16. Atom-light Interactions V

The script begins with an introduction to the MIT OpenCourseWare initiative and its mission to provide free educational resources. It then transitions into a discussion on cavity Quantum Electrodynamics (QED), focusing on the fully quantized radiation field and the phenomenon of vacuum Rabi oscillation. The professor recaps the importance of the quantized electromagnetic field for photon emission into a vacuum, referencing the Jaynes-Cummings model as a paradigm for understanding vacuum and photon emission. The lecture also touches on the Nobel Prize-winning research of Haroche and Wineland, emphasizing the experimental realization of theoretical concepts.

This paragraph delves deeper into the theoretical framework of cavity QED, explaining the transition from semiclassical to quantized descriptions of the electromagnetic field. It discusses the conditions necessary for an atom to interact with a single mode of the electromagnetic field within a cavity, highlighting the importance of the single photon Rabi frequency. The professor outlines the experimental setup involving a two-level atom and a single mode of the cavity, leading to a simplified two-level Hamiltonian system. The discussion culminates in the description of Rabi oscillations, which are oscillations between the atomic and photonic states, incorporating the quantum state of the electromagnetic field.

The script moves on to describe experimental observations of vacuum Rabi oscillations, particularly in the context of microwave and optical domains. It mentions the use of Rydberg atoms in superconducting high-Q cavities and the development of supermirrors for achieving high reflectivity and Q-factors. The professor discusses the experimental setup, including the use of mirrors, the creation of a single-mode cavity, and the interaction of atoms with the cavity mode. The audience's curiosity is piqued by a question about the composition of the mirrors, leading to an explanation of the materials and techniques used to achieve superpolishing and high reflectivity.

This paragraph explores the effects of atoms on cavity modes by examining cavity transmission. The professor explains the expected outcomes when scanning a probe laser through the cavity, from the perspective of an empty cavity to scenarios involving one or multiple atoms. The discussion includes the splitting of transmission peaks due to the presence of atoms and the adjustment of experiments to observe these phenomena over longer timescales. The paragraph concludes with a historical account of the first observation of vacuum Rabi splitting in an optical cavity.

The script introduces the concepts of coherent and thermal fields within the context of cavity QED. It discusses the initial photon state not being a vacuum state but a thermal or coherent state, leading to different expectations for Rabi oscillations. The professor explains how a superposition of flux states results in different oscillation frequencies for different states labeled by photon number n, causing dephasing. The discussion also touches on the damping of the excited state population and the eventual probability of the atom being in the excited state.

The professor discusses the phenomenon of revivals in the context of coherent states with only a few photons, explaining how partial commensurability of different frequencies can lead to revivals. The script also addresses misconceptions about spontaneous emission, emphasizing the deterministic nature of the time evolution of the system. It illustrates how the classical limit can be retrieved when the average photon number is much smaller than one, leading to the semiclassical Rabi flopping with the Rabi frequency omega_r.

This paragraph revisits the rotating wave approximation (RWA) in both the fully quantized and semiclassical pictures. The professor explains how the RWA can be applied to light-atom interactions, particularly when considering circularly polarized light and angular momentum selection rules. The discussion highlights how the RWA can lead to the simplification of the Hamiltonian, neglecting off-resonant terms, and how it can be exact under certain conditions, such as when dealing with specific angular momentum states.

The script delves into the role of circular polarization and angular momentum in light-atom interactions, discussing how these factors can influence the selection rules and the presence of counter-rotating terms. The professor uses energy diagrams to illustrate the processes of absorption and stimulated emission, and how virtual states come into play. The discussion concludes with the observation that counter-rotating terms can be eliminated due to angular momentum selection rules when using sigma plus and sigma minus light.

The final paragraph explores the impact of degeneracy and angular momentum on the rotating wave approximation, particularly in the context of p states and pi light. The professor explains how the RWA can be exact in certain situations, such as when dealing with specific angular momentum states or forbidden transitions. The discussion also touches on the modification of the RWA when considering degenerate p states and the role of different m states in the presence of circularly polarized light.