Preface ........................................................ XI
1. Introduction ................................................. 1
1.1. The Beginning ........................................... 2
1.2. Subsequent Developments ................................. 5
1.3. The dc SQUID: A First Look .............................. 7
1.4. The rf SQUID: A First Look ............................. 12
1.5. Cryogenics and Systems ................................. 16
1.6. Instruments: Amplifiers, Magnetometers and
Gradiometers ........................................... 17
1.7. Applications ........................................... 21
1.8. Challenges and Perspectives ............................ 24
1.9. Acknowledgment ......................................... 26
2. SQUID Theory ................................................ 29
2.1. Josephson Junctions .................................... 30
2.1.1. RCSJ Model ...................................... 31
2.1.2. Thermal Noise ................................... 37
2.1.3. The 1 //Noise (70, R fluctuations) .............. 41
2.2. Theory of the dc SQUID ................................. 43
2.2.1. Introduction .................................... 43
2.2.2. Basic Equations, dc SQUID Potential ............. 44
2.2.3. Thermal Fluctuations ............................ 50
2.2.3.1. General Considerations ................. 50
2.2.3.2. Numerical Simulations (Langevin
Equation) .............................. 53
2.2.3.3. Analytical Theory ofthedc SQUID ........ 59
2.2.4. Effect of Asymmetry ............................. 65
2.3. Theory of the rf SQUID ................................. 70
2.3.1. Introduction .................................... 70
2.3.2. SQUID Potential and the Equation of Motion
for the Phase Difference ........................ 72
2.3.3. Unitary Theory for Output Signal and Noise ...... 76
2.3.4. Noise as a Small Perturbation ................... 83
2.3.4.1. Introduction ........................... 83
2.3.4.2. Adiabatic Operation; Hysteretic
Phase Diagram .......................... 84
2.3.4.3. Non-adiabatic Regime ................... 86
3. SQUID Fabrication Technology ................................ 93
3.1. Junction Electrode Materials and Tunnel Barriers ....... 94
3.2. Low-temperature SQUID Devices .......................... 96
3.2.1. Refractory Junction Electrodes .................. 96
3.2.2. Tunnel Barrier Technology ....................... 97
3.2.3. Deposition Techniques ........................... 98
3.2.4. Junction Definition ............................ 101
3.2.5. Dielectric Insulation .......................... 102
3.2.6. Patterning Techniques .......................... 103
3.2.7. Passive Components for Device Fabrication ...... 105
3.2.8. Integrated SQUID Fabrication Process ........... 105
3.3. High-temperature SQUID Devices ........................ 107
3.3.1. General Requirements and Problems .............. 107
3.3.2. Thin-film Deposition ........................... 108
3.3.3. Patterning Techniques .......................... 110
3.3.4. Junction Fabrication ........................... 112
3.3.5. Fabrication of Single-layer Devices ............ 115
3.3.6. Fabrication of Multilayer Devices .............. 116
3.3.7. Device Passivation and Encapsulation ........... 128
3.4. Future Trends ......................................... 118
4. SQUID Electronics .......................................... 127
4.1. General ............................................... 128
4.2. Basic Principle of a Flux-locked Loop ................. 328
4.2.1. Linearization of the Transfer Function ......... 128
4.2.2. Noise and Dynamic Behavior ..................... 131
4.2.3. Integrator Types ............................... 135
4.3. The dc SQUID Readout .................................. 137
4.3.1. Fundamentals ................................... 137
4.3.2. Methods to Suppress Preamplifier Noise ......... 139
4.3.2.1. Flux Modulation ...................... 139
4.3.2.2. Additional Positive Feedback ......... 141
4.3.3. Methods to Suppress 1/f Noise .................. 143
4.3.4. Further Readout Concepts ....................... 148
4.3.4.1. Two-stage Configuration .............. 148
4.3.4.2. Series SQUID Arrays .................. 149
4.3.4.3. Relaxation Oscillation SQUIDs ........ 150
4.3.4.4. Digital SQUIDs ....................... 152
4.4. The rf SQUID Readout .................................. 155
4.4.1. General ........................................ 155
4.4.2. Basic Building Blocks of rf SQUID Readout
Electronics
4.4.3. Construction of the Tank Circuit ............... 157
4.4.4. Coupling of the Tank Circuit to the
Transmission Line .............................. 159
4.4.5. Cryogenic Preamplifiers ........................ 260
