Bücher
Service
Michael Mehring is the director of the Physikalische Institut at the Universität Stuttgart, Germany.
Table of Contents
Preface
Notation
List of Graphical Symbols
1 Motivation
Spin Physics
2 A Quick Tour
2.1 Classes and Objects in Hilbert Space
2.1.1 The Class of Hilbert States
2.1.2 The Class of Spin Operators
2.1.3 The Class of Propagators
2.2 Classes and Objects in Liouville Space
2.2.1 The Class of Liouville States
2.2.2 The Class of Spin Superoperators
2.2.3 The Class of Superpropagators
3 The Objects in Hilbert Space
3.1 The Discrete Hilbert Space of Spin States
3.1.1 Zeeman States
3.1.2 Hilbert State Vectors
3.2 Operators I: Operators and Representations
3.2.1 The Two-Level System
3.2.2 The Three-Level System
3.2.3 The Multi-Level System
3.3 Operators II: Sets of Independent Operators
3.3.1 The Two-Level System
3.3.2 The Three-Level System
3.3.3 The Multi-Level System
3.4 Operators III: Rotations of Operators
3.4.1 Spin Operator Rotations
3.4.2 Tensor Operator Rotations
3.5 Operators IV: Density Operator and Density Matrix
3.5.1 Ensembles of Spin-1/2 Particles
3.5.2 Ensembles of Spin-I Particles
3.6 Operators V: Basis Changes
3.6.1 The Two-Level System
3.6.2 The Multi-Level System
3.7 Operators VI: Spin Hamiltonians
3.7.1 The Zeeman Hamiltonian
3.7.2 The Quadrupole Hamiltonian
3.8 Operators VII: Composite Spin Systems
3.8.1 Spin Operators of Two Spins I = 1/2
3.8.2 The Tensor Operators of Two Spins I = 1/2
3.8.3 The Density Operator of Two Spins I = 1/2
3.8.4 Interaction Hamiltonians of Two Spins I= 1/2
4 The Dynamics in Hubert Space
4.1 The Time Evolution
4.1.1 Object Dynamics in the Schrödinger Representation
4.1.2 Object Dynamics in the Heisenberg Representation
4.1.3 Object Dynamics in the Interaction Representation
4.2 The State Representation
4.2.1 Time-Independent Perturbation Expansion
4.2.2 Time-Dependent Perturbation Expansion
4.2.3 Product Representation
4.2.4 Magnus Expansion
4.3 Periodic Hamiltonians
4.3.1 Linearly and Circularly Polarized Excitations
4.3.2 An Introduction to the Average Hamiltonian Approach (AHA)
4.3.3 An Introduction to the Secular Averaging Approach (SAA)
4.4 Periodic Excitations
4.4.1 Fundamental Circularly Polarized Excitations
4.4.2 Linearly Polarized Excitations
5 The Objects in Liouville Space
5.1 The Liouville Space
5.1.1 Liouville States and Liouville Basis
5.1.2 Orthogonality and Completeness
5.1.3 Expectation Values
5.2 Liouville Operators I: Superoperators
5.2.1 Definition
5.2.2 Matrix Elements
5.2.3 Rotation Operations
5.3 Liouville Operators II: Composite Spin Systems
5.3.1 The Two-Spin Density Operator: Basis Operators
5.3.2 The Two-Spin Density Operator: Time Evolution
5.3.3 The Liouville Matrix
6 The Way to Magnetic Resonance
6.1 Classes, Objects, and Functions
6.1.1 Objects and Functions in Hubert Space
6.1.2 Objects and Functions in Liouville Space
6.2 Pulse Sequences
6.2.1 Pulse Sequence Operators
6.2.2 The Delta Pulse Approximation
6.2.3 The Density Matrix Before the First Pulse
6.3 Pulse Response Functions
6.3.1 Magnetic Resonance Response Functions
6.3.2 Fourier and Laplace Transformations
Magnetic Resonance
7 Spin Interactions and Spectra
7.1 Hamiltonians
7.1.1 External Interactions
7.1.2 Internal Interactions (NMR)
7.1.3 Internal Interactions (ESR)
7.2 Spectra
7.2.1 Shift Interaction Spectra
7.2.2 Quadrupolar Spectra
7.2.3 Spin-Spin Interaction Spectra
7.3 Rotations
7.3.1 Sample Rotation
7.3.2 Sample Spinning
7.3.3 Molecular Reorientation
