Atomic Physics

by Foot, Christopher J.

• ISBN13: 9780198506959
• ISBN10: 0198506953
• Format: Hardcover
• Copyright: 2005-02-10
• Publisher: Oxford University Press

Summary

This book is primarily intended to accompany an advanced undergraduate course in atomic physics. However, the elementary atomic physics covered in the early chapters should be accessible to undergraduates when they are first introduced to the subject. The book describes some of the latestadvances and the applications to Bose-Einstein condensation of atoms, matter-wave interferometry and quantum computing with trapped ions. To complement the usual quantum mechanical treatment of atomic structure the book strongly emphasizes the experimental basis of the subject, especially in thelater chapters.

Table of Contents

Early atomic physics	1	(21)
Introduction	1	(1)
Spectrum of atomic hydrogen	1	(2)
Bohr's theory	3	(2)
Relativistic effects	5	(2)
Moseley and the atomic number	7	(4)
Radiative decay	11	(1)
Einstein A and B coefficients	11	(2)
The Zeeman effect	13	(5)
Experimental observation of the Zeeman effect	17	(1)
Summary of atomic units	18	(4)
Exercises	19	(3)
The hydrogen atom	22	(23)
The Schrodinger equation	22	(7)
Solution of the angular equation	23	(3)
Solution of the radial equation	26	(3)
Transitions	29	(5)
Selection rules	30	(2)
Integration with respect to θ	32	(1)
Parity	32	(2)
Fine structure	34	(11)
Spin of the electron	35	(1)
The spin--orbit interaction	36	(2)
The fine structure of hydrogen	38	(2)
The Lamb shift	40	(1)
Transitions between fine-structure levels	41	(1)
Further reading	42	(1)
Exercises	42	(3)
Helium	45	(15)
The ground state of helium	45	(1)
Excited states of helium	46	(7)
Spin eigenstates	51	(1)
Transitions in helium	52	(1)
Evaluation of the integrals in helium	53	(7)
Ground state	53	(1)
Excited states: the direct integral	54	(1)
Excited states: the exchange integral	55	(1)
Further reading	56	(2)
Exercises	58	(2)
The alkalis	60	(20)
Shell structure and the periodic table	60	(1)
The quantum defect	61	(3)
The central-field approximation	64	(4)
Numerical solution of the Schrodinger equation	68	(3)
Self-consistent solutions	70	(1)
The spin--orbit interaction: a quantum mechanical approach	71	(2)
Fine structure in the alkalis	73	(7)
Relative intensities of fine-structure transitions	74	(1)
Further reading	75	(1)
Exercises	76	(4)
The LS-coupling scheme	80	(17)
Fine structure in the LS-coupling scheme	83	(1)
The jj-coupling scheme	84	(2)
Intermediate coupling: the transition between coupling schemes	86	(4)
Selection rules in the LS-coupling scheme	90	(1)
The Zeeman effect	90	(3)
Summary	93	(4)
Further reading	94	(1)
Exercises	94	(3)
Hyperfine structure and isotope shift	97	(26)
Hyperfine structure	97	(8)
Hyperfine structure for s-electrons	97	(3)
Hydrogen maser	100	(1)
Hyperfine structure for l ≠ 0	101	(1)
Comparison of hyperfine and fine structures	102	(3)
Isotope shift	105	(3)
Mass effects	105	(1)
Volume shift	106	(2)
Nuclear information from atoms	108	(1)
Zeeman effect and hyperfine structure	108	(4)
Zeeman effect of a weak field, μBB < A	109	(1)
Zeeman effect of a strong field, μBB > A	110	(1)
Intermediate field strength	111	(1)
Measurement of hyperfine structure	112	(11)
The atomic-beam technique	114	(4)
Atomic clocks	118	(1)
Further reading	119	(1)
Exercises	120	(3)
The interaction of atoms with radiation	123	(28)
Setting up the equations	123	(3)
Perturbation by an oscillating electric field	124	(1)
The rotating-wave approximation	125	(1)
The Einstein B coefficients	126	(1)
Interaction with monochromatic radiation	127	(5)
The concepts of π-pulses and π/2-pulses	128	(1)
The Bloch vector and Bloch sphere	128	(4)
Ramsey fringes	132	(2)
Radiative damping	134	(4)
The damping of a classical dipole	135	(2)
The optical Bloch equations	137	(1)
The optical absorption cross-section	138	(6)
Cross-section for pure radiative broadening	141	(1)
The saturation intensity	142	(1)
