Syllabus

Quantum Mechanics: Fundamentals

Quantum Mechanics basic ideas, Wave particle duality, Davisson-Germer experiment (Other experiments regarding wave particle duality), Stern Gerlach experiment, Kets, Bras and Operators, Projective measurement, Observables, Quantum probabilities and Expectation values, Spin-1/2 systems and qubit.  (9 lectures) Wave packets and the uncertainty relations, The schrodinger wave equation, Particle in a box: energy eigenvalues and eigen states, Harmonic oscillator: ladder operators, energy eigenvalues and energy eigen states. (6 lectures)

Quantum Optics: Fundamentals

Quantization of the electromagnetic field, Quantum states of radiation: coherent and squeezed states and properties, χ(2) and χ(3) non-linear interactions, Twin-photon generation with non-linear interactions, Spontaneous parametric down-conversion, Optical parametric amplifiers. (8 lectures)

Linear Optics with Quantized Fields:

Beam splitter transformations, Theory of photodetection, Direct, balanced, and homodyne detection. (4 lectures)

Photon Statistics, Single Photon Sources and Detectors:

Introduction to quantum coherence, Hanbury-Brown Twiss experiment, Photon-bunching and anti-bunching, Single-photon sources and single photon detectors. (4 lectures)

Quantum Optical Technologies

Quantum superposition, Photonic qubit and photonic entangled states, Measuring the polarization of a single photon, Photon pairs and joint polarization measurements, Bell’s theorem and Bell’s inequality: CHSH Variant (4 lectures)

Introduction to key photonic technologies:

The quantum advantage in interferometry, Quantum imaging, Quantum key distribution, Quantum dense coding and quantum teleportation, Linear optical quantum computing, and Quantum metrology. (10 lectures)