Charged Particle Traps II (eBook)

Preface 6
Contents 8
Part I Electromagnetic Trap Properties 12
1 Summary of Trap Properties 13
1.1 Trapping Principles in Paul Traps 13
1.1.1 General Principles 15
1.1.2 Potential Depth 17
1.1.3 Motional Spectrum 18
1.1.4 Optimum Trapping Conditions 18
1.1.5 Storage Time 19
1.1.6 Ion Density Distribution 20
1.1.7 Storage Capability 20
1.1.8 Paul Trap Imperfections 21
1.2 Trapping Principles in Penning Traps 23
1.2.1 Theory of the Ideal Penning Trap 23
1.2.2 Motional Spectrum in Penning Traps 25
1.2.3 Penning Trap Imperfections 26
1.2.4 Storage Time 28
1.2.5 Storage Capability 30
1.2.6 Spatial Distribution 30
1.3 Trap Techniques 31
1.3.1 Trap Loading 31
In-trap Ion Creation 31
Ion Injection from Outside 31
1.3.2 Trapped Particle Detection 33
Destructive Detection 33
Nondestructive Detection 34
1.4 Ion Cooling Techniques 38
1.4.1 Buffer Gas Cooling 38
1.4.2 Resistive Cooling 39
1.4.3 Laser Cooling 40
1.4.4 Radiative Cooling 43
Part II Mass Spectrometry 45
2 Mass Spectrometry Using Paul Traps 46
2.1 The Quadrupole Ion Trap as a Mass Spectrometer 49
2.2 The ``Mass Instability Method'' of Detection 50
2.3 Sources of Mass Error in Ion Ejection Methods 53
2.4 Nonlinear Resonances in Imperfect Quadrupole Trap 53
2.5 Quadrupole Time-of-Flight Spectrometer 55
2.6 Tandem Quadrupole Mass Spectrometers 57
2.7 Tandem Quadrupole Fourier Transform Spectrometer 59
2.8 Silicon-Based Quadrupole Mass Spectrometers 61
3 Mass Spectroscopy in Penning Trap 64
3.1 Systematic Frequency Shifts 64
3.1.1 Electric Field Imperfections 64
3.1.2 Magnetic Field Imperfections 66
3.1.3 Misalignements and Trap Ellipticity 66
3.1.4 Image Charges 67
3.1.5 Magnetic Field Fluctuations 67
3.2 Observation of Motional Resonances 69
3.2.1 Nondestructive Observation 69
3.2.2 Destructive Observation 72
3.3 Line Shape of Motional Resonances 75
3.3.1 Nondestructive Detection 75
3.3.2 Destructive Detection 77
Dipole Excitation 77
Quadrupole Excitation 78
Ramsey Excitation 79
3.4 Experimental Procedures 81
3.4.1 Reference Ions 82
3.5 Selected Results 85
3.5.1 Stable and Long Lived Isotopes 86
3H–3He Mass Difference 86
Proton/Electron Mass Ratio 87
Proton/Antiproton Mass Ratio 87
Cs Mass and the Fine Structure Constant 87
SI Mass and the Kilogram 88
3.5.2 Short-Lived Isotopes 88
Part III Spectroscopy with Trapped Charged Particles 91
4 Microwave Spectroscopy 92
4.1 Zeeman Spectroscopy 92
4.1.1 g-Factor of the Free Electron 93
4.1.2 g-Factor of the Bound Electron 102
4.1.3 Atomic g-Factor 108
4.1.4 Nuclear gI-Factor 110
4.2 Hyperfine Structures in the Ground States 112
4.2.1 Summary of HFS Theory 112
4.2.2 Early Experiments 114
4.2.3 Laser Microwave Double Resonance Spectroscopy 120
4.3 Microwave Atomic Clocks 125
4.3.1 Definition of the Unit of Time 125
4.3.2 Trapped Ion Microwave Standards 128
The JPL 199Hg+ Standard 130
The NIST 199Hg+ Standard 132
Other Possible Ion Microwave Standards 135
