# PHY2203H F specialized: Quantum Optics I

Course Title | PHY2203H F specialized |
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Session | fall |

Year of Study | 1st year |

Time and Location |
Time: M 4-6, W 3-5 Room: MP 505 |

Course Homepage | Link to Course Homepage |

Joseph
Thywissen |

#### Official Description

**Topics:**

**Topics:**Quantum Optics I might be subtitled "Semi-classical treatment of atom-photon interactions". We will spend the semester treating the problem of a quantum system driven by a classical field. The central paradigm of the course is expressed by the Optical Bloch equations, with which one can understand a wide range of current experiments in AMO (atomic, molecular, and optical) physics and solid state physics. After a review of classical atom-light interaction, we discuss the failure of this model and the need for a quantum mechanical treatment. we review basic properties of atomic structure, the Zeeman effect and the Stark effect. We then show how an atom driven by a field reduces to a dipole interaction Hamiltonian. The atom-photon problem can then be mapped onto the problem of a spin one-half electron in a magnetic field, since both are driven two-level quantum systems. We develop the Bloch equations, Rabi oscillations, and magnetic resonance. Returning to the optical regime, damping is necessary, and thus a treatment using density matrices. We discuss the Optical Bloch equations and their treatment of quantum saturation. In the context of a diagonalized atom-photon Hamiltonian, we discuss inversion, dressed states and light shifts. Applications of this foundational material include Electromagnetically Induced Transparency, slow light, dark states, and laser cooling. Time permitting, we will introduce some basic features of the quantum theory of light, including nonclassical states of light, and two-photon interference.

**Background:**

**Background:**The material presented will assume mastery of quantum mechanics at the advanced undergraduate level -- including time-dependent perturbation theory, density matrices, central potential problems, operator treatment of the simple harmonic oscillator, and additional of angular momenta. Advanced undergraduate electricity and magnetism is also important -- solutions to the wave equation, polarization, and radiation. We will refer to topics in statistical mechanics that include the Bose-Einstein distribution, equipartition, black-body radiation, and the Maxwell-Boltzmann distribution.

Prerequisite: | PHY456 and PHY350, or equivalent |
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Textbook |
Grynberg, Aspect, & Fabre, “Introduction to Quantum Optics: From the Semi-classical Approach to Quantized Light” (Cambridge, 2010) |