## EE 539, 4 Units

## Fall 2024

## 10:00 am – 11:50 am, Mon/Wed, VPD110

**Location of Verna and Peter Dauterive Hall (VPD)**

*Instructor:*Tony Levi

**Office:****KAP 132**

**(**

*Phone:***213) 740-7318**

*E-mail:***alevi@usc.edu**

*Teaching Assistant*: Fugu Tian

**Email:****fugutian@usc.edu**

**Discussion session:****Thursdays at 9 am in RTH B105**

*The EE 539 Primer document download*

*The EE 539 Primer movie of the Mandel effect*

**Homework problems:**

**HW#0. Your solutions to H.14, H.16, H.23, H.24, and H.25 are due at the beginning of class on Wednesday September 4**

**HW#1. Your solutions to 1.2, 1.11, 1.13, 1.16. 1.17. 1.18. 1.19 are due at the beginning of class on Monday September 9**

**HW#2. Your solutions to 2.3, 2.8, 2.15, 2.16, 2.17, 2.18, 2.19 are due at the beginning of class on Monday September 16**

**HW#3. **

*Web sites:*

http:/www.afjlevi.org

http://classes.usc.edu/term-20243/classes/ee/

Final Examinations Schedule · USC Schedule of Classes

**Grading:***Required Text:*

**Applied Quantum Mechanics (third edition), Cambridge University Press, ISBN: 1009308076 **

*Required Text:*

*Office Hours:*Mon/Wed 8:45 a.m. – 9:45 a. m. or by appointment

First day of EE539 classes, Monday, August 26, 2024

Last day of EE539 classes, Wednesday, December 4, 2024

**Papers:**

**Wave packet tunneling and imaginary wave vector dispersion, 2023.**

**Supersymmetry with scattering states, 2021.**

**Behavioral regimes and long-lived emitter states in mesolasers, 2019.**

**Coherent control of photon resonator dynamics, 2014.**

**Single electron memory**

Huang 2004

Yano Review 1999

Huang 2004

Yano Review 1999

**Single electron transistor**

Uchida 2003

Uchida 2003

**Tunnel FET**

Saraswat 2008

Saraswat 2008

**Quantum communication**

Bennett 1992

Bienfang 2004

Gisin Review 2002

Bennett 1992

Bienfang 2004

Gisin Review 2002

__Abstract__

**Quantum mechanics is the basis for understanding physical phenomena on the atomic and nano-meter scale. There are numerous applications of quantum mechanics in biology, chemistry and engineering. Those with significant economic impact include semiconductor transistors, lasers, quantum optics and photonics. As technology advances, an increasing number of new electronic and opto-electronic devices will operate in ways that can only be understood using quantum mechanics. Over the next twenty years fundamentally quantum devices will become commonplace. The purpose of this course is to cover a few selected applications and to provide a solid foundation in the tools and methods of applied quantum mechanics and quantum engineering. The intent is that this understanding will enable insight and contributions to future, as yet unknown, applications.**

__Prerequisites__

*Mathematics:*

A basic working knowledge of differential calculus, linear algebra, statistics, and geometry.

*Computer skills:*

An ability to program numerical algorithms in C, MATLAB, Python, FORTRAN or similar language and display results in graphical form.

*Physics background:*

Should include a basic understanding of Newtonian mechanics, waves, and Maxwell’s equations.

**Introduction:** *Lectures 1 – 3*

**Lecture 1**

*TOWARDS QUANTUM MECHANICS – PARTICLES AND WAVES*

**Diffraction, interference, and correlation functions for light**

**Black-body radiation and evidence for quantization of light**

**Photoelectric effect**

*THE PHOTON PARTICLE*

**The existence of the photon particle
The photon at a beam splitter
Random number generation and stochastic computing**

**Secure quantum communication**

**Lecture 2-3**

*WAVE-PARTICLE DUALITY*

**The link between quantization of photons and quantization of other particles**

**Diffraction and interference of electrons
When is a particle a wave?**

**Feynman paths**

*THE SCHRÖDINGER WAVE EQUATION***The wave function description of an electron in free-space**

