Description
Book SynopsisThis book presents the essential ideas of coherent states and provides researchers and graduate students with the necessary tools for various applications of generalized coherent state theory. These applications include areas such as quantum information, quantum phase transitions, quantum many-body systems, quantum chaos, and quantum open systems. The aim of the book is to show how coherent states can be applied to an extensive range of physical systems. The authors provide many exercises at the end of each chapter to enhance the mastery of the subject. Throughout the first seven chapters, only an understanding of elementary quantum mechanics is assumed, and for the last six chapters, some basic knowledge of group theory is requested to follow the arguments.
Table of ContentsChapter 1. Introduction
Chapter 2. Coherent States of Harmonic Oscillator
1. Schrodinger’s wavepacket
2. Glauber’s coherent state
3. Mathematical properties
4. The uncertainty relation
Exercises
Chapter 3. Schrodinger’s Cat States
1. EPR paradox, cat states and entanglement
2. Experimental realization
3. Application to quantum information
Exercises
Chapter 4. Coherent State of Fermions
1. Graßmann algebra
2. Coherent state of Fermions
Exercises
Chapter 5. Coherent State Path Integrals
1. Path integral formalism
2. Coherent state path integral
3. Functional quantum field theory
Exercises
Chapter 6. Spin Coherent States
1. Spin coherent state in quantum optics
2. Qubit state and quantum coherence
3. Geometric phases for spin coherent states
4. Experimental realization
5. Spin cat states
Exercises
Chapter 7. Squeezed Coherent States
1. Squeezed vacuum states
2. Squeezed coherent states in quantum optics
3. Uncertainty relations
4. Detection of gravitational waves
5. Continuous variable quantum information
6. Spin squeezed states
Exercises
Chapter 8. Examples of Coherent States beyond SU(2)
5. SU(1,1) coherent states
6. SU(3) coherent states
Exercises
Chapter 9. Lie Group Generalizations of Coherent States
1. Lie group and Lie algebra
2. Generalized coherent states
3. General properties of coherent states
Exercises
Chapter 10. Many-Body Systems
1. Mean-field approach with coherent states
2. Bogoliubov transformation
3. Many-body quantum entanglement
4. Topological phases of matter
Chapter 11. Statistical Mechanics
1. Lieb inequality and large N limit
2. Coherent state representation of partition function
3. Quantum phase transitions
Chapter 12. Open Quantum Systems
7. Open quantum systems
8. Exact master equations
9. Non-equilibrium dynamics
10. Quantum thermodynamics
Bibliography
