The Jaynes-Cummings (JC) model has been at the forefront of quantum optics for six decades to date, being one of the simplest yet intricately nonlinear formulations of light-matter interaction in modern physics. Its unique nonlinear splitting of the energy levels is a benchmark of quantum electrodynamics (QED) and the goal of exemplary experiments looking for spectroscopic evidence for the quantization of the electromagnetic field. In this course, we will visit key aspects of the JC phenomenology and trace the evolution of ideas defining cavity and circuit QED, from the inception of the model in 1963 to the significance of a strong-coupling "thermodynamic limit" distinguishing quantum fluctuations from their classical counterpart. We will do so in an explicitly open-quantum-system formulation, and will employ key tools and techniques, including the numerical solution of the master equation, a semiclassical treatment of the light-matter interaction and the computer-generated counting records realizing an unraveling of the density matrix into quantum trajectories.
Lecture 1: Overview of the basic tools in open quantum systems: the master equation in the Born-Markov approximation and the quantum regression formula, calculation of the scattered field, theory and applications of quantum trajectories.
Lecture 2: Basic phenomenology of the Jaynes-Cummings model: formulation of the Hamiltonian, eigenstates and eigenenergies, collapse and revival, dynamic Stark effect and the role of quantum-fluctuation squeezing.
Lecture 3: Spontaneous dressed-state polarization as a symmetry-breaking transition: neoclassical theory of radiation vs. quantum dynamics.
Lecture 4: Breakdown of photon blockade as a driven dissipative quantum phase transition: theory and experiment.
Lecture 5: Correlations of the Jaynes-Cummings scattered fields: breakdown of detailed balance and wave/particle duality reappraised.
