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Index

absorption (saturated), 31, 131, 132,224, 225

adiabatic approximation, 7, 215Allan variances, 122, 127, 133angular momentum, 24, 76, 77, 85, 101,

105, 106, 109, 140, 144, 199, 202,221

anharmonicity, 67, 75, 77, 248, 254axial motion, 28, 74, 245, 246, 249, 250,

252–254

background (buffer) gas, 7, 21–23, 28,41, 46, 47, 123, 162, 164, 168, 174,176

barium ion, 103, 105, 113, 114, 128, 138,139, 162, 167, 168, 173, 174, 180,218

beryllium ion, 103, 202Bessel function, 150black body radiation, 120, 128, 148, 196Bloch vector, 208Bohr-Weisskopf effect, 106, 116Bolometric ion detection, 89Breit-Rabi formula, 105, 112Brewster’s angle, 155

calcium ion, 119, 134, 162, 165–169,172, 175, 184, 186, 188, 190, 214,217, 219, 225

carrier frequency, 33, 150, 154, 224, 227cavity

microwave, 121optical, 141, 144, 184, 189, 190, 242

Cirac–Zoller, 180, 212, 213, 232

coherence, 50, 114, 115, 126, 179, 180,182, 186, 190, 197, 240, 248, 255

collisions, 9, 11, 18, 22, 23, 28, 29, 41,44, 46–49, 54, 88, 101, 107, 108,112, 114, 125, 126, 137, 161, 166,172–174, 176, 179, 191, 199

charge exchange, 137

cross section, 53, 54, 88, 89, 108, 111,155, 176, 199, 216

elastic/inelastic, 88, 89, 108

spin exchange, 88, 107, 111

communication

classical, 193, 194

quantum, 184, 234

cooling of ions, 16, 18, 28, 138, 150, 217,224

buffer gas in paul trap, 28

buffer gas in penning trap, 28

Doppler, 31, 33, 126, 137, 145, 146,164, 167, 169, 185, 188, 224, 225

radiative, 33, 188

resistive, 29, 30, 60, 90

resolved sidebands, 32, 107, 225

sympathetic, 146

Coulomb interaction/scattering, 11, 30,74, 76, 146, 179, 184, 197, 199,241, 245–247, 251, 253

cyclotron motion, 19, 23, 28, 34, 56,60–62, 64, 66, 70, 71, 91, 94, 95,245, 248–250, 255

frequency, 13, 14, 16, 18, 23, 24, 51,55, 58–60, 62, 63, 73, 74, 76, 78,

272 Index

80, 86, 87, 89, 90, 94, 97, 99, 101,251

radius, 65cylindrical ion trap, 4, 5, 50, 52, 53, 61,

94, 97, 215

dark states, 202decoherence, 179, 188–190, 195, 197–

205, 212, 213, 216, 219, 227, 228,235, 239, 240, 244, 255

anomalous motion, 196, 197free subspace, 240induced, 202thermal, 203

density matrix, 183, 186, 188, 195, 203,204, 235

detection ion, 40, 64, 145axial oscillation, 23, 56, 60–62, 66, 92,

97–100, 197, 249bolometric detection, 25Fourier transform, 26, 27, 47, 50–52,

61–63, 78, 97, 144, 253optical detection, 27, 108resonant absorption, 224single electron, 34, 89, 93, 95, 138,

211, 247–250, 252, 254Dick effect, 133Dicke effect, 101diode laser, 141–145, 217, 218

distributed bragg reflector (DBR),140

extended cavity (ECDL), 140dipole excitation, 40, 68, 70dispersion, 154–156DiVincenzo criteria, 213, 255Doppler

broadening, 32, 114, 131, 132cooling, 31, 33, 126, 137, 145, 146,

164, 167, 169, 185, 188, 224, 225second order (relativistic) shift, 150shift, 31, 111, 121, 131, 150side bands, 137

double penning trap, 98, 99

eigenfrequencies, 12–14, 16, 17, 56, 69,99, 100

Einstein–Podolsky–Rosen (EPR)correlations, 192, 209, 211

elastic/inelastic collisions, 16, 88

electric quadrupole interaction, 106, 148electro-optic modulator (EOM), 152electron beam ion trap (EBIT), 81, 170electron cyclotron resonance (ECRIS),

