List of contributors ......................................... xiii
Preface ....................................................... xvi
Part I Principles and techniques ............................... 1
1 General principles and characteristics of optical
magnetometers ................................................ 3
D.F. Jackson Kimball, E.B. Alexandrov, and D. Budker
1.1 Introduction ............................................ 3
1.1.1 Fundamental sensitivity limits ................... 4
1.1.2 Zeeman shifts and atomic spin precession ......... 5
1.1.3 Quantum beats and dynamic range .................. 8
1.2 Model of an optical magnetometer ........................ 8
1.3 Density matrix and atomic polarization moments ......... 13
1.4 Sensitivity and accuracy ............................... 16
1.4.1 Variational sensitivity (short-term
resolution) and long-term stability ............. 16
1.4.2 Parameter optimization .......................... 18
1.4.3 Absolute accuracy and systematic errors ......... 19
1.5 Vector and scalar magnetometers ........................ 20
1.6 Applications ........................................... 21
2 Quantum noise in atomic magnetometers ....................... 25
M.V. Romalis
2.1 Introduction ........................................... 25
2.2 Spin-projection noise .................................. 26
2.3 Faraday rotation measurements .......................... 26
2.4 Quantum back-action .................................... 27
2.5 Time correlation of spin-projection noise .............. 28
2.6 Conditions for spin-noise dominance .................... 30
2.7 Spin projection limits on magnetic field sensitivity ... 32
2.8 Spin squeezing and atomic magnetometry ................. 36
2.9 Conclusion ............................................. 37
3 Quantum noise, squeezing, and entanglement in
radiofrequency optical magnetometers ........................ 40
K. Jensen and E.S. Polzik
3.1 Sources of noise ....................................... 40
3.1.1 Atomic projection noise ......................... 40
3.1.2 Photon shot noise ............................... 41
3.1.3 Back-action noise and QND measurements .......... 42
3.1.4 Technical (classical) noise ..................... 42
3.1.5 Entanglement and spin squeezing ................. 42
3.2 A pulsed radiofrequency magnetometer and the
projection noise limit ................................. 43
3.2.1 Pulsed RF magnetometry .......................... 44
3.2.2 Sensitivity and bandwidth ....................... 45
3.3 Light-atom interaction ................................. 46
3.3.1 A spin-polarized atomic ensemble interacting
with polarized light ............................ 47
3.3.2 Conditional spin squeezing ...................... 48
3.3.3 Larmor precession, back-action noise, and two
atomic ensembles ................................ 48
3.3.4 Swap and squeezing interaction .................. 49
3.4 Demonstration of high-sensitivity, projection-noise-
limited magnetometry ................................... 50
3.4.1 Setup, pulse sequence, and procedure ............ 50
3.4.2 The projection-noise-limited magnetometer ....... 52
3.5 Demonstration of entanglement-assisted magnetometry .... 54
3.6 Conclusions ............................................ 57
4 Mx and Mz magnetometers ..................................... 60
E.B. Alexandrov and A.K. Vershovskiy
4.1 Dynamics of magnetic resonance in an alternating
field .................................................. 60
4.1.1 Bloch equations and Bloch sphere ................ 60
4.1.2 Types of magnetic resonance signals: Mz and Mx
signals ......................................... 62
4.2 Mz and Mx magnetometers: general principles ............ 63
4.2.1 Advantages and disadvantages of Mz
magnetometers ................................... 66
4.2.2 Advantages and disadvantages of Mx
magnetometers ................................... 67
4.2.3 Attempts to combine advantages of Mx and Mz
magnetometers: Mx-Mz tandems .................... 72
4.3 Applications: radio-optical Mx and Mz magnetometers .... 73
4.3.1 Alkali Mz magnetometers ......................... 73
4.3.2 Mx magnetometers ................................ 75
4.3.3 MMx-Mz tandems .................................. 79
4.4 Summary: Mx and Mz scheme limitations, prospects, and
application areas ...................................... 82
5 Spin-exchange-relaxation-free (SERF) magnetometers .......... 85
J. Savukov and S.J. Seltzer
5.1 Introduction ........................................... 85
5.2 Spin-exchange collisions ............................... 86
