A graduate course on precision AMO physics (6 × 3h). Topics include spectroscopy, multipole and multi-photon transitions, polarizability and hyperpolarizability, and the physics & metrology of optical atomic clocks.

Full course plan (PDF): A Set of Lectures on Precision Atomic Physics

Lecture topics (from PDF plans)

Lecture 1 — Angular momentum & Addition of two AM

  • Reducible and Irreducible Representations
  • AM algebra: $[J_i,J_j]=i\hbar\,\varepsilon_{ijk}J_k$, ladders $J_\pm$; eigenkets $\lvert j,m\rangle$
  • Coupling rules: $\lvert j_1-j_2\rvert \le j \le j_1+j_2$, $m=m_1+m_2$
  • Clebsch–Gordan coefficients and Wigner $3j$ symbols; orthogonality / phase
  • Spherical basis $(\epsilon_{\pm1},\epsilon_0)$ and tensor components $A^{(1)}_q$
  • Symmetry actions: rotations ($D^{(j)}$), parity $\mathcal{P}$, time reversal $\mathcal{T}$ (overview)
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Lecture 2 — Wigner–Eckart theorem; 6-j and 9-j symbols: coupling ≥3 angular momenta

  • Review: coupling two angular momenta; CG coefficients; ladder operators
  • Rotations of states/operators; Wigner D matrices
  • Irreducible tensor operators; transformation rules
  • Wigner–Eckart theorem and reduced matrix elements
  • Coupling three/four angular momenta; 6-j and 9-j symbols; selection-rule applications
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Lecture 3 — Spectroscopy done right!

  • Review: atom–light interaction; two-level systems
  • Wigner–Weisskopf theory; linewidth/lineshape; emission patterns
  • Broadening: natural, power, collisional (homogeneous); Doppler, Stark/Zeeman gradients (inhomogeneous)
  • Doppler-free saturation spectroscopy; Ramsey & echo strategies
  • Systematic shifts: Zeeman, AC Stark, BBR, collisional; case study: beating natural linewidth
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Lecture 4 — Multipole & multi-photon transitions

  • E1, M1, E2 (and higher) transitions; general multipole formalism
  • Generalization: Polarization and propagation dependence of excitation
  • “Forbidden” transitions: spin–orbit & hyperfine mixing; clock transitions
  • Multi-photon perturbation theory; Raman transitions; STIRAP; precision applications
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Lecture 5 — Polarizability & hyperpolarizability

  • Review: Wigner–Eckart; rank-1 & 2 operators
  • Toy model: Classical picture; 2-level polarizability (trap depth, scattering)
  • Full picture: Multi-level polarizability; scalar/vector/tensor components (irreps)
  • Magic / anti-magic / tune-out $\lambda$; control via light polarization
  • Experimental techniques for differential light shifts; measuring hyperpolarizability
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Lecture 6 — The art and craft of an atomic clock

  • Clock transitions; Allan deviation & stability metrics; Ramsey variants
  • Systematics: lattice (magic $\lambda$), BBR shifts, Doppler, Zeeman, DC Stark, AC Stark, line pulling, density, AOM chirp, comb noise, lattice tunneling, differential $g$, background collisions, thermal expansion, probe shifts (incl. Gouy phase)
  • Applications: GPS; relativistic geodesy; time standards; tests of fundamental physics
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Course logistics (archival)

  • Audience: PhD students (AMO/quantum metrology)
  • Term: Michaelmas 2024, University of Cambridge
  • Contact: m.hasan1@imperial.ac.uk (for slides/notes if/when shareable)