170electron mass, 77–79energy defect, 108entanglement, 179, 183–195, 200, 211,

212, 231, 232, 239, 241error correction techniques/codes,

254–256errors systematic, 74, 147, 168europium ion, 117excitation spectrum, 32, 33

Fabry-Perot cavity, 137Fermi-Segre formula, 106field electric/magnetic, 55, 57, 58, 74,

112fluorescence, 9, 31Fourier spectrum, 63, 153

transform spectrometer, 50Fourier transform detection, 26, 253frequency shifts, 15, 55, 57, 58, 126,

135, 143, 148

g-factoranomaly, 86, 87bound state, 78, 95free electron, 86

gravitational red shift, 120

harmonic/anharmonic oscillator, 7, 34,66, 67, 91, 94, 184, 224, 226, 227,236

helium buffer gas, 112, 114helium ion, 108hydrogen-like atoms, 78, 96, 98hyperfine

anomaly, 106, 116pumping, 104, 109, 110, 112–114, 117,

121, 123qubit, 218spectroscopy, 113structure, 105, 109transitions, 107, 109, 114, 117, 118

image charges, 18, 55, 58, 60, 73, 94,247

Index 273

inelastic collisions, 108instabilities

electric/magneticfield, 78, 100Paul trap, 12, 16, 20, 22Penning trap, 16, 18

interference, 62, 210International Atomic Time (TAI), 128Invariance theorem, 15, 17, 57ion

chips, 256confinement, 3density distribution, 10, 20, 28detection, 40injection, 21motion, 6, 9, 15, 18, 28, 41, 45, 49,

51, 68, 92, 117, 143, 184, 196, 197,199, 224, 232, 236

resonance, 51, 69, 110, 111, 123, 135,138, 142, 223

temperature, 10, 17, 25, 28, 150, 221trajectory, 14, 18, 29, 42

ion sources, 41, 44, 46, 170(photo)ionization, 39, 41, 43, 47, 54,

117, 137, 164ISOLDE-facility, 22, 74, 75isotopes

stable/unstable, 37, 43, 45, 72–74, 76,77, 79, 80, 117, 120, 124, 127, 131

Johnson noise, 195, 197–199

Kingdon trap, 170, 171klystron, 112, 114

Lamb–Dicke parameter/regime, 32, 137,150, 184, 223–225, 234

Lande factor, 150Larmor frequency, 87, 99, 101Laser

diode, 142–145, 217, 218Nd:YAG, 145, 156stabilization, 131Ti:Sa, 128, 143, 144, 153, 155–157,

164lifetime

entangled states, 190, 251radiative, 114, 143, 144, 161, 162,

165, 170, 172, 174light shift, 112, 125, 128, 133

line

motional resonances, 8, 15, 60, 66, 72shapes, 53, 66–71, 93, 95, 100, 114,

115

width, 164linear ion trap, 123, 124, 126, 190, 198,

213–215, 219, 244

magnesium ion, 105, 119magnetic

dipole, 88, 103, 106, 143, 162, 226field corrections, 55, 86, 91, 111fluctuations, 58

