Charged Particle Traps (eBook)

Preface 6
Contents 8
Trap Operation Theory 13
1 Introduction 14
1.1 Historical Background 14
1.2 Principles of Particle Confinement 21
2 The Paul Trap 27
2.1 Theory of the Ideal Paul Trap 27
2.2 Motional Spectrum in Paul Trap 33
2.3 Adiabatic Approximation 34
2.4 Real Paul Traps 37
2.5 Instabilities in an Imperfect Paul Trap 43
2.6 The Role of Collisions in a Paul Trap 46
2.7 Quantum Dynamics in Paul Traps 49
3 The Penning Trap 60
3.1 Theory of the Ideal Penning Trap 60
3.2 Motional Spectrum in Penning Trap 65
3.3 Real Penning Traps 66
3.4 Shift of the Eigenfrequencies 68
3.5 Instabilities of the Ion Motion 77
3.6 Tuning the Trap 79
3.7 Quantum Dynamics in Ideal Penning Trap 81
3.8 Quantum Dynamics in Real Penning Traps 90
4 Other Traps 95
4.1 Combined Traps 95
4.2 Cylindrical Traps 103
4.3 Nested Traps 115
4.4 Multipolar Traps 116
4.5 Linear Traps 117
4.6 Ring Traps 125
4.7 Planar Paul Traps 126
4.8 Electrostatic Traps 131
4.9 Kingdon Trap 132
Trap Techniques 135
5 Loading of Traps 138
5.1 Ion Creation Inside Trap 138
5.2 Ion Injection from Outside the Trap 140
5.3 Positron Loading 142
6 Trapped Charged Particle Detection 146
6.1 Destructive Detection 146
6.2 Nondestructive Detection 148
Nonclassical States of Trapped Ions 155
7 Quantum States of Motion 157
7.1 Fock States 157
7.2 Oscillator Coherent States 158
7.3 Squeezed States 163
8 Coherent States for Dynamical Groups 165
8.1 Trap Symmetries 165
8.2 Quasienergy States for Combined Traps 166
9 State Engineering and Reconstruction 173
9.1 Trapped Ion-Laser Interaction 173
9.2 State Creation 177
9.3 State Reconstruction 187
Cooling of Trapped Charged Particles 193
10 Trapped Ion Temperature 196
10.1 Measurement of Ion Temperature 197
11 Radiative Cooling 200
12 Buffer Gas Cooling 205
12.1 Paul Trap 206
12.2 Penning Trap 208
13 Resistive Cooling 212
13.1 Negative Feedback 216
13.2 Stochastic Cooling 217
14 Laser Cooling 221
14.1 Physical Principles 221
14.2 Doppler Cooling: Semi-classical Theory 223
14.3 Resolved Sideband Cooling 226
14.4 EIT Cooling 233
14.5 Sisyphus Cooling 236
14.6 Stimulated Raman Cooling 246
14.7 Sympathetic Cooling 250
15 Adiabatic Cooling 256
Trapped Ions as Nonneutral Plasma 258
16 Plasma Properties 260
16.1 Coulomb Correlation Parameter 260
16.2 Weakly Coupled Plasmas 260
17 Plasma Oscillations 266
17.1 Rotating Wall Technique 269
18 Plasma Crystallization 272
18.1 Phase Transitions 272
18.2 Chaos and Order 275
18.3 Crystalline Structures 277
19 Sympathetic Crystallization 291
A Mathieu Equations 294
A.1 Parametric Oscillators 294
B Orbits of Trapped Ions 297
C Nonlinear Oscillator 303
C.1 Multipole Expansions 303
C.2 Normal Forms 304
C.3 Nonlinear Resonances 306
D Generating Functions for Quantum States 309
D.1 Uncertainty Relations 309
D.2 Generating Functions 310
D.3 Displacement Operators 313
D.4 Time Dependent Oscillators 314
D.5 Coherent States for Symplectic Groups 317
E Trap Design and Electronics 320
F Charged Microparticle Trapping 324
References 327
Index 340