**The electron wave packet and dispersion**

**The Bohr model of the hydrogen atom**

**Calculation of the average radius of an electron orbit in hydrogen**

**Calculation of energy difference between electron orbits in hydrogen**

**Periodic table of elements**

**Crystal structure**

**Three types of solid classified according to atomic arrangement**

**Two-dimensional square lattice, cubic lattices in three-dimensions**

**Electronic properties of semiconductor crystals**

**The semiconductor heterostructure**

**Using the Schrödinger wave equation:** *Lectures 4 – 5*

**Lecture 4-5**

*INTRODUCTION*

**The effect of discontinuities in the wave function and its derivative**

*WAVE FUNCTION NORMALIZATION AND COMPLETENESS*

*INVERSION SYMMETRY IN THE POTENTIAL*

**Particle in a one-dimensional square potential well with infinite barrier energy**

*NUMERICAL SOLUTION OF THE SCHRÖDINGER EQUATION*

**Matrix solution to the discretized Schrödinger equation**

**Nontransmitting boundary conditions. Periodic boundary conditions**

*CURRENT FLOW*

**Current flow in a one-dimensional infinite square potential well**

**Current flow due to a traveling wave**

*DEGENERACY IS A CONSEQUENCE OF SYMMETRY*

**Bound states in three-dimensions and degeneracy of eigenvalues**

*BOUND STATES OF A SYMMETRIC SQUARE POTENTIAL WELL*

**Symmetric square potential well with finite barrier energy**

*TRANSMISSION AND REFLECTION OF UNBOUND STATES*

**Scattering from a potential step when effective electron mass changes**

**Impedance matching unbound states across a potential step**

**The reflectionless sech2 potential
IMPEDANCE MATCHING BOUND STATES ACROSS A POTENTIAL STEP**

*PARTICLE TUNNELING***Electron tunneling limit to reduction in size of CMOS transistors**

