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(Chris Devlin) #1

  • 1 Early atomic physics

    • 1.1 Introduction

    • 1.2 Spectrum of atomic hydrogen

    • 1.3 Bohr’s theory

    • 1.4 Relativistic effects

    • 1.5 Moseley and the atomic number

    • 1.6 Radiative decay

    • 1.7 EinsteinAandBcoefficients

    • 1.8 The Zeeman effect

      • 1.8.1 Experimental observation of the Zeeman effect



    • 1.9 Summary of atomic units

    • Exercises



  • 2 The hydrogen atom

    • 2.1 The Schr ̈odinger equation

      • 2.1.1 Solution of the angular equation

      • 2.1.2 Solution of the radial equation



    • 2.2 Transitions

      • 2.2.1 Selection rules

      • 2.2.2 Integration with respect toθ

      • 2.2.3 Parity



    • 2.3 Fine structure

      • 2.3.1 Spin of the electron

      • 2.3.2 The spin–orbit interaction

      • 2.3.3 The fine structure of hydrogen

      • 2.3.4 The Lamb shift

      • 2.3.5 Transitions between fine-structure levels



    • Further reading

    • Exercises



  • 3 Helium

    • 3.1 The ground state of helium

    • 3.2 Excited states of helium

      • 3.2.1 Spin eigenstates

      • 3.2.2 Transitions in helium



    • 3.3 Evaluation of the integrals in helium

      • 3.3.1 Ground state

      • 3.3.2 Excited states: the direct integral

      • 3.3.3 Excited states: the exchange integral



    • Further reading x Contents

    • Exercises



  • 4 The alkalis

    • 4.1 Shell structure and the periodic table

    • 4.2 The quantum defect

    • 4.3 The central-field approximation

    • 4.4 Numerical solution of the Schr ̈odinger equation

      • 4.4.1 Self-consistent solutions

      • approach 4.5 The spin–orbit interaction: a quantum mechanical



    • 4.6 Fine structure in the alkalis

      • 4.6.1 Relative intensities of fine-structure transitions



    • Further reading

    • Exercises



  • 5TheLS-coupling scheme

    • 5.1 Fine structure in theLS-coupling scheme

    • 5.2 Thejj-coupling scheme

      • schemes 5.3 Intermediate coupling: the transition between coupling



    • 5.4 Selection rules in theLS-coupling scheme

    • 5.5 The Zeeman effect

    • 5.6 Summary

    • Further reading

    • Exercises



  • 6 Hyperfine structure and isotope shift

    • 6.1 Hyperfine structure

      • 6.1.1 Hyperfine structure for s-electrons

      • 6.1.2 Hydrogen maser

      • 6.1.3 Hyperfine structure forl=

      • 6.1.4 Comparison of hyperfine and fine structures



    • 6.2 Isotope shift

      • 6.2.1 Mass effects

      • 6.2.2 Volume shift

      • 6.2.3 Nuclear information from atoms



    • 6.3 Zeeman effect and hyperfine structure

      • 6.3.1 Zeeman effect of a weak field,μBB<A

      • 6.3.2 Zeeman effect of a strong field,μBB>A

      • 6.3.3 Intermediate field strength



    • 6.4 Measurement of hyperfine structure

      • 6.4.1 The atomic-beam technique

      • 6.4.2 Atomic clocks



    • Further reading

    • Exercises



  • 7 The interaction of atoms with radiation

    • 7.1 Setting up the equations

      • 7.1.1 Perturbation by an oscillating electric field Contents xi

      • 7.1.2 The rotating-wave approximation



    • 7.2 The EinsteinBcoefficients

    • 7.3 Interaction with monochromatic radiation

      • 7.3.1 The concepts ofπ-pulses andπ/2-pulses

      • 7.3.2 The Bloch vector and Bloch sphere



    • 7.4 Ramsey fringes

    • 7.5 Radiative damping

      • 7.5.1 The damping of a classical dipole

      • 7.5.2 The optical Bloch equations



    • 7.6 The optical absorption cross-section

      • 7.6.1 Cross-section for pure radiative broadening

      • 7.6.2 The saturation intensity

      • 7.6.3 Power broadening



    • 7.7 The a.c. Stark effect or light shift

    • 7.8 Comment on semiclassical theory

    • 7.9 Conclusions

    • Further reading

    • Exercises



  • 8 Doppler-free laser spectroscopy

    • 8.1 Doppler broadening of spectral lines

    • 8.2 The crossed-beam method

