前半6回(平山 担当分)
1. Ab initio Calculation
1.1 Density functional theory
1.2 Band structure
1.3 Effective model
2. Topology in Crystals
2.1 topology in real space
2.2 topology in k space
2.3 Berry phase and Zak phase
3. Topological Materials (Insulator)
3.1 Quantum spin Hall effect
3.2 3D Topological insulator
3.3 Quantum anomalous insulator
4. Topological Materials (Semimetal)
4.1 Weyl semimetal
4.2 Dirac semimetal
4.3 Nodal-line semimetal
5. Strong Correlation
5.1 Correlation in ab initio calculation
5.2 Many body Hamiltonian
5.3 Strongly correlated systems
6. Exotic Materials
6.1 Correlation in topology
6.2 Topological superconductivity
6.3 Other materials
後半6回(江澤 担当分)
1. Quantum optics
1.1 Quantization of electromagnetic field
1.2 boson and photon
1.3 Many bosons
1.4 Baker-Campbell-Hausdorff formula
1.5 Coherent state
1.5.1 quantum fluctuation
1.5.2 Number operator and phase operator
1.5.3 Hamiltonian for coherent states
1.5.4 su(2) and su(1,1) algebra
1.5.5 su(2) algebra of photon
1.5.6 cat states
1.6 Squeezing
1.6.1 Bogoliubov transformation of bosons
1.6.2 Interaction picture
1.6.3 Hamiltonian for squeezed states
1.6.4 Parametric down conversion
1.6.5 Four-wave mixing
1.6.6 Squeezed vacuum state
1.6.7 Quadrature squeezing
1.6.8 Squeezed coherent state
1.6.9 Amplitude squeezing
1.6.10 Phase squeezing
1.6.12 Degenerate parametric amplifier
1.6.13 Schwinger boson
1.6.15 su(1,1) algebra of distinguishable photon
1.6.16 Two-mode squeezed states
1.6.17 Two-mode squeezed vacuum states
1.6.18 Quadrature squeezing
1.6.19 Hamiltonian for the two-mode squeezed state
1.6.20 Non-degenerate parametric amplifier
1.6.21 fluctuation
1.6.22 Frequency up-converter
1.7 NOON stat
1.8 Beam splitter
1.9 Balanced homodyne measurement
1.10 Photonic qubit
1.10.1 Fock qubit
1.10.2 Polarization qubit
1.10.3 Cat qubit
2. Open quantum system
2.1 Density operator, pure states and mixed states
2.2 von Neumann equation
2.3 Kraus operator
2.4 Projective measurement
2.5 Positive Operator Valued Measure (POVM)
2.6 Lindblad equation
2.7 Spontaneous emission
2.7 Spontaneous emission
2.8 Relaxation
2.9 Dephasing
3. Cavity QED
3.1 Rabi Hamiltonian
3.2 Jaynes-Cummings Hamiltonian
4 Quantum computation
4.1 Qubit
4.2 One-qubit gates
4.2.1 Hadmard gate
4.2.2 Phase-shift gate
4.3 Two-qubit gates
4.3.1 CNOT gate
4.3.2 SWAP gate
4.3.3 CZ gate
4.4 Solovay-Kitaev theorem and universal quantum computation
4.5 No cloning theorem