Charged Particle Traps: Physics and Techniques of Charged Particle Field Confinement

346 Pages·2005·9.529 MB·English

by  Dr. Fouad G. Major, Professor Dr. Viorica N. Gheorghe, Professor Dr. Günther Werth (auth.)

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37 ChargedParticleTraps
PhysicsandTechniquesofChargedParticleFieldConfinement
By F.G.Major,V.N.Gheorghe, G.Werth
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F.G. Major V.N. Gheorghe G. Werth
Charged Particle Traps
Physics and Techniques
of Charged Particle Field Confinement
With187Figures
123
Dr.FouadG.Major
284MichenerCourtE,SevernaPark,MD,USA
E-mail:[email protected]
ProfessorDr.VioricaN.Gheorghe
ProfessorDr.Gu¨ntherWerth
JohannesGutenbergUniversita¨t,FachbereichPhysik(18),Institutfu¨rPhysik
Staudingerweg7,55099Mainz,Deutschland
E-mail:[email protected],[email protected]
ISSN1615-5653
ISBN3-540-22043-7SpringerBerlinHeidelbergNewYork
LibraryofCongressControlNumber:2004107650
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Preface
Overthelastquarterofthiscentury,revolutionaryadvanceshavebeenmade
bothinkindandinprecisionintheapplicationofparticletrapstothestudy
ofthephysics ofchargedparticles,leadingtointensifiedinterestin,andwide
proliferation of, this topic. This book is intended as a timely addition to the
literature, providing a systematic unified treatment of the subject, from the
point of view of the application of these devices to fundamental atomic and
particle physics.
Thetechniqueofusingelectromagneticfieldstoconfineandisolateatomic
particles in vacuo, rather than by material walls of a container, was initially
conceivedbyW.Paulintheformofa3Dversionoftheoriginalrfquadrupole
mass filter, for which he shared the 1989 Nobel Prize in physics [1], whereas
H.G. Dehmelt who also shared the 1989 Nobel Prize [2] saw these devices
(including the Penning trap) as a way of isolating electrons and ions, for the
purposes of high resolution spectroscopy. These two broad areas of applica-
tion have developed more or less independently, each attaining a remarkable
degreeofsophisticationandgeneratingwidespreadinterestandexperimental
activity.
In the case of mass spectrometry, starting in the 1960s there was initially
a rapid proliferation of the use of the 3D rf quadrupole in many fields, such
as residual gas analysis, upper atmospheric research, environmental studies,
gas chromatography. Since then the field has continued to grow and become
refined along differentiated specialized directions, for example sequential ion
mass spectrometry. The extant literature on the mass spectrometry uses of
ion traps is comprehensive, both in the form of monographs and published
proceedings of conferences, such as [3,4].
On the other hand, it was not until tunable laser radiation sources be-
came available that the application of particle traps to the study of atomic
and particle physics saw an explosive expansion in interest and laboratory
activity. By combining laser techniques with those of particle trapping it be-
came possible to fully exploit the particle isolation property of the latter.
Beforethat,withthenotableexceptionoftheexquisitelypreciseworkonthe
freeelectronspectrumbyDehmelt’sgroup,theearlydifficultexperimentsto
exploitthelongperturbation-freespectralobservationtimeiniontrapswere
severelyhandicappedbysmallsignal-to-noiseratios.Theseexperimentswere
carried out by students of Dehmelt and Major on the magnetic resonance
VI Preface
spectrum of He+, and Jefferts on H+. The first successful attempt to detect
2
optical resonance fluorescence from trapped ions using a conventional light
source was achieved at NASA Goddard by Major and Werth in measuring
the hyperfine interval in Hg+. It was first shown by Werth at Mainz that
the scattering of laser light, even from a diffuse distribution of trapped ions,
could be readily detected. The ultimate break-through in the laser detection
of trapped ions came in the work of Toschek et al., in which single ions were
visuallyobserved.This,combinedwiththedemonstrationoflasercoolingby
Wineland et al. led to the incorporation of laser technology into ion trap-
ping, from which evolved a technique in which not only is the signal-to-noise
ratio problem eliminated, but also through laser cooling, the Doppler broad-
ening of the particle spectrum is effectively annulled, ultimately leading to
the formation of ion crystals as first observed by Walther and coworkers and
transforming the technique into one of great power and elegance.
