Quantum is rapidly emerging as a game-changer in technology.
The end of Moore's Law for exponential growth is rapidly approaching and engineers and physicist alike are looking at moving past the classical limitations of modern technology and are exploring the new opportunities that quantum behaviour creates in sensing, metrology, communications and information processing.
This book serves as introduction to quantum theory with emphasis on dynamical behaviour and applications of quantum mechanics, with minimal discussion of formalism. The goal is to help students begin to learn the tools for a quantum toolbox they will need to work in this area.
It is aimed at upper level undergraduates and first year graduate students and assumes the reader has not had any training in quantum mechanics beyond what might be encountered in two semesters of introductory physics.
The language of quantum is mathematics and builds on what is covered in typically the first two years.
The first six chapters introduce Schrödinger's equation and develop the quantized description of common systems that exist in real space like a vibrator, nano-particles, atoms, crystals, etc.
Beginning in Ch. 7 and for the remaining nine chapters, the focus is primarily on dynamical behaviour and how to think about real quantum systems.
Spin, the quantized electromagnetic field, dissipation, loss and spontaneous emission, are discussed as well as quantum optics and the operator equations for common two-state systems such as the quantum flip flop and the density matrix equations.
The book is structured so that a two semester course sequence is possible or a single semester course with options discussed in the preface to set different learning objectives.
Even a one semester course based on this text covers much more material than a typical upper quantum course for undergraduates in physics, but at the expense of more detailed discussions about solutions to various differential equations such as for angular momentum and the hydrogen atom or band theory for semiconductors.
Chapter 1. Introduction to Applied Quantum Mechanics - Why quantum behavior is impacting technology. Chapter 2. Nano Mechanical Oscillator and Basic Dynamics: Part I 2.1: Introduction 2.2: The Classical Approach: Finding 2.3: The Quantum Approach: Finding 2.4: Is it Classical or Quantum? 2.5: What is Knowable in a Quantum System? 2.6: Coherent Superposition States and Coherent Dynamics 2.7: The Particle and the Wave 2.8: Summary Chapter 3. Free Particle, Wave Packet and Dynamics, Quantum Dots and Defects/Traps Scattering and Transport. 3.1: Introduction 3.2: The Free Particle 3.3: Localized State in Free Space: The Wave Packet 3.4: Nano-Heterostructures: Quantum Dots and Deep Traps 3.5: A Particle Trapped in a Shallow Defect 3.6: A Particle Trapped in a Point Defect Represented by a Dirac Delta-Function Potential 3.7: Physical Interpretation of the Dirac -function potential 3.8: Summary Chapter 4. Periodic Hamiltonians and the Emergence of Band Structure: The Bloch Theorem and the Dirac Kronig-Penney model. 4.1: Introduction 4.2: The Translation Operator 4.3: Crystals and Periodic Potentials: The Bloch Theorem and the Dirac Kronig-Penney Model 4.4: Summary Chapter 5. Scattering, Quantum Current, and Resonant Tunneling 5.1: Introduction 5.2: Scattering 5.3: Tunneling Through a Repulsive Point Defect Represented by a Dirac -Function Potential 5.4: Resonant Tunneling 5.5: Summary Chapter 6. Bound States in 3-dimensions: The Atom. 6.1: Introduction 6.2: The Hydrogenic Atom 6.3: Summary Chapter 7. The New Design Rules for Quantum: The Postulates. 7.1: Introduction 7.2: The Postulates of Quantum Mechanics 7.3: The Heisenberg Uncertainty Principle: The Minimum Uncertainty State 7.4: Interpreting the Expansion Coefficients: Relating Functional Form to Dirac Form 7.5: Summary Chapter 8. Heisenberg Matrix Approach: Nano-Mechanical Oscillator and the Quantum LC Circuit. 8.1: Introduction 8.2: Heisenberg or Matrix Approach to Solving the Time Independent Schrödinger Equation 8.3: Matrix Representation of Operators and Eigenvectors in Quantum Mechanics 8.4: The Quantum LC Circuit 8.5: Summary Chapter 9. Quantum Dynamics: Rabi Oscillations and Quantum Flip-Flops. 9.1: Introduction 9.2: Time Evolution Operator 9.3: The Heisenberg Picture of Dynamics 9.4: The Interaction Picture 9.5: A Quantum Flip-Flop: Coherent Control of a Two-Level System and Rabi Oscillations 9.6: Summary Chapter 10. The Quantum Gyroscope: The Emergence of Spin. 10.1: Introduction 10.2: Angular Momentum with the Heisenberg Approach 10.3: Intrinsic Angular Momentum: Spin 10.4: The Bloch Sphere and Spin 10.5: Addition of Angular Momentum 10.6: Angular Momentum and the Rotation Operator 10.7: Summary Chapter 11. Time Independent and Time Dependent Perturbation Theory. 