5.2.1 The density-matrix equation ..................... 86
5.2.2 Simple model of spin exchange ................... 90
5.3 Bloch equation description ............................. 92
5.4 Experimental realization ............................... 95
5.4.1 Classic SERF atomic magnetometer arrangement .... 95
5.4.2 Zeroing the magnetic field ...................... 98
5.4.3 Use of antirelaxation coatings .................. 98
5.4.4 Comparison with SQUIDs .......................... 99
5.5 Fundamental sensitivity ............................... 101
6 Optical magnetometry with modulated light .................. 104
D.F. Jackson Kimball, S. Pustelny, V.V. Yashchuk, and
D. Budker
6.1 Introduction .......................................... 104
6.2 Typical experimental arrangements ..................... 106
6.3 Resonances in the magnetic field dependence ........... 108
6.3.1 Frequency modulation ........................... 108
6.3.2 Amplitude modulation ........................... 111
6.3.3 Polarization modulation ........................ 113
6.4 Effects at high light powers .......................... 113
6.5 Nonlinear Zeeman effect ............................... 116
6.6 Magnetometric measurements with modulated light ....... 118
6.7 Conclusion ............................................ 122
7 Microfabricated atomic magnetometers ....................... 125
S. Knappe and J. Kitching
7.1 Introduction .......................................... 125
7.2 Sensitivity scaling with size ......................... 126
7.3 Sensor fabrication .................................... 131
7.4 Vapor cells ........................................... 133
7.5 Heating and thermal management ........................ 134
7.6 Performance ........................................... 135
7.7 Applications of microfabricated magnetometers ......... 137
7.8 Outlook ............................................... 139
8 Optical magnetometry with nitrogen-vacancy centers in
diamond .................................................... 142
V.M. Acosta, D. Budker, P.R. Hemmer, J.R. Maze, and
R.L. Walsworth
8.1 Introduction .......................................... 142
8.1.1 Comparison with existing technologies .......... 143
8.2 Historical background ................................. 144
8.2.1 Single-spin optically detected magnetic
resonance ...................................... 145
8.3 NV center physics ..................................... 146
8.3.1 Intersystem crossing and optical pumping ....... 146
8.3.2 Ground-state level structure and ODMR-based
magnetometry ................................... 148
8.3.3 Interaction with environment ................... 150
8.4 Experimental realizations ............................. 152
8.4.1 Near-field scanning probes and single-NV
magnetometry ................................... 152
8.4.2 Wide-field array magnetic imaging .............. 157
8.4.3 NV-ensemble magnetometers ...................... 158
8.5 Outlook ............................................... 161
9 Magnetometry with cold atoms ............................... 167
W. Gawlik and J.M. Higbie
9.1 Introduction .......................................... 167
9.2 Experimental conditions ............................... 168
9.2.1 Constraints and advantages of using cold
atoms for magnetometry ......................... 168
9.2.2 Cold samples of atoms above quantum
degeneracy ..................................... 168
9.3 Linear Faraday rotation with trapped atoms ............ 170
9.4 Nonlinear Faraday rotation ............................ 173
9.4.1 Low-field, DC magnetometry ..................... 173
9.4.2 Coherence evolution ............................ 174
9.4.3 High-field, amplitude-modulated magneto-
optical rotation ............................... 175
9.4.4 Paramagnetic nonlinear rotation ................ 175
9.5 Magnetometry with ultra-cold atoms .................... 176
9.5.1 Overview of ultra-cold atomic magnetometry
methods ........................................ 176
9.5.2 Figures of merit ............................... 180
9.5.3 Details of spinor magnetometry ................. 182
9.5.4 Comparison with thermal-atom magnetometry ...... 185
9.5.5 Applications ................................... 187
10 Helium magnetometers ....................................... 190
R.E. Slocum, D.D. McGregor, and A.W. Brown
10.1 Introduction .......................................... 190
10.2 Helium magnetometer principles of operation ........... 191
10.2.1 Helium resonance element ....................... 192
