Atomic and Optical Physics I

What this course covers

• AMO Physics as a Modern Research Field
• Course Philosophy: Classical and Quantum Foundations
• Definition of Resonance
• Damping and Finite Linewidth
• Quality Factor (Q) of an Oscillator
• Atomic Resonances and Precision Measurement
• Lorentzian Line Shape and Resonance Parameters
• Units: Angular Frequency vs. Frequency vs. Decay Rate
• Frequency measurement precision limit
• Fourier limit and frequency uncertainty
• Line splitting and signal-to-noise ratio
• Heisenberg uncertainty and single quantum systems
• Improving precision with multiple measurements
• Harmonic oscillator vs. two-level system equivalence
• Saturation as the quantum hallmark of two-level systems
• Fock states and anharmonicity in cavity QED
• Classical magnetic moment as two-level system analog
• Electron g-factor and precession frequency
• Rotating frame transformation
• Cesium fountain atomic clock
• Strontium optical lattice clock
• Magnetic moment in a rotating field (on resonance)
• Off-resonance rotating field and generalized Rabi frequency
• Spin-flip probability formula
• Adiabatic condition for rapid adiabatic passage
• Derivation of the adiabatic sweep-rate criterion
• Landau-Zener parameter preview
• Heisenberg equation of motion for angular momentum
• Quantum precession of magnetic moment
• Universality of precession across spin systems
• Electron spin energy levels in a magnetic field
• Landau-Zener transition and coherent amplitude transfer
• Limitations of the Schrödinger equation (pure states only)
• Complex energy eigenvalues for state-dependent loss
• Density matrix formalism: definition and matrix elements
• Two types of averages in the density matrix
• Pure states vs. mixed states: Tr(ρ²) criterion
• Open systems and non-unitary time evolution
• General two-level Hamiltonian via Pauli matrices
• Bloch vector representation of the density matrix
• Bloch vector equation of motion (precession)
• Atomic units and natural units
• Bohr radius and Hartree energy
• The fine structure constant α
• Non-relativistic consistency of atomic electrons
• Weakness of electromagnetic interaction
• Quantum defect for alkali atoms
• Spectroscopic term notation
• Helium atom and electron–electron interaction
• Singlet-triplet transitions in helium
• Spin-space separation and exchange symmetry
• Spin-orbit coupling as mechanism to mix singlet and triplet
• Fine structure and the fine structure constant
• Three contributions to fine structure (Pauli approximation)
• Relativistic kinetic energy correction
• Spin-orbit coupling from motional magnetic field
• Thomas precession and the factor of one-half
• Darwin term and Zitterbewegung
• Lamb shift and vacuum fluctuations
• Low-frequency cutoff justification
• Vacuum polarization contribution to Lamb shift
• Sources of hyperfine structure
• Magnetic hyperfine interaction Hamiltonian
• Contact (delta function) term for S-state hyperfine structure
• Nuclear magnetic moment and nuclear magneton
• Parity and time-reversal constraints on nuclear multipoles
• Minimum angular momentum for multipole moments
• Internal magnetic field from orbital and spin motion
• Isotope shift: mass vs. volume effect
• Lab frame vs. body-fixed frame for deformation
• Minimum angular momentum to observe multipole moments
• Historic development of hydrogen spectroscopy
• Discovery and significance of the Lamb shift
• Proton radius puzzle
• Atoms in external magnetic fields: the Zeeman Hamiltonian
• Weak-field limit and the vector model for fine structure
• Landé g-factor derivation
• Atoms in magnetic fields: two limiting cases
• Vector model of angular momentum coupling
• Paschen-Back regime: very strong magnetic fields
• Hyperfine structure of hydrogen vs. positronium
• Multipole expansion of atom–electric field energy
• Parity selection rule and permanent electric dipole moment
• Singlet vs. triplet states in helium
• Fine structure contributions beyond L·S coupling
• DC Stark effect and polarizability
• Validity of perturbation theory for ground states
• N-scaling of matrix elements and energy splittings
• Critical field scaling with principal quantum number
• Rydberg atom level mixing regimes
• Field ionization and the saddle-point model
• Critical ionization field formula (1/16N⁴)
• Oscillator strength and sum rules
• Dipole approximation validity
• Index of refraction from atomic polarizability
• Complex index of refraction and absorption
• Canonical momentum and electromagnetic coupling Hamiltonian
• Dipole approximation: A·P equivalence to E·R
• Higher-order radiation: magnetic dipole and electric quadrupole
• Matrix elements and Rabi frequency
• Beyond dipole: higher multipole transitions
• Spherical tensors and rotational symmetry
• Wigner-Eckart theorem
• Selection rules from angular momentum conservation
• Dipole selection rules (E1 and M1)
• Quadrupole selection rules (E2)
• Polarization-dependent selection rules
• Perturbation theory with broadband light
• Short-time vs. long-time excitation regimes
• Fermi's golden rule
• Coherent vs. rate-equation (irreversible) evolution
• Einstein's A and B coefficient framework
• Einstein B coefficient from perturbation theory
• Planck black-body spectral density
• Einstein A coefficient and spontaneous emission rate
• Stimulated emission as N × spontaneous emission
• Need for field quantization to treat spontaneous emission microscopically
• Einstein A coefficient and natural linewidth