5 Optical Spectroscopy 136
5.1 Optical Frequency Standards 136
5.1.1 Theoretical Limit to Laser Spectral Purity 136
5.1.2 Laser Stabilization 138
5.1.3 Single Ion Optical Frequency Standards 140
Servo-Related Limit on Stability: The Dick Effect 140
Quantum Projection Noise 142
The 199Hg+ Optical Standard 143
Optical Frequency Standards Based on Alkaline Earth Ions 145
Optical Frequency Standard Based on 171Yb+ Ion 148
Optical Frequency Standard based on 115In+ Ion 151
Optical Frequency Standard Based on 27Al+ Ion 152
5.1.4 Correction of Systematic Errors 154
The Electric Quadrupole Shift 155
The Quadratic Zeeman Shift 156
Relativistic Doppler Shift 157
Quadratic Stark Shifts 158
Gravitational Red Shift 158
Other Systematic Biases 158
5.1.5 Optical Frequency Measurement 159
5.2 Progress in Standards 164
6 Lifetime Studies in Traps 167
6.1 Radiative Lifetimes 167
6.1.1 Experimental Methods of Lifetime Measurement 168
Direct Decay Method 168
Sequential Pulsed Laser Methods 171
Methods Using the Static (Kingdon) Ion Trap 176
6.1.2 Systematic Effects on the Lifetimes 178
Mixing of States 178
Light Scattering Effects 179
Effect of Collisions 179
6.1.3 Quenching Collisions 182
Part IV Quantum Topics 183
7 Quantum Effects in Charged Particle Traps 184
7.1 Quantum Jumps 185
7.2 The Quantum Zeno Effect 185
7.3 Entanglement of Trapped Ion States 188
7.3.1 Entanglement of Two-Trapped Ions 189
7.3.2 Entanglement of Three-Trapped Ions 191
7.3.3 Multi-ion Entanglement 192
7.3.4 Trapped Ion–Photon Entanglement 194
7.3.5 Lifetime of Entangled States 195
7.4 Quantum Teleportation 196
7.5 Sources of Decoherence 200
7.5.1 Decoherence Reservoirs 200
7.5.2 Motional Decoherence 201
7.5.3 Collisions with Background Gas 204
7.5.4 Internal State Decoherence 205
7.5.5 Induced Decoherence 207
7.5.6 Control of Thermal Decoherence 208
Dynamical Decoupling 209
Quantum Zeno Control 210
8 Quantum Computing with Trapped Charged Particles 211
8.1 Background Fundamentals 212
8.1.1 Quantum Bits: Qubits 212
8.1.2 Some History 214
8.1.3 Possible Alternatives: The DiVincenzo Criteria 216
8.2 Ion Traps for Quantum Computing 219
8.2.1 Trap Electrode Design 219
8.2.2 Choice of Ion 220
8.3 Qubits with Trapped Ions 223
8.4 Quantum Registers: Qregister 224
8.4.1 Initialisation of the Qubits 227
Initialisation of the Bus Qubit 228
8.5 Creation of Nonclassical States 230
8.5.1 Fock States 230
8.5.2 Coherent States 231
8.5.3 Schrödinger Cat States 231
8.6 Quantum Logic Gates 232
8.7 Qubit Entanglement 235
8.8 Quantum Information Processing 236
8.8.1 Speed of Operation 238
8.8.2 Nonclassical State Reconstruction 239
8.9 Qubit Decoherence 243
8.10 Scalability 244
8.11 Penning Trap as Quantum Information Processor 249
8.11.1 Computing with Electrons 249
8.11.2 Linear Multi-trap Processor 249
8.11.3 Planar Multi-trap Processor 251
8.11.4 Expected Performance 258
8.12 Future Developments 259
References 261
Index 275