10.2.2 Helium optical pumping radiation sources ....... 192
10.2.3 Optical pumping of metastable helium ........... 194
10.2.4 Observation of optically pumped helium ......... 196
10.2.5 Observation of magnetic resonance signals in
optically pumped helium ........................ 197
10.3 Conclusions ........................................... 202
11 Surface coatings for atomic magnetometry ................... 205
S.J. Seltzer, M.-A. Bouchiat, and M.V. Balabas
11.1 Introduction and history .............................. 205
11.2 Wall relaxation mechanisms ............................ 208
11.2.1 Origin and time dependence of the
disorienting interaction ....................... 208
11.2.2 Methods of investigation ....................... 209
11.2.3 Quantitative interpretation .................... 212
11.3 Coating preparation ................................... 213
11.4 Light-induced atomic desorption (LIAD) ................ 217
11.5 Recent characterization methods ....................... 219
12 Magnetic shielding ......................................... 225
V.V. Yashchuk, S.-K. Lee, and E. Paperno
12.1 Introduction .......................................... 225
12.2 Ferromagnetic shielding ............................... 225
12.2.1 Simplified estimation of ferromagnetic
shielding efficiency for a static magnetic
field .......................................... 226
12.2.2 Multilayer ferromagnetic shielding ............. 227
12.2.3 Optimization of permeability: annealing,
degaussing, shaking, tapping ................... 232
12.2.4 Magnetic-field noise in ferromagnetic
shielding ...................................... 235
12.2.5 Examples of ferromagnetic shielding systems .... 236
12.3 Ferrite shields ....................................... 238
12.3.1 Permeability ................................... 238
12.3.2 Fabrication and the effect of an air gap ....... 239
12.3.3 Thermal noise .................................. 240
12.4 Superconducting shields ............................... 241
12.4.1 Principles ..................................... 242
12.4.2 Materials and fabrication ...................... 243
12.4.3 Image field .................................... 244
Part II Applications ......................................... 249
13 Remote detection magnetometry .............................. 251
S.M. Rochester, J.M. Higbie, B. Patton, D. Budker,
R. Holzlöhner, and D. Bonaccini Calia
13.1 Introduction .......................................... 251
13.2 A remotely interrogated all-optical 87Rb
magnetometer .......................................... 252
13.3 Magnetometry with mesospheric sodium .................. 256
14 Detection of nuclear magnetic resonance with atomic
magnetometers .............................................. 265
M.P. Ledbetter, I. Savukov, S.J. Seltzer, and D. Budker
14.1 Introduction .......................................... 265
14.2 The NMR Hamiltonian ................................... 267
14.3 Challenges associated with detection of NMR using
atomic magnetometers .................................. 268
14.4 Remote detection ...................................... 269
14.5 Solenoid matching of Zeeman resonance frequencies ..... 272
14.6 Flux transformer ...................................... 273
14.7 Nuclear quadrupole resonance .......................... 274
14.8 Zero-field nuclear magnetic resonance ................. 275
14.8.1 Thermally polarized zero-field NMR J
spectroscopy ................................... 275
14.8.2 Parahydrogen-enhanced zero-field NMR ........... 278
14.8.3 Zeeman effects on J-coupled multiplets ......... 281
14.9 Conclusions ........................................... 282
15 Space magnetometry ......................................... 285
B. Patton, A.W. Brown, R.E. Slocum, and E.J. Smith
15.1 Introduction .......................................... 285
15.1.1 Achievements of space magnetometry ............. 285
15.1.2 Challenges unique to space magnetometers ....... 286
15.1.3 Magnetic sensors used in space missions ........ 287
15.2 Alkali-vapor magnetometers in space applications ...... 287
15.2.1 Initial development of Earth's-field alkali
magnetometers .................................. 287
15.2.2 Sensor design .................................. 288
15.2.3 NASA missions employing alkali-vapor
magnetometers .................................. 289
15.3 Helium magnetometers in space applications ............ 293
15.3.1 Introduction ................................... 293
15.3.2 Future helium space magnetometers .............. 298
16 Detection of biomagnetic fields ............................ 303
