Coherent States: New Insights Into Quantum Mechanics with Applications

ISBN-13: 9783031207655 / Angielski / Miękka / 2023 / 351 str.

Chon-Fai Kam; Wei-Min Zhang; Da-Hsuan Feng

Opis

This 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. 

Spis treści

Chapter 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

O autorze

Chon-Fai Kam received his Ph.D. degree in theoretical condensed matter physics from the Chinese University of Hong Kong in 2018. From 2019 to 2021, he was a Postdoc Fellow at the Department of Mathematics of University of Macau. Since 2022, he has been a Postdoc Fellow at the Department of Physics of University at Buffalo. His research interests include squeezed coherent states, multipartite entanglement, quantum information, quantum phase transition, non-Hermitian systems, and non-adiabatic transitions. He developed a nonlinear quantum mechanics approach to interacting quantum systems, a quantum information approach to quantum phase transitions, and the Majorana star representation for general multipartite entangled states. He is now working on enhanced spin qubit readout using optical squeezed states. 

Wei-Min Zhang is a Distinguished Professor of the Physics Department at National Cheng Kung University (NCKU) in Taiwan. He received his PhD in theoretical physics from Drexel University, USA, in 1989. He was Post-Doctoral Research Fellows at the University of Washington in Seattle (1990-1991), and at the Ohio-State University (1992-1993). From 1994 to 1998, he was a Visiting Associate Professor at the Institute of Physics of Academic Sinica at Taipei and became a Full Professor in 1999 and, then, a Distinguished Professor in 2004 at NCKU. His research interests cover many different fields in theoretical physics, including quantum information and quantum computing, mesoscopic physics, quantum optics, open quantum systems and quantum decoherence, quantum transport, strongly correlated many-body physics, quantum chromodynamics (QCD), quantum field theory, quantum chaos, nuclear physics, quantum phase transitions and quantum thermodynamics. He developed the transport theory for heavy-ion collisions, the two component theory of light-front QCD, a SU(2)xU(1) gauge theory for high-temperature superconductivity, the fermionic decoherent theory of nanoelectronics, the photonic transport theory of nanophotonics, the general non-Markovian theory for open quantum systems and the quantum dissipative theory of topological matter.

Da-Hsuan Feng received his Ph.D. in theoretical nuclear physics from the University of Minnesota in 1972. From 1991-2000, he was M. Russell Wehr Professor of Physics at Drexel University. From 2001-2007, he was Vice President (VP) of Research and Professor of Physics at the University of Texas in Dallas. From 2007-2017, he was Senior Executive VP at National Tsing Hua University, National Cheng Kung University and Special Advisor to the President of University of Macau, respectively. Between 1983-1985, he was the Program Director of Theoretical Physics of the National Science Foundation.  In 1996, he became a Fellow of the American Physical Society: “For outstanding contributions to the understanding of nuclear structure physics, particularly for the use of coherent states.” In 1990, together with Wei-Min Zhang and Robert Gilmore published a review article entitled Coherent States: Theory and Some Applications in the Review of Modern Physics, cited more than 1600 times.