17. Atom-light Interactions VI and Line Broadening I

The professor begins by reminding students of the lecture schedule and the importance of supporting MIT OpenCourseWare. The main focus of the lecture is to conclude the chapter on light-atom interaction and transition into the topics of line shifts and broadening. The professor revisits the rotating wave approximation, addressing student confusion and delving into the nuances of time-dependent Hamiltonian terms related to absorption and emission. The discussion is grounded in Schrodinger's equation, exploring how different frequency terms in the Hamiltonian affect state transitions.

This paragraph delves deeper into quantum mechanics, discussing the time-dependent perturbation theory and the role of the drive field in state transitions. The professor explains the integral of the Schrodinger equation and the significance of the resonance condition for absorption and emission processes. The lecture touches on energy conservation, the role of the Fourier component in the drive term, and the implications of energy-time uncertainty. It also contrasts the semi-classical approach with the fully quantized electromagnetic field, highlighting the differences in the treatment of photon absorption and emission.

The professor discusses the complexities of circular polarization and its interaction with atomic systems, focusing on the angular momentum conservation and the implications for light-atom interactions. The paragraph explores the creation and annihilation of photons through stimulated emission and the potential presence of counter-rotating terms. It also addresses the conditions under which these terms may be neglected or considered essential, providing examples and clarifying potential misunderstandings from previous lectures.

The lecture shifts focus to the concept of saturation in atomic systems, examining the general principles and introducing key terms such as saturation intensity and absorption cross section. The professor explains the independence of the absorption cross section from the strength of the transition and the differences between monochromatic and broadband light. The discussion also touches on the homework assignment related to saturation and the importance of understanding these concepts for experiments involving light interactions with atoms.

This paragraph provides a detailed analysis of saturation, introducing rate equations to define the saturated rate and its dependence on the population difference between atomic states. The professor derives the steady-state solutions, leading to the concept of power broadening, where the line width increases with the square root of the power. The lecture also addresses the student's questions about the resonance and the graphical representation of power broadening effects.

The discussion moves to the case of broadband radiation, explaining how the unsaturated rate is determined by the spectral intensity and Einstein's B coefficient. The professor defines the saturation intensity for broadband light and highlights its dependence on the speed of light and the transition frequency cubed. The paragraph also emphasizes the independence of saturation intensity from the strength of the transition, contrasting it with the monochromatic case.

The professor introduces the concept of cross section in the context of atomic physics, explaining its relevance for understanding the interaction of atoms with light. The paragraph discusses how the cross section is used to describe the absorption rate and how it changes with saturation. It also addresses the difference between monochromatic and broadband radiation in terms of saturation intensity and the physical interpretation of these phenomena.

This paragraph explores the concept of saturation in the context of black body radiation, discussing the occupation number of photons per mode and its relation to saturation. The professor provides a physical argument for the saturation threshold, suggesting that any two-level system should be saturated at a certain photon occupation number. The discussion also touches on the time scale for reaching equilibrium in a black body cavity and the implications for hyperfine transitions.

The lecture concludes with an introduction to the chapter on line shifts and broadening, motivating the importance of understanding these phenomena for accurate spectroscopic interpretation. The professor lists various causes of line broadening and shifting, such as external fields, motion of atoms, collisions, and spontaneous emission. The paragraph sets the stage for a deeper exploration of these effects in subsequent lectures.

The professor categorizes line broadening mechanisms into homogeneous and inhomogeneous broadening, explaining the differences in their physical origins and effects on spectroscopic lines. The paragraph discusses how certain mechanisms, such as Doppler broadening and collisional broadening, can be classified and the conditions under which they apply. The lecture also introduces the concept of coherence time and its role in understanding line broadening phenomena.

In the final paragraph, the professor emphasizes the importance of coherence time in explaining all line broadening mechanisms. The discussion highlights how interruptions in the coherent evolution of atomic states, whether due to spontaneous emission, collisions, or other factors, lead to line broadening. The lecture concludes with the intention to explore these phenomena further using correlation functions in future lectures, providing a unified formalism for understanding various line broadening and shifting effects.