Lectures
Lecture notes
Part I: Review of Quantum Mechanics
Review of quantum mechanics, commutation
relations, measurement theory,
Heisenberg and Shrodinger pictures, density operators, two-level
systems, Fermi's Golden rule, decoherence, joint Hilbert spaces,
entangled states, partial traces and density operators of
sub-systems.
Part II: Semiclassical Light-Matter Interactions
Semiclassical description of the interaction of radiation with a two-level system, optical Bloch equations, Bloch sphere, Rabi oscillations, decoherence and relaxation, photon echo experiments, Ramsey fringes, atomic clocks, atom-light interactions, doppler shifts, forces on atoms, dissipative or radiation pressure force, reactive or dipole force, laser cooling.
Optical linear response, optical susceptibility,
stimulated emission and absorption, spontaneous emission, semiclassical
rate equations, dielectric constant,
Part III: Quantization of Light and Quantum States of Light
Review of quantum mechanical simple harmonic oscillator, commutation relations, creation and destruction operators, energy spectrum and energy eigenstates.
Quantum electrodynamics, quantization of
radiation in cavities and in free space, photon number states,
photon momentum, photon position, photon angular momentum, phootn spin,
introduction to vaccum fluctuations.
Introduction to random signals and classical
noise, correlation functions, power
spectral densities, Wiener-Khinchin theorem, shot noise, Brownian noise,
classical Langevin equations, phasor description of narrow band
signals and signal quadratures.
Basic quantum states of light, Fock states,
coherent states, quadrature squeezed states, two-mode squeezed
states, methods of generating quantum states of light, amplitude-phase
squeezed states, phase in quantum optics, number-phase uncertainty relation for quantum
states of light.
Quantization of propagating light fields, photon flux operator, quantum slowly varying
envelope approximation, travelling quantum states, single photon and
multi-photon packets, coherent state packets, continuous wave
coherent states, quadrature operators for propagating states, photon flux
operator and photon flux fluctuations.
Part IV: Quantum Descriptions of Light-Matter Interactions
Quantum description of optical loss, optical beam splitters, classical and quantum description of cavities and waveguides with loss, role of vacuum fluctuations, quantum Langevin equations for loss, photon statistics for loss, role of vacuum fluctuations.
Quantum description of a two-level system, spontaneous emission and decoherence in a two-level system, role of operator ordering in spontaneous emission, Lamb shift, Langevin-equations, Bloch-Langevin equations for a driven two-level system, atom-photon interaction in a waveguide.
Light-matter interaction and the electrical dipole Hamiltonian, quantum two-level systems interacting with radiation, cavity quantum optics, dressed states, quantum rabi oscillations, Jaynes-Cummings model, Tavis-Cummings model and angular momentum algebra, ,Dicke superradiance, cavity enhanced spontaneous emission and the Purcell effect, cavity quantum electrodynamics in strong, moderate, and weak limits, photon blockade, noise and decoherence associated with optical/transitions, quantum Langevin equations.
Optical amplifiers, fundamental performance limits of
linear phase insensitive and phase sensitive optical amplifiers,
quantum cloning, Heisenberg principle, and light amplification,
spontaneous emission and stimulated emission noise in phase
insensitive amplifiers, amplified spontaneous emission noise,
parametric optical amplifiers and squeezing, heralded probabilistic
noise-free phase insensitive amplifiers.
Laser oscillators, semi-classical rate equations,
stability and relaxation oscillations, analogy with phase
transitions and spontaneous breaking of phase symmetry in lasers
above threshold (or not ... ), laser phase noise and laser
linewidth, laser light inside and outside the laser cavity,
photon number and photon flux noise,
quantum state of a laser; a statistical mixture of coherent states
vs a statistical mixture of number states (lessons from
Bose-Einstein Condenstates), phase coherence of a laser.
Cavity opto-mechanics,
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