ATOMIC PHYSICS

By A. RAANN

CONTENTS EARLY ATOMIC PHYSICS INTRODUCTION SPECTRUM OF ATOMIC HYDROGEN BOHR’S THEORY RELATIVISTIC E?ECTS MOSELEY AND THE ATOMIC NUMBER RADIATIVE DECAY EINSTEIN A AND B COE?CIENTS THE ZEEMAN E?ECT EXPERIMENTAL OBSERVATION OF THE ZEEMAN E?ECT SUMMARY OF ATOMIC UNITS EXERCISES THE HYDROGEN ATOM THE SCHR¨ODINGER EQUATION SOLUTION OF THE ANGULAR EQUATION SOLUTION OF THE RADIAL EQUATION TRANSITIONS SELECTION RULES INTEGRATION WITH RESPECT TO ? PARITY FINE STRUCTURE SPIN OF THE ELECTRON THE SPIN–ORBIT INTERACTION THE ?NE STRUCTURE OF HYDROGEN THE LAMB SHIFT TRANSITIONS BETWEEN ?NE-STRUCTURE LEVELS FURTHER READING HELIUM THE GROUND STATE OF HELIUM EXCITED STATES OF HELIUM SPIN EIGENSTATES TRANSITIONS IN HELIUM EVALUATION OF THE INTEGRALS IN HELIUM GROUND STATE EXCITED STATES: THE DIRECT INTEGRAL EXCITED STATES: THE EXCHANGE INTEGRAL CONTENTS FURTHER READING THE ALKALIS SHELL STRUCTURE AND THE PERIODIC TABLE THE QUANTUM DEFECT THE CENTRAL-?ELD APPROXIMATION NUMERICAL SOLUTION OF THE SCHR¨ODINGER EQUATION SELF-CONSISTENT SOLUTIONS THE SPIN–ORBIT INTERACTION: A QUANTUM MECHANICAL APPROACH FINE STRUCTURE IN THE ALKALIS RELATIVE INTENSITIES OF ?NE-STRUCTURE TRANSITIONS THE LS-COUPLING SCHEME FINE STRUCTURE IN THE LS-COUPLING SCHEME THE JJ-COUPLING SCHEME INTERMEDIATE COUPLING: THE TRANSITION BETWEEN COUPLING SCHEMES SELECTION RULES IN THE LS-COUPLING SCHEME SUMMARY HYPER?NE STRUCTURE AND ISOTOPE SHIFT HYPER?NE STRUCTURE HYPER?NE STRUCTURE FOR S-ELECTRONS HYDROGEN MASER HYPER?NE STRUCTURE FOR L ?= COMPARISON OF HYPER?NE AND ?NE STRUCTURES ISOTOPE SHIFT MASS E?ECTS VOLUME SHIFT NUCLEAR INFORMATION FROM ATOMS ZEEMAN E?ECT AND HYPER?NE STRUCTURE ZEEMAN E?ECT OF A WEAK ?ELD, µBB < A ZEEMAN E?ECT OF A STRONG ?ELD, µBB > A INTERMEDIATE ?ELD STRENGTH MEASUREMENT OF HYPER?NE STRUCTURE THE ATOMIC-BEAM TECHNIQUE ATOMIC CLOCKS THE INTERACTION OF ATOMS WITH RADIATION SETTING UP THE EQUATIONS PERTURBATION BY AN OSCILLATING ELECTRIC ?ELD THE ROTATING-WAVE APPROXIMATION THE EINSTEIN B COE?CIENTS INTERACTION WITH MONOCHROMATIC RADIATION THE CONCEPTS OF ?-PULSES AND ?