Power broadening	143	(1)
The a.c. Stark effect or light shift	144	(1)
Comment on semiclassical theory	145	(1)
Conclusions	146	(5)
Further reading	147	(1)
Exercises	148	(3)
Doppler-free laser spectroscopy	151	(27)
Doppler broadening of spectral lines	151	(2)
The crossed-beam method	153	(2)
Saturated absorption spectroscopy	155	(8)
Principle of saturated absorption spectroscopy	156	(3)
Cross-over resonances in saturation spectroscopy	159	(4)
Two-photon spectroscopy	163	(5)
Calibration in laser spectroscopy	168	(10)
Calibration of the relative frequency	168	(1)
Absolute calibration	169	(2)
Optical frequency combs	171	(4)
Further reading	175	(1)
Exercises	175	(3)
Laser cooling and trapping	178	(40)
The scattering force	179	(3)
Slowing an atomic beam	182	(3)
Chirp cooling	184	(1)
The optical molasses technique	185	(5)
The Doppler cooling limit	188	(2)
The magneto-optical trap	190	(4)
Introduction to the dipole force	194	(3)
Theory of the dipole force	197	(6)
Optical lattice	201	(2)
The Sisyphus cooling technique	203	(5)
General remarks	203	(1)
Detailed description of Sisyphus cooling	204	(3)
Limit of the Sisyphus cooling mechanism	207	(1)
Raman transitions	208	(3)
Velocity selection by Raman transitions	208	(2)
Raman cooling	210	(1)
An atomic fountain	211	(2)
Conclusions	213	(5)
Exercises	214	(4)
Magnetic trapping, evaporative cooling and Bose--Einstein condensation	218	(28)
Principle of magnetic trapping	218	(2)
Magnetic trapping	220	(4)
Confinement in the radial direction	220	(1)
Confinement in the axial direction	221	(3)
Evaporative cooling	224	(2)
Bose--Einstein condensation	226	(2)
Bose--Einstein condensation in trapped atomic vapours	228	(6)
The scattering length	229	(5)
A Bose--Einstein condensate	234	(5)
Properties of Bose--condensed gases	239	(3)
Speed of sound	239	(1)
Healing length	240	(1)
The coherence of a Bose--Einstein condensate	240	(2)
The atom laser	242	(1)
Conclusions	242	(4)
Exercises	243	(3)
Atom interferometry	246	(13)
Young's double-slit experiment	247	(2)
A diffraction grating for atoms	249	(2)
The three-grating interferometer	251	(1)
Measurement of rotation	251	(2)
The diffraction of atoms by light	253	(4)
Interferometry with Raman transitions	255	(2)
Conclusions	257	(2)
Further reading	258	(1)
Exercises	258	(1)
Ion traps	259	(23)
The force on ions in an electric field	259	(1)
Earnshaw's theorem	260	(1)
The Paul trap	261	(5)
Equilibrium of a ball on a rotating saddle	262	(1)
The effective potential in an a.c. field	262	(1)
The linear Paul trap	262	(4)
Buffer gas cooling	266	(1)
Laser cooling of trapped ions	267	(2)
Quantum jumps	269	(2)
The Penning trap and the Paul trap	271	(4)
The Penning trap	272	(2)
Mass spectroscopy of ions	274	(1)
The anomalous magnetic moment of the electron	274	(1)
Electron beam ion trap	275	(2)
Resolved sideband cooling	277	(2)
Summary of ion traps	279	(3)
Further reading	279	(1)
Exercises	280	(2)
Quantum computing	282	(16)
Qubits and their properties	283	(4)
Entanglement	284	(3)
A quantum logic gate	287	(2)
Making a CNOT gate	287	(2)
Parallelism in quantum computing	289	(2)
Summary of quantum computers	291	(1)
Decoherence and quantum error correction	291	(2)
Conclusion	293	(5)
Further reading	294	(1)
Exercises	294	(4)
Appendix A: Perturbation theory	298	(4)
A.1 Mathematics of perturbation theory	298	(1)
A.2 Interaction of classical oscillators of similar frequencies	299	(3)
Appendix B: The calculation of electrostatic energies	302	(3)
Appendix C: Magnetic dipole transitions	305	(2)
Appendix D: The line shape in saturated absorption spectroscopy	307	(3)
Appendix E: Raman and two-photon transitions	310	(5)
E.1 Raman transitions	310	(3)
E.2 Two-photon transitions	313	(2)
Appendix F: The statistical mechanics of Bose--Einstein condensation	315	(4)
F.1 The statistical mechanics of photons	315	(1)
F.2 Bose--Einstein condensation	316	(3)
F.2.1 Bose--Einstein condensation in a harmonic trap	318	(1)
References	319	(7)
Index	326