8 Relaxation and Decoherence
8.1 Principles of Relaxation Measurements
8.1.1 The Spin-Lattice Relaxation
8.1.2 Spin-Spin Relaxation
8.1.3 Spin-Locking
8.2 Relaxation in the Rapid Motion Limit
8.2.1 Relaxation Rate and Memory Function
8.2.2 Fluctuating Local Fields
8.2.3 Relaxation Rates for Special Spin Interactions
8.2.4 Spin Fluctuations
8.3 Relaxation in the Slow Motion Limit
8.3.1 Relaxation and Memory Effects
8.3.2 Rapid Motion Limit
8.4 Models of Molecular Motion
8.4.1 Isotropie Molecular Reorientations
8.4.2 Anisotropie Molecular Reorientations
8.4.3 Discrete Jump Models
9 Spin Echos
9.1 The Hahn Echo in Inhomogeneous Fields
9.1.1 The Pulse Sequence of the Hahn Echo
9.1.2 The Response Function of the Hahn Echo
9.1.3 The Generalized Spin Echo Response Function
9.1.4 Phase Cycling
9.2 The Rotary Echo
9.2.1 The Pulse Sequence of the Rotary Echo
9.2.2 The Response Function of the Rotary FID
9.2.3 The Response Function of the Rotary Echo
9.3 The Driven Echo
9.3.1 The Pulse Sequence of the Driven Echo
9.3.2 The Response Function of the Driven Echo
9.4 The Stimulated Echo
9.4.1 Pulse Sequence and Response Function
9.4.2 The Genuine Stimulated Echo
9.5 The Quadrupolar Echo
9.5.1 The Pulse Sequence of the Quadrupolar Echo
9.5.2 The Response Function of the Quadrupolar Echo
9.5.3 The Primary Quadrupole Echo
9.5.4 Separation of Magnetic and Quadrupole Echos
9.5.5 Multiple Quadrupole Echos
9.6 The Solid Echo
9.6.1 The Pulse Sequence of the Solid Echo
9.6.2 The Response Function of the Solid Echo
9.7 The Magic Echo
9.7.1 The Magic Echo Pulse Sequence
9.7.2 The Magic Echo Condition
9.7.3 The Magic Sandwich Superpropagator
9.8 Echo Envelope Modulation
9.8.1 The Envelope Function of the Two-Pulse Echo
9.8.2 The Envelope Function of the Stimulated Echo
10 Double Resonance
10.1 Double Resonance in Three-Level Spin Systems
10.1.1 The Boltzmann Equilibrium
0.1.4 Spin Alignment
10.2 Double Resonance in Multi-Level Spin Systems
10.2.1 The «-Level Population
10.2.2 The z Magnetization
10.2.3 The Inverse Spin Temperatures
10.3 Electron Nuclear Double Resonance (ENDOR)
10.3.1 Population and Polarization Dynamics
10.3.2 Dynamic Nuclear Spin Polarization (DNP)
10.4 Spin Echo Double Resonance (SEDOR)
10.4.1 The Spin Echo Response Function without / Pulse
10.4.2 The Spin Echo Response Function with / Pulse
10.4.3 The Spin Echo Response Function with Time Variation
10.5 Proton Enhanced Nuclear Induction Spectroscopy
10.5.1 Cross Polarization (CP)
10.5.2 Adiabatic Demagnetization and Cross Polarization
10.5.3 Cross Polarization Dynamics
10.5.4 Spin Decoupling Dynamics
10.6 Pulsed ENDOR
10.6.1 Davies and TRIPLE ENDOR
10.6.2 Mims ENDOR
11 Multiple-Pulse Experiments
11.1 What are Multiple-Pulse Experiments?
11.2 Carr-Purcell-Meiboom-Gill Multiple-Spin Echo Train
11.2.1 The Carr-Purcell Pulse Sequence
11.2.2 The Meiboom-Gill Pulse Sequence
11.3 Chemical Shift Concertina
11.3.1 The Chemical Shift Concertina Pulse Sequence
11.3.2 Application of the Average Hamiltonian Theory
11.4 The WAHUHA Four-Pulse Experiment
11.4.1 The WAHUHA Pulse Sequence
11.4.2 Application of the Average Hamiltonian Theory
11.4.3 High-Resolution Solid State Spectra
11.5 The Flip-Flop Lee-Goldburg (FFLG) Experiment
11.5.1 The Lee-Goldburg (LG) Pulse Sequence
11.5.2 The Flip-Flop Lee-Goldburg (FFLG) Pulse Sequence
11.6 Advanced Multiple-Pulse Experiments
11.6.1 Eight-Pulse Cycles (HW-8 and MREV-8)
11.6.2 24-Pulse and 52-Pulse Cycles (BR-24 and BR-52)