/2-PULSES THE BLOCH VECTOR AND BLOCH SPHERE RAMSEY FRINGES RADIATIVE DAMPING THE DAMPING OF A CLASSICAL DIPOLE THE OPTICAL BLOCH EQUATIONS THE OPTICAL ABSORPTION CROSS-SECTION CROSS-SECTION FOR PURE RADIATIVE BROADENING THE SATURATION INTENSITY POWER BROADENING THE A C STARK E?ECT OR LIGHT SHIFT COMMENT ON SEMICLASSICAL THEORY CONCLUSIONS DOPPLER-FREE LASER SPECTROSCOPY DOPPLER BROADENING OF SPECTRAL LINES THE CROSSED-BEAM METHOD SATURATED ABSORPTION SPECTROSCOPY PRINCIPLE OF SATURATED ABSORPTION SPECTROSCOPY CROSS-OVER RESONANCES IN SATURATION SPECTROSCOPY TWO-PHOTON SPECTROSCOPY CALIBRATION IN LASER SPECTROSCOPY CALIBRATION OF THE RELATIVE FREQUENCY ABSOLUTE CALIBRATION OPTICAL FREQUENCY COMBS LASER COOLING AND TRAPPING THE SCATTERING FORCE SLOWING AN ATOMIC BEAM CHIRP COOLING THE OPTICAL MOLASSES TECHNIQUE THE DOPPLER COOLING LIMIT THE MAGNETO-OPTICAL TRAP INTRODUCTION TO THE DIPOLE FORCE THEORY OF THE DIPOLE FORCE OPTICAL LATTICE THE SISYPHUS COOLING TECHNIQUE GENERAL REMARKS DETAILED DESCRIPTION OF SISYPHUS COOLING LIMIT OF THE SISYPHUS COOLING MECHANISM RAMAN TRANSITIONS VELOCITY SELECTION BY RAMAN TRANSITIONS RAMAN COOLING AN ATOMIC FOUNTAIN 10 MAGNETIC TRAPPING, EVAPORATIVE COOLING AND BOSE–EINSTEIN CONDENSATION PRINCIPLE OF MAGNETIC TRAPPING MAGNETIC TRAPPING 10 2 1 CON?NEMENT IN THE RADIAL DIRECTION 10 2 2 CON?NEMENT IN THE AXIAL DIRECTION EVAPORATIVE COOLING BOSE–EINSTEIN CONDENSATION BOSE–EINSTEIN CONDENSATION IN TRAPPED ATOMIC VAPOURS 10 5 1 THE SCATTERING LENGTH A BOSE–EINSTEIN CONDENSATE PROPERTIES OF BOSE-CONDENSED GASES 10 7 1 SPEED OF SOUND 10 7 2 HEALING LENGTH 10 7 3 THE COHERENCE OF A BOSE–EINSTEIN CONDENSATE 10 7 4 THE ATOM LASER 11 ATOM INTERFEROMETRY YOUNG’S DOUBLE-SLIT EXPERIMENT A DI?RACTION GRATING FOR ATOMS THE THREE-GRATING INTERFEROMETER MEASUREMENT OF ROTATION THE DI?RACTION OF ATOMS BY LIGHT 11 5 1 INTERFEROMETRY WITH RAMAN TRANSITIONS 12 ION TRAPS THE FORCE ON IONS IN AN ELECTRIC ?ELD EARNSHAW’S THEOREM THE PAUL TRAP 12 3 1 EQUILIBRIUM OF A BALL ON A ROTATING SADDLE 12 3 2 THE E?ECTIVE POTENTIAL IN AN A C ?ELD 12 3 3 THE LINEAR PAUL TRAP BU?ER GAS COOLING LASER COOLING OF TRAPPED IONS QUANTUM JUMPS THE PENNING TRAP AND THE PAUL TRAP CONTENTS 12 7 1 THE PENNING TRAP 12 7 2 MASS SPECTROSCOPY OF IONS 12 7 3 THE ANOMALOUS MAGNETIC MOMENT OF THE ELECTRON ELECTRON BEAM ION TRAP RESOLVED SIDEBAND COOLING 12 10 SUMMARY OF ION TRAPS 13 QUANTUM COMPUTING QUBITS AND THEIR PROPERTIES 13 1 1 ENTANGLEMENT A QUANTUM LOGIC GATE 13 2 1 MAKING A CNOT GATE PARALLELISM IN QUANTUM COMPUTING SUMMARY OF QUANTUM COMPUTERS DECOHERENCE AND QUANTUM ERROR CORRECTION CONCLUSION REFERENCES