    • 8.3 Saturated absorption spectroscopy

      • 8.3.1 Principle of saturated absorption spectroscopy

      • 8.3.2 Cross-over resonances in saturation spectroscopy



    • 8.4 Two-photon spectroscopy

    • 8.5 Calibration in laser spectroscopy

      • 8.5.1 Calibration of the relative frequency

      • 8.5.2 Absolute calibration

      • 8.5.3 Optical frequency combs



    • Further reading

    • Exercises



  • 9 Laser cooling and trapping

    • 9.1 The scattering force

    • 9.2 Slowing an atomic beam

      • 9.2.1 Chirp cooling



    • 9.3 The optical molasses technique

      • 9.3.1 The Doppler cooling limit



    • 9.4 The magneto-optical trap

    • 9.5 Introduction to the dipole force

    • 9.6 Theory of the dipole force

      • 9.6.1 Optical lattice



    • 9.7 The Sisyphus cooling technique

      • 9.7.1 General remarks

      • 9.7.2 Detailed description of Sisyphus cooling

      • 9.7.3 Limit of the Sisyphus cooling mechanism



    • 9.8 Raman transitions xii Contents

      • 9.8.1 Velocity selection by Raman transitions

      • 9.8.2 Raman cooling



    • 9.9 An atomic fountain

    • 9.10 Conclusions

    • Exercises

    • Bose–Einstein condensation 10 Magnetic trapping, evaporative cooling and

    • 10.1 Principle of magnetic trapping

    • 10.2 Magnetic trapping

      • 10.2.1 Confinement in the radial direction

      • 10.2.2 Confinement in the axial direction



    • 10.3 Evaporative cooling

    • 10.4 Bose–Einstein condensation

    • 10.5 Bose–Einstein condensation in trapped atomic vapours

      • 10.5.1 The scattering length



    • 10.6 A Bose–Einstein condensate

    • 10.7 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



    • 10.8 Conclusions

    • Exercises



  • 11 Atom interferometry

    • 11.1 Young’s double-slit experiment

    • 11.2 A diffraction grating for atoms

    • 11.3 The three-grating interferometer

    • 11.4 Measurement of rotation

    • 11.5 The diffraction of atoms by light

      • 11.5.1 Interferometry with Raman transitions



    • 11.6 Conclusions

    • Further reading

    • Exercises



  • 12 Ion traps

    • 12.1 The force on ions in an electric field

    • 12.2 Earnshaw’s theorem

    • 12.3 The Paul trap

      • 12.3.1 Equilibrium of a ball on a rotating saddle

      • 12.3.2 The effective potential in an a.c. field

      • 12.3.3 The linear Paul trap



    • 12.4 Buffer gas cooling

    • 12.5 Laser cooling of trapped ions

    • 12.6 Quantum jumps

    • 12.7 The Penning trap and the Paul trap

      • 12.7.1 The Penning trap Contents xiii

      • 12.7.2 Mass spectroscopy of ions

      • 12.7.3 The anomalous magnetic moment of the electron



    • 12.8 Electron beam ion trap

    • 12.9 Resolved sideband cooling

    • 12.10 Summary of ion traps

    • Further reading

    • Exercises



  • 13 Quantum computing

    • 13.1 Qubits and their properties

      • 13.1.1 Entanglement



    • 13.2 A quantum logic gate

      • 13.2.1 Making a CNOT gate



    • 13.3 Parallelism in quantum computing

    • 13.4 Summary of quantum computers

    • 13.5 Decoherence and quantum error correction

    • 13.6 Conclusion

    • Further reading

    • Exercises



  • A Appendix A: Perturbation theory

    • A.1 Mathematics of perturbation theory

    • A.2 Interaction of classical oscillators of similar frequencies



  • B Appendix B: The calculation of electrostatic energies

  • C Appendix C: Magnetic dipole transitions

    • spectroscopy D Appendix D: The line shape in saturated absorption



  • E Appendix E: Raman and two-photon transitions

    • E.1 Raman transitions

    • E.2 Two-photon transitions

    • Bose–Einstein condensation F Appendix F: The statistical mechanics of

    • F.1 The statistical mechanics of photons

    • F.2 Bose–Einstein condensation

      • F.2.1 Bose–Einstein condensation in a harmonic trap





  • References

  • Index

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