Exactly Solvable Problems of Atom Interaction with External Electromagnetic Field

This chapter serves as a foundational component of the book, delving into precisely solvable scenarios involving the interaction of atoms with external electromagnetic fields. This chapter plays a crucial role in acquainting readers with the fundamental concepts essential for the book’s comprehension. In particular, we rigorously establish a critical principle: within closed Hermitian systems comprising a finite number of subsystems, stationary states are unattainable for individual subsystems. This principle lays the groundwork for our subsequent discussions. Furthermore, we meticulously demonstrate that an atom interacting with a single mode of either classical or quantum fields does not emit photons. Within this chapter, we elucidate the quantization of electromagnetic fields. Employing the rotating wave approximation, we tackle the well-known problem of Rabi oscillations, exploring the population inversion in a two-level atom. The chapter also delves into essential frameworks for describing quantum systems, such as the Schrödinger and Heisenberg pictures. We introduce notations and concepts used in the book’s narrative, including the model of a two-level atom, Dirac’s bra and ket vectors, Pauli matrices, raising and lowering operators, as well as the gauge calibration of electromagnetic fields. These foundational elements set the stage for a deeper understanding of the subsequent chapters.