resonance, 107, 207, 214shielding, 137

magnetron frequency, 14, 20, 23, 71, 75,91, 251

masers, 124, 127, 128

mass, 60cesium, 78

comparison, 57, 74, 78, 79, 81, 101neutrino, 78proton, 103

proton/antiproton, 78proton/electron, 78

reduced, 203resolution, 37, 39, 41–43, 48, 49, 51,

53, 54

SI standard, 79spectra, 53

uncertainty, 31unstable isotopes, 80

mass filter Paul, 38, 41, 215mass spectrometers, 48, 52, 72, 76

microquadrupole, 43, 53, 54

tandem, 39, 46, 48–50time-of-flight, 46

Mathieu equation, 6parameters, 197

mean free path, 22, 53

mercury ion, 109, 110, 122, 127, 128,137, 141, 217, 218

metastable states, 32, 161, 163, 165,170, 172, 174, 176, 180, 200

micromotion, 7, 10, 28, 33, 145, 150,151, 164, 198, 242

microwave transition, 104, 114, 121, 128motional spectrum, 8, 13, 15

274 Index

natural linewidth, 142, 145nitrogen, 132noise

induced by ions, 26, 63, 78, 97, 100quantum projection, 123, 135spectrum, 68

nuclear g-factor, 105, 106nuclear magnetic resonance (NMR), 213

optical pumping, 101, 104, 109, 113,114, 117, 121, 122, 124, 140,143, 169, 181, 185, 186, 213, 223,224

Paul trap, 198imperfections, 11, 15mass filter, 37non-linear resonances, 45operations, 9, 41, 43, 49, 51, 53

Penning trapcylindrical, 5, 94, 181imperfections, 16–18, 55, 57, 60, 66,

73non-linear resonances, 16operation, 11

photodissociation, 108potential saddle point, 248, 252Pound–Drever–Hall method, 138pressure shift, 112, 132pseudopotential, 49, 50

QED effects, 79, 95quadrupole potential, 4, 5, 11, 13, 215

excitation, 65, 70, 71transitions, 107, 133, 135–137, 162,

167, 228quality-factor, 26, 30, 61, 62, 66, 128,

133, 199, 253quantum

error correction, 212, 214jumps, 144, 173, 174, 180, 254logic gates, 199, 213, 228oscillator, 213register, 220zero point, 107, 121, 137, 146, 186,

188, 213qubits, 190, 192, 202, 208, 209, 212–214,

216, 219, 220, 223, 224, 228,

230–232, 235, 240, 241, 243, 245,249–256

quenching collisions, 166, 176

Rabi frequency, 115, 134, 226, 234, 235radiative lifetime, 114, 143, 144, 161,

162, 165, 170, 172, 180, 201radioactive isotopes, 117Raman scattering, 155Raman transitions, 146, 219, 227, 228Ramsey excitation, 70–72register capacity, 209, 210, 212residual gas analyzer;, 40resolution spectral, 46, 107, 109, 200resonance

fluorescence, 10, 31line shape, 13, 53, 66, 67, 69–72, 95,

100, 115motional, 8

ring trap, 215rotating wall, 20

saddle point, 4saturation (intensity), 27, 131, 164, 166scattering, 11, 30, 49, 87, 111, 137, 155,

165, 172, 173Schrodinger

Cat state, 187, 188, 226, 227, 232equation, 91, 226

secular motion, 7, 44, 126, 137, 150selection rules, 114semiconductor, 179, 244servo control, 127, 131, 133, 138, 142,

148, 203shot noise, 122, 135, 202side-band ion cooling, 145silicon-based mass spectrometer, 52, 53space charge, 9–11, 17, 18, 44, 55spectral purity, 122, 125, 129–131, 137,

138, 143spontaneous emission, 107, 129, 173,

179, 189, 216, 224, 235squeezed states, 237stability parameters, 11stability/instability ion motion, 6, 9,

11, 12, 18, 40–46, 60, 80, 122, 123,128, 129, 131–135, 138, 147, 154,203, 245

Stark shift, 113, 128, 151, 200, 202

Index 275

Stern–Gerlach continuous, 86, 92, 93,97, 121, 253

stimulated emission/force/effect, 107,129

storagecapacity, 16, 20time, 9, 12, 18, 19, 117, 161, 172

strong correlation, 209strontium ion, 119, 134, 139, 141, 142,

162superposition, 13, 15, 90, 147, 186, 192,

195, 208, 210, 219, 223, 226–228,239, 241, 254

surface ionization, 101, 117, 190synchrotron radiation, 90, 250systematic frequency shifts, 143

