Advances in Atomic, Molecular, and Optical Physics (eBook)

Cover 1
Contents 6
Contributors 10
Exploring Quantum Matter with Ultracold Atoms in Optical Lattices 12
Introduction 13
Optical Lattices 14
Optical Dipole Force 14
Optical Lattice Potentials 16
1D Lattice Potentials 17
2D Lattice Potentials 17
3D Lattice Potentials 18
Spin-Dependent Optical Lattice Potentials 19
Bose-Einstein Condensates in Optical Lattices 21
Bloch Bands 21
Wannier Functions 24
Ground State Wave Function of a BEC in an Optical Lattice 26
Discretization 26
Ground State 28
Adiabatic Mapping of Crystal Momentum to Free Particle Momentum 29
Bose-Hubbard Model of Interacting Bosons in Optical Lattices 31
Ground States of the Bose-Hubbard Hamiltonian 33
Double Well Case 33
Multiple Well Case 35
SF-MI Transition in Inhomogeneous Potentials 36
Superfluid to Mott Insulator Transition 37
Collapse and Revival of a Macroscopic Quantum Field 41
Quantum Gate Arrays via Controlled Collisions 45
Spin-Dependent Transport 45
Controlled Collisions 48
Using Controlled Collisional Quantum Gates 51
Outlook 51
Acknowledgements 54
References 54
The Kicked Rydberg Atom 60
Introduction 61
Impulsively-Driven or ``Kicked' Systems 61
Related Problems 63
Realization of the Impulsive Limit 64
Experimental Apparatus 64
Freely-Propagating Half-Cycle Pulses 64
Studies at Very-High n 66
Creation of Quasi-One-Dimensional Atoms 68
Effect of a Single HCP 71
Energy Transfer and Ionization 71
Wavepacket Production and Evolution 75
Characterization of Quasi-1D Atoms 79
Effect of Multiple HCPs 82
Dynamical Stabilization 82
3D Atoms 82
1D and Quasi-1D Atoms: Effect of Kick Direction 86
Classical-Quantum Correspondence 90
Freely-Propagating Attosecond HCP Trains 93
Alternating Kicks 97
Phase-Space Localization 99
Dynamical Filtering 99
Navigating in Phase-Space 100
Transient Phase-Space Localization 103
Outlook 109
Atomic Engineering 109
Classical Limit of Quantum Mechanics 110
Further Applications 110
Acknowledgements 111
References 112
Photonic State Tomography 116
State Representation 118
Representation of Single-Qubit States 118
Pure States, Mixed States, and Diagonal Representations 118
The Stokes Parameters and the Poincaré Sphere 121
Representation of Multiple Qubits 125
Pure States, Mixed States, and Diagonal Representations 125
Fidelity. 126
Tangle. 127
Entropy and the linear entropy. 127
Multiple Qubit Stokes Parameters 128
Representation of Nonqubit Systems 130
Pure, Mixed, and Diagonal Representations 130
Qudit Stokes Parameters 131
Tomography of Ideal Systems 133
Single-Qubit Tomography 134
Visualization of Single-Qubit Tomography 134
A Mathematical Look at Single-Qubit Tomography 135
Multiple-Qubit Tomography 136
Tomography of Nonqubit Systems 138
General Qubit Tomography 138
Collecting Tomographic Measurements 140
Projection 140
Arbitrary Single-Qubit Projection 140
Compensating for Imperfect Waveplates 142
Wedged waveplates 145
Multiple-Qubit Projections and Measurement Ordering 145
n vs. 2n Detectors 145
Electronics and Detectors 148
Collecting Data and Systematic Error Correction 149
Accidental Coincidences 149
Beamsplitter Crosstalk 150
Detector-Pair Efficiency Calibration 151
Intensity Drift 152
Analyzing Experimental Data 153
Types of Errors and State Estimation 154
The Maximum Likelihood Technique 156
Optimization Algorithms and Derivatives of the Fitness Function 159
Choice of Measurements 160
How Many Measurements? 160
How Many Counts per Measurement? 161
Error Analysis 164
A Complete Example of Tomography 165
Outlook 167
Acknowledgements 168
References 168
Fine Structure in High-L Rydberg States: A Path to Properties of Positive Ions 172
Introduction 173
Experimental Methods 177
Early Studies 177
Stepwise Excitation Microwave Studies 179
Resonant Excitation Stark Ionization Spectroscopy (RESIS) 181
Other Experimental Methods 186
Theoretical Methods 187
Long-Range Model for Atoms 187
Adiabatic Model with S-State Cores 189
Nonadiabatic Corrections 190
Other Corrections 193
Core penetration and exchange 193
Second-order polarization energies 193
Spin Structure 194
Tensor Fine Structure 196
Long-Range Model for H2 198
Coulomb Interactions 198
Spin and Hyperfine Interactions 200
Comparison with Traditional Methods 201
Results 203
Theoretical Progress 203
Relativistic corrections. 206
Retardation corrections. 206
Reduced mass corrections. 206
Lamb shift corrections. 207
Ion Property Measurements 207