11.6.3 Time Reversal Multiple-Pulse Cycles
12 Multiple-Quantum Spectroscopy
12.1 Multiple-Quantum Transitions
12.1.1 Multiple-Quantum Transitions in Multi-Spin Systems
12.1.2 Excitations by Strong Irradiation
12.1.3 Double-Quantum Decoupling
12.2 Time Domain Multiple-Quantum Spectroscopy
12.2.1 Multiple-Quantum Excitation, Evolution, and Detection
12.2.2 Multiple-Quantum Spectra
12.2.3 Time Reversal Sequences
12.2.4 Generalized Multiple-Quantum Theory
12.2.5 Selective MQ Pumping
12.3 Multiple-Quantum and Transient Sublevel ENDOR
12.3.1 Preparation for Sublevel ENDOR
12.3.2 Multiple-Quantum ENDOR
12.3.3 Transient Sublevel ENDOR
13 Two-Dimensional Spectroscopy
13.1 What is Two-Dimensional Spectroscopy?
13.2 Principles of 2D Fourier Spectroscopy
13.2.1 Magnetic Resonance Line Shapes in 2D Spectroscopy
13.2.2 Quantum Evolution in 2D Spectroscopy
13.2.3 Skewed and Sheared 2D Spectra
13.3 Separation of Interactions
13.3.1 Spin-Spin versus Shift Interactions
13.3.2 Correlation Spectroscopy (COSY)
13.3.3 Exchange Spectroscopy
13.4 Hyperfine Correlation Spectroscopy (HYSCORE)
13.4.1 The HYSCORE Response Function
13.4.2 The Case of S = 1/2 and I= 1/2
13.4.3 The Case of S = 1/2 and I=1
14 Spin Quantum Computing
14.1 First Steps in Quantum Computing
14.1.1 The NOT Gate
14.1.2 The CNOT Gate
14.1.3 The Toffoli Gate
14.1.4 The Quantum Bit
14.1.5 The Quantum Measurement
14.2 Elementary Spin Quantum Gates
14.2.1 The Spin Implementation of the NOT Gate
14.2.2 The Spin Implementation of the ?NOT Gate
14.2.3 The Spin Implementation of the CNOT Gate
14.2.4 The Spin Implementation of the SWAP Gate
14.2.5 The Spin Implementation of the Alternative Toffoli Gate
14.2.6 The NMR Implementation by Cory et al
14.2.7 The 2D NMR Representation of Quantum Gates
14.3 Entangled Spin States
14.3.1 Two-Qubit Systems
14.3.2 Three-Qubit Systems
14.3.3 Two-Bit Entangled State by CNOT Operation
14.4 Pseudo Pure and Mixed States
14.4.1 Mixed States
14.4.2 Pseudo Pure States
14.5 The Implementation of the Deutsch Algorithm
14.5.1 The Deutsch Algorithm
14.5.2 The NMR Implementation
14.6 The Implementation of the Grover Search Algorithm
14.6.1 The Grover Search Algorithm
14.6.2 The NMR Implementation
14.7 Quantum Error Correction and Teleportation
Complementary Analytical and Numerical Methods
15 Analytical Methods
15.1 The Floquet Approach (FA)
15.1.1 The Floquet Theorem
15.1.2 The Floquet Strategy
15.2 The Perturbation-Theoretical Approach (PTA)
15.2.1 The Evolution Operator
15.2.2 The Density Operator
15.2.3 The Operator Modes
15.2.4 The Decomposition Process
15.3 The Secular Averaging Approach (SAA)
15.3.1 The Evolution Operator
15.3.2 The Decomposition Process
15.4 Application: Linearly Polarized Excitations
15.4.1 The Total Evolution Operator in a Two-Level Spin System
15.4.2 The Total Density Operator in a Two-Level Spin System
15.4.3 The Magnetization Vector in a Two-Level Spin System
15.4.4 A Numerical Analysis
15.4.5 Remarks on the SAA
15.4.6 Remarks on the FA
15.5 FA, PTA, or SAA?
16 GAMMA
16.1 Installation
16.2 Programming Structures
16.3 Classes, Objects, and Functions
16.4 GNUPLOT
Appendix
17 Lists
17.1 Objects
17.1.1 Tensor Operators
17.1.2 Hamiltonians
17.2 Object Transformation
17.2.1 Rotations of Tensor Operators
17.2.2 Rotations of Hamiltonians
17.3 Object Commutation
Bibliography
Index
About the Authors
This book presents, for the first time, a unified treatment of the quantum mechanisms of magnetic resonance, including both nuclear magnetic resonance (NMR) and electron spin resonance (ESR). Magnetic resonance is perhaps the most advanced type of spectroscopy and it is applied in biology, chemistry, physics, material science, and medicine. If applied in conjunction with spectroscopy, the imaging version of magnetic resonance has no counterpart in any type of experimental technique.
The authors present explanations and applications from fundamental to advanced levels.