• Omega-cubed frequency dependence of spontaneous emission
• Quadrupole transitions driven by plane waves
• Vacuum fluctuations vs. spontaneous emission rate
• Spontaneous emission rate in reduced dimensions
• Degeneracy factors in Einstein A and B coefficients
• Fully quantized atom-field Hamiltonian (Jaynes-Cummings form)
• Vacuum Rabi oscillations
• Rotating wave approximation and counter-rotating terms
• Lamb shift as AC Stark effect of vacuum fluctuations
• Jaynes-Cummings model and cavity QED setup
• Hilbert space segmentation into doublets
• Mapping to spin-1/2 in a magnetic field
• Vacuum Rabi oscillations
• Vacuum Rabi splitting in cavity transmission
• Rabi splitting scaling with atom and photon number
• Collapse and revival of Rabi oscillations
• Absorption and emission via rotating wave terms
• Counter-rotating terms and third-level requirement
• Rate-equation model for saturation
• Saturated vs. unsaturated rate
• Absorption cross section of a two-level system
• Saturation intensity for monochromatic vs. broadband light
• Black-body saturation criterion
• Power broadening
• Motivation for line shifts and line broadening
• Coherence time as universal broadening denominator
• Rabi resonance and finite interaction time broadening
• Velocity distribution averaging in atomic beams
• Ramsey method of separated oscillatory fields
• Rabi vs. Ramsey: advantages and trade-offs
• Line shape with exponential decay
• Recoil shift in absorption and emission
• Doppler broadening: first and second order
• Doppler-free spectroscopy methods
• Spectroscopy of tightly confined particles
• Perturbation theory framework for spectral broadening
• Correlation function and power spectrum
• Quadratic-to-linear transition in excitation probability
• Fermi's Golden Rule as a special case of the correlation function formalism
• Natural linewidth as Lorentzian from exponential decay
• Doppler broadening via velocity-dependent correlation function
• Coherence time and Doppler linewidth
• Wave-packet picture of Doppler decoherence
• Lamb-Dicke regime and suppression of Doppler broadening
• Sideband spectrum of a trapped particle
• Recovery of Doppler broadening from the sideband limit
• Dicke Narrowing Overview
• Coherence Time and Mean Free Path
• Diffusive Motion and Linewidth Estimate
• Dicke Linewidth vs. Doppler Broadening
• Correlation Function Approach to Dicke Narrowing
• Lorentzian Lineshape from Diffusive Motion
• Ballistic vs. Diffusive Motion and Pedestal
• Collisional Broadening Basics
• Fluorescence Spectrum of a Driven Atom
• Two-photon absorption via perturbation theory
• Two-photon Rabi frequency and Fermi's golden rule
• Raman processes
• Spontaneous Raman scattering
• Recoil and Doppler shifts in two-photon processes
• Doppler-free two-photon spectroscopy
• Second-order Doppler effect and its limits
• Virtual intermediate states
• Two-photon emission (one stimulated, one spontaneous)
• Spontaneous emission as unitary evolution
• Mapping atomic state onto photon field
• Phase of the spontaneously emitted photon
• Phase-space representation of photon states
• Number-phase uncertainty relation
• Homodyne measurement of photon phase
• Phase coherence for π/2 vs. π pulses
• Random phase from vacuum fluctuations
• Phase correlations between two atoms
• Interference in three-level systems
• Dark states and coherent superposition
• Hamiltonian for the three-level lambda system
• Proof that the dark state has zero coupling
• Coherent population trapping
• Two-photon resonance condition
• Bright state as the orthogonal basis state
• Electromagnetically induced transparency (EIT)
• Slow light via steep dispersion
• STIRAP: adiabatic population transfer
• Dark state in three-level systems
• Coherent population transfer (STIRAP)
• Lasing without inversion (LWI)
• Hydrogen 2S–2P mixing as LWI realization
• Hidden population and basis-set ambiguity in LWI
• Electromagnetically induced transparency (EIT)
• Dressed-state splitting and transparency window width
• Applications of EIT
• Eigenstate (dressed-atom) Hamiltonian for three-level systems
• Single atom spontaneous emission
• Two-atom system with one excitation
• Symmetric and antisymmetric two-atom states
• Collective spin (Dicke state) formalism
• Transition matrix elements and emission rates
• N-atom superradiance and N² intensity scaling
• Classical antenna picture of superradiance
• Role of photon indistinguishability in superradiance
• Localization condition and extended samples
• Experimental observation: diatomic molecules as two-atom Dicke systems

Syllabus

1. Lectures

   1. 1. Resonance I
   2. 2. Resonance II
   3. 3. Resonance III
   4. 4. Resonance IV
   5. 5. Resonance V and Atoms I
   6. 6. Atoms II
   7. 7. Atoms III
   8. 8. Atoms IV
   9. 9. Atoms V and Atoms in External Fields I
   10. 10. Atoms in External Fields II
   11. 11. Atoms in External Fields III
   12. 12. Atoms in External Fields IV and Atom-light Interactions I
   13. 13. Atom-light Interactions II
   14. 14. Atom-light Interactions III
   15. 15. Atom-light Interactions IV
   16. 16. Atom-light Interactions V
   17. 17. Atom-light Interactions VI and Line Broadening I
   18. 18. Line Broadening II
   19. 19. Line Broadening III
   20. 20. Line Broadening IV and Two-photon Excitation I
   21. 21. Two-photon Excitation II and Coherence I
   22. 22. Coherence II
   23. 23. Coherence III
   24. 24. Coherence IV
   25. 25. Coherence V