Unlike the application of ion traps to mass spectrometry, the literature
on ion trap physics is diffuse, covering many aspects in the form of extensive
review articles, including for example [5–8]. Also an overview on different
aspectsofiontrapphysicscanbefoundintheformofconferenceproceedings,
suchas[9–11].AsinglemonographIonTraps byP.Ghosh(Oxford)appeared
in 1995.
Neverthelessinviewoftheacceleratedadvancesinthetechniqueinrecent
years,andthefundamentalimportanceofthemanyapplications,itisevident
that a serious gap in the literature exists, which this volume is meant to fill.
Thetreatmentofthesubjectmatterisdesigned,ontheonehand,todevelop
an appreciation of the practical evolution of the technique, its current power
and limitations, and, on the other hand, to provide the necessary theoretical
underpinning, also through appendices and a comprehensive bibliography. It
is left for a future volume to deal with the many important applications,
such as ultrahigh resolution spectroscopy, atomic frequency/time standards,
particle physics, and quantum computation. Having been associated as ex-
perimentalists with the development and application of ion trapping from
the time of its inception, F.G. Major and G. Werth have a natural desire
to attempt an integrated treatment of the subject, which it is hoped will
prove authoritative and useful. With the cooperation of V.N. Gheorghe the
treatment of the experimental areas is nicely complemented by supporting
theory.
V.N.GheorgheacknowledgessupportfromtheJohannesGutenbergUni-
versity, Mainz, Germany and the Alexander von Humboldt Foundation, en-
abling fruitful international cooperation while on leave from the National
Institute for Laser, Plasma, and Radiation and the Physics Department at
the University in Bucharest, Romania.
Mainz, Fouad G. Major
July 2004 Viorica N. Gheorghe
Gu¨nter Werth
Contents
Part I Trap Operation Theory
1 Introduction.............................................. 3
1.1 Historical Background................................... 3
1.2 Principles of Particle Confinement ........................ 10
2 The Paul Trap............................................ 17
2.1 Theory of the Ideal Paul Trap............................ 17
2.2 Motional Spectrum in Paul Trap ......................... 23
2.3 Adiabatic Approximation................................ 24
2.3.1 Potential Depth .................................. 25
2.3.2 Optimum Trapping Conditions..................... 26
2.4 Real Paul Traps........................................ 27
2.4.1 Models for Ion Clouds ............................ 28
2.5 Instabilities in an Imperfect Paul Trap .................... 33
2.6 The Role of Collisions in a Paul Trap ..................... 36
2.7 Quantum Dynamics in Paul Traps........................ 39
2.7.1 Quantum Parametric Oscillator .................... 39
2.7.2 Quantum Dynamics in Ideal Paul Trap.............. 43
2.7.3 Effective Potentials ............................... 46
3 The Penning Trap ........................................ 51
3.1 Theory of the Ideal Penning Trap ........................ 51
3.2 Motional Spectrum in Penning Trap ...................... 56
3.3 Real Penning Traps..................................... 57
3.4 Shift of the Eigenfrequencies ............................. 59
3.4.1 Electric Field Imperfections........................ 59
3.4.2 Magnetic Field Inhomogeneities .................... 62
3.4.3 Distortions and Misalignments ..................... 64
3.4.4 Space Charge Shift ............................... 67
3.4.5 Image Charges ................................... 68
3.5 Instabilities of the Ion Motion............................ 68
3.6 Tuning the Trap........................................ 70
3.7 Quantum Dynamics in Ideal Penning Trap................. 72
3.7.1 Spinless Particle Dynamics ........................ 72
3.7.2 Spin Motion ..................................... 78
VIII Contents
3.8 Quantum Dynamics in Real Penning Traps ................ 81
3.8.1 Electric Field Perturbations ....................... 81
3.8.2 Magnetic Field Perturbations ...................... 83
3.8.3 The General Hamiltonian ......................... 84
4 Other Traps .............................................. 87
4.1 Combined Traps........................................ 87
4.1.1 Equations of Motion .............................. 87
4.1.2 Magnetron-free Operation ......................... 90
4.1.3 Quantum Dynamics in Combined Traps ............. 91
4.2 Cylindrical Traps....................................... 95
4.2.1 Electrostatic Field in a Cylindrical Trap............. 96
4.2.2 Inherent Anharmonicity of the Field ................ 98
4.2.3 Control for Anharmonicity ........................ 99
4.2.4 Dipole Field in a Cylindrical Trap .................. 102
4.2.5 Open-ended Cylindrical Traps ..................... 105
4.3 Nested Traps .......................................... 107
4.4 Multipolar Traps ....................................... 108
4.5 Linear Traps........................................... 109
4.5.1 The Ideal Linear Trap ............................ 109
