Cavity quantum electrodynamics (QED) studies the interaction between an atom and a cavity field. This chapter extends the general theory of a small system coupled to a large reservoir to a single-mode cavity field interacting with a reservoir of harmonic oscillators. The master equation, Fokker–Planck equation, and Heisenberg–Langevin equations are derived for the cavity field. The behavior of a two-level atom in a leaky cavity is analyzed, showing that the atom-cavity system can exhibit damped Rabi oscillations or modified spontaneous emission rates. Additionally, STIRAP techniques with a three-level atom in a leaky cavity can generate a deterministic single-photon source. A single-mode cavity field, confined between reflecting boundaries like a Fabry–Perot resonator, represents a quantum harmonic oscillator. Its eigenmodes are equally spaced in frequency, with spacing inversely proportional to the cavity length. In practical cases, only one mode is considered when it interacts near-resonantly with a system like an atom. The cavity field is described by creation and annihilation operators obeying bosonic commutation relations. Its Hamiltonian is $ H^F = \hbar \omega a^\dagger a $, with eigenstates being Fock states $ |n\rangle $. The reservoir consists of an infinite set of harmonic oscillators, described by $ H^R = \sum_k \hbar \omega_k b_k^\dagger b_k $. The interaction between the cavity field and the reservoir is bilinear, given by $ V = A \cdot B $, where $ \mathcal{A} $ and $ \mathcal{B} $ are system and reservoir operators, respectively. The coupling strength $ \varphi $ depends on the cavity's transmission or absorption losses. In transmission losses, $ \varphi $ is determined by the electric field transmission coefficient of the mirrors, while in absorption losses, it represents the coupling to bound electrons in the cavity material. In general, $ \varphi $ may depend on frequency, but here it is approximated as constant near the resonant frequency.Cavity quantum electrodynamics (QED) studies the interaction between an atom and a cavity field. This chapter extends the general theory of a small system coupled to a large reservoir to a single-mode cavity field interacting with a reservoir of harmonic oscillators. The master equation, Fokker–Planck equation, and Heisenberg–Langevin equations are derived for the cavity field. The behavior of a two-level atom in a leaky cavity is analyzed, showing that the atom-cavity system can exhibit damped Rabi oscillations or modified spontaneous emission rates. Additionally, STIRAP techniques with a three-level atom in a leaky cavity can generate a deterministic single-photon source. A single-mode cavity field, confined between reflecting boundaries like a Fabry–Perot resonator, represents a quantum harmonic oscillator. Its eigenmodes are equally spaced in frequency, with spacing inversely proportional to the cavity length. In practical cases, only one mode is considered when it interacts near-resonantly with a system like an atom. The cavity field is described by creation and annihilation operators obeying bosonic commutation relations. Its Hamiltonian is $ H^F = \hbar \omega a^\dagger a $, with eigenstates being Fock states $ |n\rangle $. The reservoir consists of an infinite set of harmonic oscillators, described by $ H^R = \sum_k \hbar \omega_k b_k^\dagger b_k $. The interaction between the cavity field and the reservoir is bilinear, given by $ V = A \cdot B $, where $ \mathcal{A} $ and $ \mathcal{B} $ are system and reservoir operators, respectively. The coupling strength $ \varphi $ depends on the cavity's transmission or absorption losses. In transmission losses, $ \varphi $ is determined by the electric field transmission coefficient of the mirrors, while in absorption losses, it represents the coupling to bound electrons in the cavity material. In general, $ \varphi $ may depend on frequency, but here it is approximated as constant near the resonant frequency.