A. Ben-Amar Baranga, T.G. Walker, and R.T. Wakai
16.1 Sources of biomagnetism ............................... 303
16.2 Development of biomagnetic field detection ............ 304
16.3 Medical applications .................................. 308
16.4 Magnetocardiography with atomic magnetometers ......... 310
16.5 Magnetoencephalography with an atomic magnetometer .... 313
16.6 Summary ............................................... 316
17 Geophysical applications ................................... 319
M.D. Prouty, R. Johnson, I. Hrvoic, and A.K. Vershovskiy
17.1 Airborne magnetometers and gradiometers ............... 319
17.2 Ground magnetometers/gradiometers ..................... 321
17.3 Marine magnetometers/gradiometers ..................... 323
17.4 Vector magnetometry with optically pumped
magnetometers ......................................... 324
17.5 Earthquake studies .................................... 329
17.6 Applications of magnetometers to detecting
unexploded ordnance (UXO) ............................. 331
17.6.1 Introduction to the problem .................... 331
17.6.2 Using magnetometers for UXO detection .......... 332
17.6.3 Mathematics of UXO detection ................... 333
Part III Broader impact ....................................... 337
18 Tests of fundamental physics with optical magnetometers .... 339
D.F. Jackson Kimball, S.K. Lamoreaux, and Т.E. Chupp
18.1 Overview and introduction ............................. 339
18.2 Searches for permanent electric dipole moments ........ 341
18.2.1 Basic experimental setup for an EDM
experiment ..................................... 344
18.2.2 Sensitivity to EDMs ............................ 345
18.2.3 Electric fields and coherence times for
various systems ................................ 346
18.2.4 Magnetometry and comagnetometry in EDM
experiments .................................... 349
18.3 Anomalous spin-dependent forces ....................... 352
18.3.1 Background ..................................... 352
18.3.2 Experiments .................................... 355
18.4 CPT and local Lorentz invariance tests ................ 361
18.5 Conclusion ............................................ 364
19 Nuclear magnetic resonance gyroscopes ...................... 369
E.A. Donley and J. Kitching
19.1 Introduction .......................................... 369
19.2 NMR frequency shifts and relaxation ................... 373
19.2.1 Spin exchange .................................. 374
19.2.2 Quadrupole surface frequency shifts ............ 375
19.2.3 General wall relaxation ........................ 377
19.2.4 Magnetic-field gradients ....................... 377
19.2.5 Noble-gas self-relaxation ...................... 378
19.3 Alkali shifts and relaxation mechanisms ............... 379
19.4 Two-spin NMR gyroscope ................................ 379
19.5 Comagnetometer ........................................ 381
19.6 Miniaturization ....................................... 383
19.7 Conclusion ............................................ 383
20 Commercial magnetometers and their application ............. 387
D.С. Hovde, M.D. Prouty, I. Hrvoic, and R.E. Slocum
20.1 Introduction .......................................... 387
20.2 Specifications ........................................ 388
20.2.1 Noise .......................................... 388
20.2.2 Resolution ..................................... 391
20.2.3 Sensitivity .................................... 391
20.2.4 Sample rate and cycle time ..................... 392
20.2.5 Bandwidth ...................................... 392
20.2.6 Absolute error and drift ....................... 393
20.2.7 Gradient tolerance ............................. 394
20.2.8 Dead zones ..................................... 395
20.2.9 Heading error .................................. 395
20.2.10 Range of measurement .......................... 397
20.3 History of commercial magnetometry .................... 398
20.3.1 Fluxgate magnetometers ......................... 398
20.3.2 SQUID magnetometers ............................ 399
20.3.3 Proton-precession and Overhauser
magnetometers .................................. 399
20.3.4 Alkali metal magnetometers: rubidium, cesium,
and potassium .................................. 401
20.3.5 Helium-3 and helium-4 magnetometers ............ 402
20.4 Military applications ................................. 403
20.5 Anticipated improvements .............................. 404
Index ......................................................... 406
|