4.4.6. Optimization for Maximum Sensitivity ........... 162
4.4.7. Multiplexed Readouts for Multichannel rf
SQUID Systems .................................. 164
4.5. Trends in SQUID Electronics ........................... 265
5. Practical DC SQUIDS: Configuration and Performance ......... 172
5.1. Introduction .......................................... 172
5.2. Basic dc SQUID Design ................................. 175
5.2.1. Uncoupled SQUIDs ............................... 175
5.2.2. Coupled SQUIDs ................................. 177
5.3. Magnetometers ......................................... 186
5.3.1. Overview ....................................... 186
5.3.2. Magnetometers for High Spatial Resolution ...... 187
5.3.3. Magnetometers for High Field Resolution ........ 188
5.4. Gradiometers .......................................... 193
5.4.1. Overview ....................................... 193
5.4.2. Thin-Film Planar Gradiometers .................. 195
5.4.3. Wire-Wound Axial Gradiometers .................. 198
5.5. l/f Noise and Operation in Ambient Field .............. 200
5.5.1. General Remarks on l/f Noise ................... 200
5.5.2. Critical Current Fluctuations .................. 200
5.5.3. Thermally Activated Motion of Vortices ......... 202
5.5.4. Generation of vortices ......................... 203
5.5.5. Reduction of l/f Noise Generated by Vortex
Motion ......................................... 205
5.5.5.1. Overview .............................. 205
5.5.5.2. Vortex pinning ........................ 205
5.5.5.3. Narrow Linewidth Device
Structures ............................ 206
5.5.5.4. Flux Dams ............................. 207
5.6. Other Performance Degrading Effects ................... 208
5.6.1. Hysteresis ..................................... 208
5.6.2. Radio-Frequency Interference ................... 209
5.6.3. Temperature Fluctuations and Drift ............. 220
6. Practical RF SQUIDs: Configuration and Performance ......... 229
6.1. Introduction .......................................... 220
6.2. Rf SQUID Magnetometers ................................ 220
6.2.1. Practical Device Optimization .................. 220
6.2.2. Low-Temperature rf SQUID Magnetometers ......... 223
6.2.2.1. Low-Temperature Bulk
Magnetometers ......................... 223
6.2.2.2. Low-Temperature Thin-Film
Magnetometers ......................... 226
6.2.3. High-Temperature rf SQUID Magnetometers ........ 228
6.2.3.1. Technological Limitations ............. 228
6.2.3.2. Bulk High-Tc Magnetometers ............ 229
6.2.3.3. Early Thin-Film High-Tc
Magnetometers ......................... 229
6.2.3.4. Magnetometers with Coplanar
Resonators ............................ 230
6.2.3.5. Magnetometers with Dielectric
Resonators ............................ 234
6.2.3.6. Thin-Film HTS Magnetometers with
Flux Transformers .................... 235
6.3. Rf SQUID Gradiometers ................................. 236
6.3.1. Low-Temperature Gradiometers ................... 236
6.3.2. High-Temperature Gradiometers .................. 236
6.3.2.1. Hardware rf SQUID Gradiometers ........ 236
6.3.2.2. Electronic rf SQUID
gradiometers .......................... 237
6.4. Low-Frequency Excess Noise in rf SQUIDs ............... 237
6.5. Response of rf SQUIDs to High-Frequency
Electromagnetic Interference .......................... 239
6.6. Characterization and Adjustment of rf SQUIDs .......... 241
6.7. The rf SQUID versus the dc SQUID ...................... 244
6.8. Concluding Remarks and Outlook ........................ 246
7. SQUID System Issues ........................................ 251
7.1. Introduction .......................................... 254
7.2. Cryogenics ............................................ 255
7.2.1. Introduction ................................... 255
7.2.2. Liquid Cryogen Cooling (Cryostats) ............. 256
7.2.3. Cryogenic Refrigerators (Cryocoolers) .......... 258
7.2.3.1. Introduction .......................... 258
7.2.3.2. Joule-Thomson Coolers ................. 259
7.2.3.3. Stirling Coolers ...................... 260
7.2.3.4. Gifford-McMahon Coolers ............... 261
7.2.3.5. Pulse-tube Coolers .................... 262
7.2.3.6. Comparison of Cryocoolers ............. 264
7.2.3.7. Trends in Cryocooling ................. 265
7.2.4. Cryostat or Cryocooler? ........................ 266
7.2.5. Cryocooler-interference Reduction .............. 267
7.2.5.1. Interference Mechanisms ............... 267
7.2.5.2. Time Separation ....................... 268
7.2.5.3. Space Separation ...................... 268
7.2.5.4. Low-noise Coolers ..................... 269
7.2.5.5. Noise Suppression Techniques .......... 269
7.2.6. Material Properties ............................ 270