11.1: Introduction 11.2: Time Independent Perturbation Theory. 11.3: Time Dependent Perturbation Theory: Fermi's Golden Rule 11.4: Summary Chapter 12. Bosons and Fermions: Indistinguishable particles with intrinsic spin. 12.1: Introduction 12.2: Eigenfunctions and Eigenvalues of the Exchange Operator 12.3: The Exchange Symmetry Postulate: Bosons and Fermions 12.4: The Heitler-London Model 12.5: Summary Chapter 13. Quantum Measurement and Entanglement: Wave-Function Collapse 13.1: Introduction 13.2: Quantum Measurement 13.3: Quantum Entanglement and the Impact of Measurement 13.4: Quantum Teleportation 13.5: Summary Chapter 14. Loss and Decoherence: The RLC Circuit 14.1: Introduction 14.2: Coupling to a Continuum of States: The Weisskopf-Wigner Approximation 14.3: Decay in the Nano-Vibrator Problem 14.4: The RLC Circuit 14.5: Summary Chapter 15. The Quantum Radiation Field: Spontaneous Emission and Entangled Photons 15.1: Introduction 15.2: Finding the Hamiltonian for the Transverse Electromagnetic Field 15.3: Quantizing the Field 15.4: Spontaneous Emission 15.5: The Effects of the Quantum Vacuum on Linear Absorption and Dispersion 15.6: Rabi Oscillations in the Vacuum: The Jaynes Cummings Hamiltonian 15.7: Summary Chapter 16. Atomic Operators 16.1: Introduction 16.2: Defining the Atomic Operators 16.3: The Physical Meaning of the Atomic Operators 16.4: The Atomic Operators in the Heisenberg Picture 16.5: The Exact Solution for the Atomic Operators for a Monochromatic Field 16.6: The Operator Equations of Motion Including Spontaneous Emission Chapter 17. Quantum Electromagneticst 17.1: Introduction 17.2: The Number State Representation 17.3: The Coherent State 17.4: Quantum Beam Splitter: Quantum Interference 17.5: Resonant Rayleigh Scattering: A Single Quantum Emitter 17.6: Creating a Quantum Entangled State Between a Photon and an Electron 17.7: Engineering the Quantum Vacuum 17.8: Summary Chapter 18. The Density Matrix: Bloch Equations 18.1: Introduction 18.2: The Density Matrix Operator 18.3: The Density Matrix Equations Including Relaxation 18.4: Solving the Reduced Density Matrix for a Two-Level System in the Presence of Resonant Classical Electromagnetic Field 18.5: Rate Equation Approximation 18.6: The Three-Level System: Emerging Importance in Quantum Technology 18.7: Summary Appendices A: Essential Mathematics Review B: Power Series for important Functions C: Properties and Representations for the Dirac Delta Function D: Vector Calculus and Vector IdentifiesThe Electromagnetic Hamiltonian and the Göpert-Mayer Transformation E: The Electromagnetic Hamiltonian and the Göpert-Mayer Transformation F: Maxwell's Equations in Media, the Wave Equation and Coupling to a two-level system G: Wigner-Eckart Theorem for evaluating matrix elements.
Duncan G. Steel, The Robert J. Hiller Professor, Professor of Electrical Engineering and Computer Science, Professor of Physics, The University of Michigan - Ann Arbor. PhD in 1976 in Electrical and Nuclear Science, University of Michigan. Guggenheim Fellow (1999), APS Isakson Prize (2010), Elected Fellow of APS, OSA, and IEEE. 10 years at Hughes Research Laboratories (senior staff physicist), faculty at the University of Michigan (1985-), Area Chair for Optics and Director of the Optical Sciences Laboratory 1988-2007, Director of Biophysics 2007-2009.
Reviews for Introduction to Quantum Nanotechnology: A Problem Focused Approach
This book presents a combination of quantum physics and nanotechnology which is appealing and quite distinctive. The author has a huge amount of experience in presenting the material in the book to an undergraduate audience, and in working with the same range of ideas in a research context. The nature of the presentation of the material reflects this experience. * Richard Phillips, University of Cambridge * Duncan Steel has written an excellent textbook for intermediate engineering students, based on his experience in teaching classes in the area of quantum mechanics for engineers and in mentoring research students in the basic physics issues in quantum technology. His selection of topics is right on the mark. His consideration for the accessibility by the students is detailed, valuable and quite rare. The book has a lot of appeal. * Lu J. Sham, University of California at San Diego *
