Graduate short-course (4 × 2 h).

Lecture – 1: Optical Lattices

  • Review:
    • Bloch’s Theorem
  • Main Topics:
    • Experimental realization of different types of optical lattices
    • Band structure
    • Wannier states
    • Hubbard model (for Boson & Fermion)
    • First-principles calculation of the parameters in the Hubbard model (e.g., hopping matrix elements, on-site energies, one-body density-induced hopping, etc.) and their significances

Lecture – 2: Quantum Phases of Atoms and Molecules in Optical Lattices

  • Review:
    • Landau-Ginzburg Phase transition criterion, one-body Density matrix & correlation functions, Feshbach resonances
  • Main Topics:
    • Thermodynamics in optical Lattice
    • Quantum phases of matter in optical lattice for Bose-Hubbard & Fermi-Hubbard models
    • Extended Hubbard model (eHM) for molecule and various phases in eHM
    • Momentum-space probing (time-of-flight) of quantum phases
    • Real-space probing (quantum gas microscope) of quantum phases
    • Measurement of the Hubbard model parameters

Lecture – 3: Artificial Gauge Fields and Lattice Gauge Theory in Optical Lattices

  • Review:
    • Landau levels, Quantum Hall effects, Hofstadter model
  • Main Topics:
    • Realization of U(1), SU(2), and SU(3) artificial gauge fields with neutral particles (static gauge field)
    • Fractional quantum Hall effect in optical lattices
    • Density-dependent gauge field (dynamic gauge field) in optical lattices
    • Toy models of lattice gauge theory with optical lattices

Lecture – 4: Metrology with Optical lattices

  • Review:
    • Doppler broadening, Dynamic polarizability & hyperpolarizability, operation of an optical clock
  • Main Topics:
    • Metrological advantages in optical lattices
    • Neutral-atom and molecular optical clocks in an optical lattice
    • Spectroscopic measurement of dynamic polarizability & hyperpolarizability
    • Atom interferometry with optical lattices

Note: This course will be jointly taught by me, focusing on the optical lattice systems (4 Lectures); and another colleague, focusing on the continuum systems (4 Lectures)

Logistics (planned)

  • Target Audience: PhD students or Researchers working on AMO/Condensed Matter Physics
  • Term: Winter 2026, Imperial College London
  • Contact: m.hasan1@imperial.ac.uk