer Filter Cotiuatio Problem (Sprig, Exam A) Give is the sigal W t, which is a Gaussia white oise with expectatio zero ad power spectral desity fuctio
More informationEE 6885 Statistical Pattern Recognition
EE 6885 Statistical Patter Recogitio Fall 5 Prof. Shih-Fu Chag http://www.ee.columbia.edu/~sfchag Lecture 6 (9/8/5 EE6887-Chag 6- Readig EM for Missig Features Textboo, DHS 3.9 Bayesia Parameter Estimatio
More informationLecture 1 Probability and Statistics
Wikipedia: Lecture 1 Probability ad Statistics Bejami Disraeli, British statesma ad literary figure (1804 1881): There are three kids of lies: lies, damed lies, ad statistics. popularized i US by Mark
More informationIntroduction to Probability I: Expectations, Bayes Theorem, Gaussians, and the Poisson Distribution. 1
Itroductio to Probability I: Expectatios, Bayes Theorem, Gaussias, ad the Poisso Distributio. 1 Pakaj Mehta February 25, 2019 1 Read: This will itroduce some elemetary ideas i probability theory that we
More informationLecture 4. Random variable and distribution of probability
Itroductio to theory of probability ad statistics Lecture. Radom variable ad distributio of probability dr hab.iż. Katarzya Zarzewsa, prof.agh Katedra Eletroii, AGH e-mail: za@agh.edu.pl http://home.agh.edu.pl/~za
More informationMark Lundstrom Spring SOLUTIONS: ECE 305 Homework: Week 5. Mark Lundstrom Purdue University
Mark udstrom Sprig 2015 SOUTIONS: ECE 305 Homework: Week 5 Mark udstrom Purdue Uiversity The followig problems cocer the Miority Carrier Diffusio Equatio (MCDE) for electros: Δ t = D Δ + G For all the
More informationThe Poisson Distribution
MATH 382 The Poisso Distributio Dr. Neal, WKU Oe of the importat distributios i probabilistic modelig is the Poisso Process X t that couts the umber of occurreces over a period of t uits of time. This
More informationThe Fizeau Experiment with Moving Water. Sokolov Gennadiy, Sokolov Vitali
The Fizeau Experimet with Movig Water. Sokolov Geadiy, Sokolov itali geadiy@vtmedicalstaffig.com I all papers o the Fizeau experimet with movig water, a aalysis cotais the statemet: "The beams travel relative
More information577. Estimation of surface roughness using high frequency vibrations
577. Estimatio of surface roughess usig high frequecy vibratios V. Augutis, M. Sauoris, Kauas Uiversity of Techology Electroics ad Measuremets Systems Departmet Studetu str. 5-443, LT-5368 Kauas, Lithuaia
More informationHydrogen (atoms, molecules) in external fields. Static electric and magnetic fields Oscyllating electromagnetic fields
Hydroge (atoms, molecules) i exteral fields Static electric ad magetic fields Oscyllatig electromagetic fields Everythig said up to ow has to be modified more or less strogly if we cosider atoms (ad ios)
More informationI. Existence of photon
I. Existee of photo MUX DEMUX 1 ight is a eletromageti wave of a high frequey. Maxwell s equatio H t E 0 E H 0 t E 0 H 0 1 E E E Aos( kzt ) t propagatig eletrial field while osillatig light frequey (Hz)
More information= (1) Correlations in 2D electron gas at arbitrary temperature and spin polarizations. Abstract. n and n )/n. We will. n ( n
Correlatios i D electro gas at arbitrary temperature ad spi polarizatios Nguye Quoc Khah Departmet of Theoretical Physics, Natioal Uiversity i Ho Chi Mih City, 7-Nguye Va Cu Str., 5th District, Ho Chi
More informationPHYS-3301 Lecture 3. EM- Waves behaving like Particles. CHAPTER 3 The Experimental Basis of Quantum. CHAPTER 3 The Experimental Basis of Quantum
CHAPTER 3 The Experimetal Basis of Quatum PHYS-3301 Lecture 3 Sep. 4, 2018 3.1 Discovery of the X Ray ad the Electro 3.2 Determiatio of Electro Charge 3.3 Lie Spectra 3.4 Quatizatio 3.5 Blackbody Radiatio
More informationSPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS PAPER 1 SPECIMEN PAPER. 45 minutes INSTRUCTIONS TO CANDIDATES
SPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS STANDARD LEVEL PAPER 1 SPECIMEN PAPER 45 miutes INSTRUCTIONS TO CANDIDATES Do ot ope this examiatio paper util istructed to do so. Aswer all the questios. For each questio,
More informationExercises and Problems
HW Chapter 4: Oe-Dimesioal Quatum Mechaics Coceptual Questios 4.. Five. 4.4.. is idepedet of. a b c mu ( E). a b m( ev 5 ev) c m(6 ev ev) Exercises ad Problems 4.. Model: Model the electro as a particle
More informationKinetics of Complex Reactions
Kietics of Complex Reactios by Flick Colema Departmet of Chemistry Wellesley College Wellesley MA 28 wcolema@wellesley.edu Copyright Flick Colema 996. All rights reserved. You are welcome to use this documet
More informationQuantum Mechanics I. 21 April, x=0. , α = A + B = C. ik 1 A ik 1 B = αc.
Quatum Mechaics I 1 April, 14 Assigmet 5: Solutio 1 For a particle icidet o a potetial step with E < V, show that the magitudes of the amplitudes of the icidet ad reflected waves fuctios are the same Fid
More informationDISTRIBUTION LAW Okunev I.V.
1 DISTRIBUTION LAW Okuev I.V. Distributio law belogs to a umber of the most complicated theoretical laws of mathematics. But it is also a very importat practical law. Nothig ca help uderstad complicated
More informationDirection: This test is worth 150 points. You are required to complete this test within 55 minutes.
Term Test 3 (Part A) November 1, 004 Name Math 6 Studet Number Directio: This test is worth 10 poits. You are required to complete this test withi miutes. I order to receive full credit, aswer each problem
More informationLecture 3-7 Semiconductor Lasers.
Laser LED Stimulated emissio Spotaeous emissio Laser I th I Typical output optical power vs. diode curret (I) characteristics ad the correspodig output spectrum of a laser diode.?1999 S.O. Kasap, Optoelectroics
More informationECE 8527: Introduction to Machine Learning and Pattern Recognition Midterm # 1. Vaishali Amin Fall, 2015
ECE 8527: Itroductio to Machie Learig ad Patter Recogitio Midterm # 1 Vaishali Ami Fall, 2015 tue39624@temple.edu Problem No. 1: Cosider a two-class discrete distributio problem: ω 1 :{[0,0], [2,0], [2,2],
More information