Quantum Mechanics II: Advanced Topics

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
About the Authors
1. Quantum Field Theory
	1.1. Introduction
	1.2. Why Quantum Field Theory?
	1.3. What is a Field?
	1.4. Classical Field Theory
	1.5. Quantum Equations for Fields
	1.6. Quantization of Nonrelativistic Wave Equation
	1.7. Electromagnetic Field in Vacuum
	1.8. Interaction of Charged Particles with Electromagnetic Field
	1.9. Quantization of Klein–Gordon Equation
	1.10. Quantization of Dirac Field
	1.11. Gauge Field Theories
	1.12. Concluding Remarks
	1.13. Bibliography
	1.14. Exercises
2. Path Integral Formulation
	2.1. Introduction
	2.2. Time Evolution of Wave Function and Propagator
	2.3. Path Integral Representation of Propagator
	2.4. Connection Between Propagator and Classical Action
	2.5. Schrodinger Equation From Path Integral Formulation
	2.6. Transition Amplitude of a Free Particle
	2.7. Systems with Quadratic Lagrangian
	2.8. Path Integral Version of Ehrenfest's Theorem
	2.9. Concluding Remarks
	2.10. Bibliography
	2.11. Exercises
3. Supersymmetric Quantum Mechanics
	3.1. Introduction
	3.2. Supersymmetric Potentials
	3.3. Relations Between the Eigenstates of Two Supersymmetric Hamiltonians
	3.4. Hierarchy of Supersymmetric Hamiltonians
	3.5. Applications
	3.6. Generation of Complex Potentials with Real Eigenvalues
	3.7. Concluding Remarks
	3.8. Bibliography
	3.9. Exercises
4. Coherent and Squeezed States
	4.1. Introduction
	4.2. The Uncertainty Product of Harmonic Oscillator
	4.3. Coherent States: De nition, Uncertainty Product and Physical Meaning
	4.4. Generation and Properties of Coherent States
	4.5. Spin Coherent States
	4.6. Coherent States of Position-Dependent Mass Systems
	4.7. Squeezed States
	4.8. Deformed Oscillators and Nonlinear Coherent States
	4.9. Concluding Remarks
	4.10. Bibliography
	4.11. Exercises
5. Berry's Phase, Aharonov–Bohm and Sagnac Effects
	5.1. Introduction
	5.2. Derivation of Berry's Phase
	5.3. Origin and Properties of Berry's Phase
	5.4. Classical Analogue of Berry's Phase
	5.5. Berry's Phase in Solid State Physics
	5.6. Examples and E ects of Berry's Phase
	5.7. Applications of Berry's Phase
	5.8. Experimental Veri cation of Berry's Phase
	5.9. Pancharatnam's Work
	5.10. Cumulants Associated with Geometric Phases
	5.11. The Aharonov–Bohm Effect
	5.12. Sagnac Effect
	5.13. Concluding Remarks
	5.14. Bibliography
	5.15. Exercises
6. Phase Space Picture and Canonical Transformations
	6.1. Introduction
	6.2. Squeeze and Rotation in Phase Space
	6.3. Linear Canonical Transformations
	6.4. Wigner Function
	6.5. Time Evolution of the Wigner Function
	6.6. Applications
	6.7. Advantages of the Wigner Function
	6.8. Concluding Remarks
	6.9. Bibliography
	6.10. Exercises
7. Quantum Entanglement
	7.1. Introduction
	7.2. States in Classical Mechanics
	7.3. Quantum Entangled States
	7.4. Mixed States
	7.5. Bipartite Systems
	7.6. Separability Criteria
	7.7. Multipartite Entanglement
	7.8. Quantifying Entanglement
	7.9. Applications of Entanglement
	7.10. Concluding Remarks
	7.11. Bibliography
	7.12. Exercises
8. Quantum Decoherence
	8.1. Introduction
	8.2. Decoherence and Interference Damping
	8.3. Interaction of a Detector on the Double-Slit Experiment
	8.4. Decoherence Due to Phase Randomization
	8.5. Position Decoherence Due to Environmental Scattering
	8.6. Master Equations
	8.7. Decoherence Models
	8.8. Decoherence Experiments