Dipole Polarizability 208
Quadrupole Moments 209
Other Ion Properties 210
Applications 211
Summary and Outlook 212
Acknowledgements 213
References 214
A Storage Ring for Neutral Molecules 220
Introduction 221
Manipulating Polar Molecules 223
The Stark Effect in Deuterated Ammonia 224
Focusing a Beam of Polar Molecules 227
Decelerating and Trapping of Polar Molecules 232
A Storage Ring for Polar Molecules 234
Manipulating Polar Molecules in Phase Space 235
Phase-Space Matching 237
Phase-Space Transformations 240
A Prototype Storage Ring for Neutral Molecules 244
Motion of Molecules in a Hexapole Ring 244
Equilibrium Orbit 244
Betatron Oscillations 248
Motion of Molecules in the Dipole Ring 250
Experimental Set-up 254
Results and Discussion 257
Longitudinal Focusing and Cooling of a Molecular Beam 259
Principle and Design of the Buncher 261
Longitudinal Focusing of a Molecular Beam 263
Longitudinal Cooling of a Molecular Beam 264
Dynamics of Molecules in the Storage Ring 268
Experimental Setup and Alternative Bunching Scheme 268
Longitudinal Temperature of Molecules in the Ring 274
Betatron Oscillations in the Dipole Ring 278
Betatron Oscillations in the Hexapole Ring 279
Design of a Sectional Storage Ring 284
Transverse Stability in a Sectional Storage Ring 284
A Linear Array of Hexapoles 284
Bend Hexapoles 289
Longitudinally Focusing in a Sectional Ring 290
Conclusions and Outlook 294
Acknowledgements 294
References 295
Nonadiabatic Alignment by Intense Pulses. Concepts, Theory, and Directions 300
Preliminaries 301
Basic Concepts 303
Rotational Excitation and Coherent Alignment 303
Time Evolution 305
Role of the Molecular Symmetry. From Diatomic Molecules to Complex Systems 307
Role of the Field Polarization. Three-Dimensional Alignment 309
Molecular Orientation 310
Alignment in Dissipative Media 311
Theory 312
General Formulation 312
Nonresonant, Nonadiabatic Alignment 314
Numerical Implementation 317
Case Studies 322
Recent Developments 331
Conclusions and Outlook 333
Acknowledgements 335
Derivation of Equation (5) 335
References 337
Relativistic Nonlinear Optics 342
Orientation and Background 343
Introduction to Relativistic Optics and High Field Science 343
Guiding Principles of Laser Plasma Physics 346
Single-Particle Motion 348
Constants of the Motion 351
Role of Initial Phase 352
Direct Laser Acceleration of Electrons in Vacuum 354
Self-Modulated Laser Wakefield Electron Beam Characterization 356
A General Plane Wave Electron Scattering Model 357
Nonparaxial Solutions of the Maxwell Wave Equation 361
Series Solution of the Wave Equation for Monochromatic Beams 362
A Spectral Method Solution of the Wave Equation 365
The Solution Assuming a Gaussian Laser at Focus 365
Comparison of the Series and Spectral Solutions 367
The Asymmetric Laser Field Solutions 367
The Symmetric Laser Field Solutions 368
The Solution Assuming a Flattened Gaussian Laser at Focus 369
Radiation from Relativistic Electrons 371
Collective Plasma Response 376
Propagation 377
Relativistic Self-focusing 379
Raman Scattering, Plasma Wave Excitation and Electron Acceleration 381
Relativistic Phase Modulation 390
Interactions with Solid-Density Targets 395
Concluding Remark 396
Acknowledgements 397
References 397
Coupled-State Treatment of Charge Transfer 402
Introduction 402
Coupled-State Treatments 403
Impact-Parameter Approaches 403
Atomic-State and Atomic-Pseudostate Approaches 404
Two-center 404
Atomic-state. 405
Atomic-plus-pseudostate. 405
Continuum-distorted-wave. 406
Three-center 406
Molecular-State Approaches 407
Perturbed-stationary-state 407
Plane-wave-factor, molecular-state 408
Molecular-state with other a priori translational factors 409
Molecular-state with optimized or variationally determined translational factors 409
Hylleraas 410
Three-center molecular-state 410
Two-Center, Momentum-Space Approach 410
Quantum Approaches 411
Translational Factor Approaches 411
Common-Reaction-Coordinate Method 412
Hidden Crossing Approach 412
Hyperspherical Approach 412
Results 413
The alphaH System 413
Charge Transfer to All States 414
Intermediate energies 414
Lower energies 417
Charge Transfer to the 2s and 2p States 418
The pHe+ System 420
The pH System 423
Charge Transfer to All States 424
Charge Transfer to the Ground State 425
Charge Transfer to the 2s and 2p States 426
Conclusion 431
References 432
Index 436
Contents of Volumes in this Serial 440