**Scattering in one-dimension:** *The propagation method: Lectures 6 – 8*

**Lecture 6**

*THE PROPAGATION MATRIX METHOD*

**Writing a computer program for the propagation method**

*TIME REVERSAL SYMMETRY*

*CURRENT CONSERVATION AND THE PROPAGATION MATRIX*

**Lecture 7**

*THE RECTANGULAR POTENTIAL BARRIER*

**Tunneling**

*RESONANT TUNNELING*

**Resonant tunneling between two quantum wells**

**Resonant tunneling between three potential barriers and unity transmission threshold**

*ENERGY BANDS IN PERIODIC POTENTIALS: THE KRONIG-PENNY POTENTIAL*

**Bloch’s theorem**

**Real, imaginary, and complex band structure**

**Lecture 8**

*THE TIGHT BINDING MODEL FOR ELECTRONIC BAND STRUCTURE*

**Nearest neighbor and long-range interactions**

**Crystal momentum and effective electron mass
The nonequilibrium electron transistor**

*USE OF THE PROPAGATION MATRIX TO SOLVE OTHER PROBLEMS IN ENGINEERING*

*THE WKB APPROXIMATION***Tunneling**

**Related mathematics:** *Lectures 9 – 10*

**Lecture 9-10**

*ONE PARTICLE WAVE FUNCTION SPACE*

*PROPERTIES OF LINEAR OPERATORS*

**Hermitian operators**

**Commutator algebra**

*DIRAC NOTATION*

*MEASUREMENT OF REAL NUMBERS*

**Time dependence of expectation values. Indeterminacy in expectation value**

**The generalized indeterminacy relation**

*THE NO CLONING THEOREM*

*DENSITY OF STATES*

**Density of states of particle mass m in 3D, 2D, 1D and 0D**

**Quantum conductance**

**Numerically evaluating density of states from a dispersion relation**

**Density of photon states**

**The harmonic oscillator:** *Lectures 11 – 12*

**Lecture 11**

*THE HARMONIC OSCILLATOR POTENTIAL*

*CREATION AND ANNIHILATION OPERATORS*

**The ground state. Excited states**

*HARMONIC OSCILLATOR WAVE FUNCTIONS*

**Classical turning point**

*TIME DEPENDENCE*

**The superposition operator. Measurement of a superposition state**

**Lecture 12**

**Time dependence in the Heisenberg representation**

**Charged particle in harmonic potential subject to constant electric field**

*ELECTROMAGNETIC FIELDS*

**Laser light**

**Quantization of an electrical resonator**

**Quantization of lattice vibrations**

**Quantization of mechanical vibrations**

**Fermions and Bosons:** *Lecture 13*

**Lecture 13**

*INTRODUCTION*

**The symmetry of indistinguishable particles. Slater determinant**

**Pauli exclusion principle. Fermion creation and annihilation operators – application to tight-binding Hamiltonian**

*FERMI-DIRAC DISTRIBUTION FUNCTION*

**Equilibrium statistics**

**Writing a computer program to calculate the chemical potential and Fermi-Dirac distribution at finite temperature**

*BOSE-EINSTIEN DISTRIBUTION FUNCTION*

*CURRENT AS FUNCTION OF VOLTAGE BIAS*

**Semiconductor heterostructure diode structures in the depletion approximation.**

**Metal-insulator-metal.**

**Reduced dimensions**

**Review:** *Lecture 14*

**Midterm:**

**Fermions and Bosons continued:** *Lectures 16 – 17*

**Lecture 16 – 17**

*PHOTON FOCK STATES*

**The Mandel effect**

**n-photons at a beam splitter**

**n-photons at a FP resonator**

*THE MANDEL EFFECT*

**Dual photon source**

**Fiber-optic beam splitter and delay line**

**Photon counting and correlation**

**Time dependent perturbation theory and the laser diode:** *Lectures 18 – 20*

**Lecture 18**

*FIRST-ORDER TIME-DEPENDENT PERTURBATION THEORY*

**Abrupt change in potential**

**Time dependent change in potential**

*CHARGED PARTICLE IN A HARMONIC POTENTIAL*

*FIRST-ORDER TIME-DEPENDENT PERTURBATION*

*THE GOLDEN RULE*

*IONIZED IMPURITY ELASTIC SCATTERING RATE IN GaAs*

**The coulomb potential. Linear screening of the coulomb potential**

**Correlation effects in position of dopant atoms**

**Calculating the electron mean free path**

**Lecture 19**

*EMISSION OF PHOTONS DUE TO TRANSITIONS BETWEEN ELECTRONIC STATES*

**Density of optical modes in three dimensions**

**Light intensity**

**Background photon energy density at thermal equilibrium**

**Fermi’s golden rule for stimulated optical transitions**

**The Einstein A and B coefficients**

**Occupation factor for photons in thermal equilibrium in a two-level system**

**Derivation of the relationship between spontaneous emission rate and gain**

*THE SEMICONDUCTOR LASER DIODE*

**Spontaneous and stimulated emission. Optical gain in a semiconductor. Optical gain in the presence of electron scattering**

*DESIGNING A LASER CAVITY*

**Resonant optical cavity. Mirror loss and photon lifetime**

**The Fabry-Perot laser diode. Rate equation models**

**Lecture 20**

*NUMERICAL METHOD OF SOLVING RATE EQUATIONS*

**The Runge-Kutta method. Large-signal transient response. Cavity formation**

*NOISE IN LASER DIODE LIGHT EMISSION*

**Effect of photon and electron number quantization**

**Langevin and semiclassical master equations**

*QUANTUM THEORY OF LASER OPERATION*

**Density matrix**

**Single and multiple quantum dot, saturable absorber**

**Time independent perturbation theory:** *Lecture 21*

**Lecture 21**

*NON-DEGENERATE CASE*

**Hamiltonian subject to perturbation W**

**First-order correction. Second order correction**

**Harmonic oscillator subject to perturbing potential in x, x2 and x3**

*DEGENERATE CASE*

**Secular equation**

**Two states**

**Perturbation of two-dimensional harmonic oscillator**

**Perturbation of two-dimensional potential with infinite barrier**

**Angular momentum, the hydrogenic atom, and bonds:** *Lectures 22 – 23*

**Lecture 22**

*ANGULAR MOMENTUM*

**Classical angular momentum**

**The angular momentum operator**

**Eigenvalues of the angular momentum operators Lz and L2**

**Geometric representation**

*SPHERICAL HARMONICS AND THE HYDROGEN ATOM*

**Spherical coordinates and spherical harmonics**

**The rigid rotator**

**Quantization of the hydrogenic atom**

**Radial and angular probability density**

**Lecture 23**

*ELECTROMAGNETIC RADIATION*

**No eigenstate radiation**

**Superposition of eigenstates**

**Hydrogenic selection rules for dipole radiation**

**Fine structure**

*BONDS.*

**The hydrogen molecule ion.**

**The hydrogen molecule covalent bond**

**Valence bond description.**

**Molecular orbital description**

**The ionic bond**

**Towa****rd quantum engineering: ***Lecture 24*

Lecture 24

OPTIMAL DEVICE DESIGN

**Optimal design of a heterojunction tunnel diode
Optimal design of density of states
Coherent quantum control
QUANTUM INFORMATION PROCESSING
**

**Representations of a single qubit on the Bloch sphere and unitary operations**

**Two-qubit entangled Bell states**

**Two-qubit controlled gates**

Bell’s inequality

Bell’s inequality

**Teleportation**

*The contents of this web page may be subject to change. Weekly information may be updated without notice.*