Tandem mass spectrometer, 50teleportation, 180, 191–194, 212thermal, 26

equilibrium, 10, 11, 20, 27, 28, 67, 68,78, 90, 91, 150, 197, 199, 226

noise, 25, 27, 61, 62, 67, 89, 135time-of-flight spectrometer, 46, 47, 65trajectory of charged (micro)particles,

7, 29transition probability, 27, 71, 114, 134,

161, 162, 176, 183trap

elliptical, 242hyperbolic, 3, 4, 16, 25, 61, 90, 94,

198, 213, 249miniature, 137

planar, 217, 247, 248storage ring, 215

triple resonance experiment, 104two-level atomic system, 27, 31, 116,

216, 219, 255two-photon transition, 131

ultra-low expansion (ULE) material,141, 144, 145

vacuum Rabi frequency, 235vacuum system, 50, 126, 137

cryogenic pumping, 137

wavefunction, 106, 108, 179, 193, 223,227, 234

waveguide, 155wavelength, 32, 39, 107–109, 111, 113,

117, 125, 128, 132, 136, 138, 140,141, 144, 145, 147, 150, 155, 164,189, 198, 213, 217, 219

ytterbium ion, 119, 128, 134, 141–143,162, 174, 175, 182, 183, 217, 218

Zeemancorrection, 146shifts, 140, 146, 147, 149, 200, 239spectrum, 85, 102–104, 107, 151, 219,

240Zeno

effect, 204quantum control, 203, 205

zero point energy, 107, 137, 184, 213

Springer Series on

atomic, optical, and plasma physics

Editors-in-Chief:

Professor G.W.F. DrakeDepartment of Physics, University of Windsor401 Sunset, Windsor, Ontario N9B 3P4, Canada

Professor Dr. G. EckerRuhr-Universitat Bochum, Fakultat fur Physik und AstronomieLehrstuhl Theoretische Physik IUniversitatsstrasse 150, 44801 Bochum, Germany

Professor Dr. H. Kleinpoppen, EmeritusStirling University, Stirling, UK, andFritz-Haber-InstitutMax-Planck-GesellschaftFaradayweg 4–6, 14195 Berlin, Germany

Editorial Board:

Professor W.E. BaylisDepartment of Physics, University of Windsor401 Sunset, Windsor, Ontario N9B 3P4, Canada

Professor Uwe BeckerFritz-Haber-InstitutMax-Planck-GesellschaftFaradayweg 4–6, 14195 Berlin, Germany

Professor Philip G. BurkeSchool of Mathematics and PhysicsQueen’s UniversityDavid Bates Building, Belfast BT7 1NN, UK

Professor R.N. ComptonOak Ridge National LaboratoryBuilding 4500S MS6125Oak Ridge, TN 37831, USA

Professor M.R. FlannerySchool of PhysicsGeorgia Institute of TechnologyAtlanta, GA 30332-0430, USA

Professor C.J. JoachainFaculte des SciencesUniversite Libre BruxellesBvd du Triomphe, 1050 Bruxelles, Belgium

Professor B.R. JuddDepartment of PhysicsThe Johns Hopkins UniversityBaltimore, MD 21218, USA

Professor K.P. KirbyHarvard-Smithsonian Center for Astrophysics60 Garden Street, Cambridge, MA 02138, USA

Professor P. Lambropoulos, Ph.D.Max-Planck-Institut fur Quantenoptik85748 Garching, Germany, andFoundation for Researchand Technology – Hellas (F.O.R.T.H.),Institute of Electronic Structureand Laser (IESL),University of Crete, PO Box 1527Heraklion, Crete 71110, Greece

Professor G. LeuchsFriedrich-Alexander-UniversitatErlangen-NurnbergLehrstuhl fur Optik, Physikalisches InstitutStaudtstrasse 7/B2, 91058 Erlangen, Germany

Professor P. MeystreOptical Sciences CenterThe University of ArizonaTucson, AZ 85721, USA