7.3. Cabling and Electronics ............................... 272
7.3.1. Shielding and Filtering of Noise Sources ....... 272
7.3.1.1. Introduction to Shielding
Effectiveness ......................... 272
7.3.1.2. Absorption ............................ 273
7.3.1.3. Reflection ............................ 274
7.3.1.4. High-frequency Shielding .............. 276
7.3.1.5. Low-frequency Shielding ............... 277
7.3.1.6. Filtering in an Unshielded Urban
Environment ........................... 281
7.3.1.7. Determination of Low-frequency
Shielding, Filtering or Noise
Cancellation Requirements ............. 282
7.3.2. Electronics and Cables ......................... 283
7.3.2.1. RF Screening of Electronics ........... 283
7.3.2.2. Cables and Conductors ................. 284
7.3.2.3. Cable Junctions, Terminations,
Connectors and Grounding .............. 285
7.3.2.4. Crosstalk ............................. 286
7.3.2.5. Power Consumption and Supply .......... 287
7.3.2.6. Choice of SQUIDs and Electronics ...... 289
7.4. Data Acquisition and Rudimentary Signal Processing .... 289
7.4.1. Introduction ................................... 289
7.4.2. Hardware Considerations ........................ 290
7.4.3. Dynamic Range, Accuracy and Linearity .......... 290
7.4.4. Sampling Rate and Signal Conditioning .......... 292
7.4.5. Digital Signal Conditioning and Storage ........ 292
7.5. Characterization, Calibration and Testing ............. 292
7.5.1. Introduction ................................... 292
7.5.2. Characterizing SQUIDs .......................... 293
7.5.2.1. Introduction .......................... 293
7.5.2.2. Transfer Coefficient .................. 293
7.5.2.3. Effective Area of a Magnetometer ...... 294
7.5.2.4. Effective Volume of a Gradiometer ..... 294
7.5.2.5. SQUID Noise and Bandwidth
Measurements .......................... 295
7.5.2.6. Dynamic Range ......................... 296
7.5.2.7. Slew Rate ............................. 296
7.5.2.8. Nonlinearity .......................... 297
7.5.3. Characterization in Various Magnetic Field
Situations ..................................... 298
7.5.3.1. Introduction .......................... 298
7.5.3.2. Field-applied (FA) Characterization ... 299
7.5.3.3. Field-removed (FR) Characterization ... 299
7.5.3.4. Hysteresis ............................ 301
7.5.4. Calibration .................................... 301
7.5.4.1. Setting up Calibration Fields ......... 301
7.5.4.2. Magnetometer and Gradiometer
Calibration ........................... 305
7.5.5. Testing and Practical Tips ..................... 305
7.5.5.1. Drifts and Offsets .................... 305
7.5.5.2. SQUID or Flux Jumps ................... 305
7.5.5.3. Excess Noise .......................... 307
7.5.5.4. Electronic Noise from Other Systems ... 307
7.5.5.5. Adequate Shielding of the Cryostat .... 307
7.5.5.6. Consequences of Cryogen Boil-off ...... 308
7.5.5.7. Mechanical Vibration .................. 308
7.5.5.8. Increase in Noise of the System
Compared to a SQUID ................... 309
7.6. Conditions Imposed on SQUID Systems by the
Environment and Applications .......................... 309
7.6.1. Introduction ................................... 309
7.6.2. Signals Acting on SQUID Systems ................ 310
7.6.3. Noise Acting on a SQUID System ................. 311
7.6.3.1. Environmental Noise in Stationary
Applications .......................... 311
7.6.3.2. Additional Noise in Mobile
Instrumentation ....................... 315
7.7. Noise Suppression ..................................... 315
7.7.1. Introduction ................................... 315
7.7.2. Active Shielding ............................... 315
7.7.3. Noise Cancellation by Primary Sensors .......... 316
7.7.4. Noise Cancellation Using References ............ 319
7.7.4.1. Introduction .......................... 319
7.7.4.2. Static Systems ........................ 323
7.7.4.3. Mobile Systems ........................ 330
7.7.5. Noise Cancellation Without the References ...... 332
7.8. Signal and Noise Implications for the SQUID System
Design ................................................ 335
7.8.1. Introduction ................................... 335
7.8.2. Static SQUID Systems ........................... 335
7.8.3. Mobile SQUID Systems ........................... 339
7.8.4. Summary of Parameters .......................... 342
7.9. Concluding Remarks and System Trends .................. 344
Appendix 1 .................................................... 357
Appendix 2 .................................................... 367
Index ......................................................... 383
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