	8.9. The Role of Decoherence in the Interpretation of Quantum Mechanics
	8.10. Concluding Remarks
	8.11. Bibliography
	8.12. Exercises
9. Quantum Computers
	9.1. Introduction
	9.2. What is a Quantum Computer?
	9.3. Why is a Quantum Computer?
	9.4. Fundamental Properties
	9.5. Quantum Algorithms
	9.6. Testing Quantum Computers Using Grover's Algorithm
	9.7. Features of Quantum Computation
	9.8. Quantum Computation Through NMR
	9.9. Why is Making a Quantum Computer Extremely Diffcult?
	9.10. Concluding Remarks
	9.11. Bibliography
	9.12. Exercises
10. Quantum Cryptography
	10.1. Introduction
	10.2. Standard Cryptosystems
	10.3. Quantum Cryptography–Basic Principle
	10.4. Types of Quantum Cryptography
	10.5. Multiparty Quantum Secret Sharing
	10.6. Applications of Quantum Cryptography
	10.7. Implementation and Limitations
	10.8. Fiber-Optical Quantum Key Distribution
	10.9. Quantum Cheque Scheme
	10.10. Concluding Remarks
	10.11. Bibliography
	10.12. Exercises
11. No-Cloning Theorem and Quantum Cloning Machines
	11.1. Introduction
	11.2. Proof of No-Cloning Theorem
	11.3. No-Broadcasting Theorem
	11.4. No-Cloning and No-Superluminar Signalling
	11.5. Quantum Cloning Machines
	11.6. Quantum Telecloning
	11.7. Other No-Go Theorems
	11.8. Concluding Remarks
	11.9. Bibliography
	11.10. Exercises
12. Quantum Tomography
	12.1. Introduction
	12.2. Pauli Problem
	12.3. Recovery of Density Matrix from Wigner Function
	12.4. Optical Homodyne Tomography
	12.5. Qubit Quantum Tomography
	12.6. Experimental Measure of Polarization of a Photonic Qubit
	12.7. Multiqubit Tomography
	12.8. Quantum Process Tomography
	12.9. Conclusion
	12.10. Bibliography
	12.11. Exercises
13. Quantum Simulation
	13.1. Introduction
	13.2. Limitations of Classical Computers in Simulating Quantum Systems
	13.3. Quantum Simulators
	13.4. Analog Quantum Simulators
	13.5. Digital Quantum Simulators
	13.6. Theory of Quantum Simulation of the Schrodinger Equation
	13.7. Quantum Simulators Using Quantum Computers
	13.8. Quantum Circuits
	13.9. Quantum Circuits for Final Measurements
	13.10. Concluding Remarks
	13.11. Bibliography
	13.12. Exercises
14. Quantum Error Correction
	14.1. Introduction
	14.2. Sources of Errors in Quantum Information Processing
	14.3. Di culties of Using Classical Error Correction Techniques to QEC
	14.4. Digitization of Quantum Errors
	14.5. QEC Mechanisms Using Quantum Redundancy
	14.6. QEC with Stabilizer Codes
	14.7. The Surface Code
	14.8. Practical Issues in the Implementation of QEC Codes
	14.9. Concluding Remarks
	14.10. Bibliography
	14.11. Exercises
15. Some Other Advanced Topics
	15.1. Introduction
	15.2. Quantum Theory of Gravity
	15.3. Quantum Cosmology
	15.4. Quantum Zeno Effect
	15.5. Quantum Teleportation
	15.6. Quantum Games
	15.7. Quantum Pseudo-Telepathy Games
	15.8. Quantum Steering
	15.9. Quantum Diffusion
	15.10. Quantum Chaos
	15.11. Concluding Remarks
	15.12. Bibliography
	15.13. Exercises
16. Quantum Technologies
	16.1. Introduction
	16.2. Quantum Entangled Photons
	16.3. Ghost Imaging
	16.4. Detection of Weak Amplitude Object
	16.5. Entangled Two-Photon Microscopy
	16.6. Detection of Small Displacements
	16.7. Quantum Lithography
	16.8. Quantum Metrology
	16.9. Quantum Teleportation of Optical Images
	16.10. Quantum Sensors
	16.11. Quantum Batteries
	16.12. Quantum Internet
	16.13. Concluding Remarks
	16.14. Bibliography
	16.15. Exercises
Solutions to Selected Exercises
Index