4.5.2 Electrostatic Field in a Linear Quadrupole Trap...... 113
4.5.3 Electric Field in a Linear Multipole Trap ............ 115
4.6 Ring Traps ............................................ 117
4.7 Planar Paul Traps ...................................... 118
4.8 Electrostatic Traps ..................................... 123
4.9 Kingdon Trap.......................................... 124
Part II Trap Techniques
5 Loading of Traps ......................................... 131
5.1 Ion Creation Inside Trap ................................ 131
5.2 Ion Injection from Outside the Trap ...................... 133
5.3 Positron Loading ....................................... 135
6 Trapped Charged Particle Detection...................... 139
6.1 Destructive Detection ................................... 139
6.1.1 Nonresonant Ejection ............................. 139
6.1.2 Resonant Ejection ................................ 140
6.2 Nondestructive Detection................................ 141
6.2.1 Electronic Detection .............................. 141
6.2.2 Bolometric Detection ............................. 142
6.2.3 Fourier Transform Detection....................... 145
6.2.4 Optical Detection ................................ 146
Contents IX
Part III Nonclassical States of Trapped Ions
7 Quantum States of Motion ............................... 153
7.1 Fock States ............................................ 153
7.2 Oscillator Coherent States ............................... 154
7.2.1 The Ideal Penning Trap ........................... 155
7.2.2 The Harmonic Paul Trap.......................... 156
7.3 Squeezed States ........................................ 159
8 Coherent States for Dynamical Groups ................... 161
8.1 Trap Symmetries ....................................... 161
8.2 Quasienergy States for Combined Traps ................... 162
8.2.1 A Single Trapped Charged Particle ................. 162
8.2.2 Quantum Multiparticle States...................... 165
9 State Engineering and Reconstruction .................... 169
9.1 Trapped Ion-Laser Interaction............................ 169
9.1.1 Atom-Field Hamiltonians.......................... 169
9.1.2 Two-Level Approximation ......................... 170
9.2 State Creation ......................................... 173
9.2.1 Number States................................... 173
9.2.2 Coherent States .................................. 174
9.2.3 Squeezed States .................................. 175
9.2.4 Arbitrary States.................................. 176
9.2.5 Thermal States .................................. 177
9.2.6 Schro¨dinger-Cat States............................ 178
9.3 State Reconstruction.................................... 183
9.3.1 Wigner Functions ................................ 183
9.3.2 Experimental State Reconstruction ................. 185
Part IV Cooling of Trapped Charged Particles
10 Trapped Ion Temperature ................................ 193
10.1 Measurement of Ion Temperature......................... 194
11 Radiative Cooling ........................................ 197
12 Buffer Gas Cooling ....................................... 203
12.1 Paul Trap ............................................. 204
12.2 Penning Trap .......................................... 206
13 Resistive Cooling ......................................... 211
13.1 Negative Feedback...................................... 215
13.2 Stochastic Cooling...................................... 216
X Contents
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 ........................................ 257
Part V Trapped Ions as Nonneutral Plasma
16 Plasma Properties ........................................ 263
16.1 Coulomb Correlation Parameter.......................... 263
16.2 Weakly Coupled Plasmas................................ 263
16.2.1 Penning Traps ................................... 263
16.2.2 Paul Traps ...................................... 266
17 Plasma Oscillations ....................................... 269
17.1 Rotating Wall Technique ................................ 272
18 Plasma Crystallization.................................... 275
18.1 Phase Transitions ...................................... 275
18.2 Chaos and Order ....................................... 278
18.3 Crystalline Structures................................... 280
18.3.1 Crystals in Paul Traps ............................ 281
18.3.2 Crystals in Penning Traps ......................... 290
18.3.3 Crystals in Storage Rings.......................... 291
19 Sympathetic Crystallization .............................. 295
A Mathieu Equations ....................................... 299
A.1 Parametric Oscillators .................................. 299
B Orbits of Trapped Ions ................................... 303
C Nonlinear Oscillator ...................................... 309
C.1 Multipole Expansions ................................... 309
C.2 Normal Forms ......................................... 310
C.3 Nonlinear Resonances ................................... 312