This section discusses the dynamics of a single-mode cavity field coupled to a reservoir of harmonic oscillators, focusing on the relaxation of the cavity field. The cavity field is described by creation and annihilation operators \(a^\dagger\) and \(a\), with a Hamiltonian \(\mathcal{H}^\mathrm{F} = \hbar \omega a^\dagger a\). The reservoir, composed of an infinite set of harmonic oscillators, is described by a Hamiltonian \(\mathcal{H}^\mathrm{R} = \sum_k \hbar \omega_k b_k^\dagger b_k\). The interaction between the cavity field and the reservoir is bilinear, represented by \(\mathcal{V} = \mathcal{A} \cdot \mathcal{B}\), where \(\mathcal{A} = \boldsymbol{\varphi} (a + a^\dagger)\) and \(\mathcal{B} = \sum_k \boldsymbol{\beta}_k = \mathrm{i} \sum_k \boldsymbol{\epsilon}_k (b_k^\dagger - b_k)\). The coupling matrix element \(\boldsymbol{\varphi}\) depends on the electric field transmission coefficient for transmission losses or the coupling with bound electrons for absorption losses. The section also introduces the master equation, Fokker–Planck equation, and Heisenberg–Langevin equations of motion for the cavity field, and discusses aspects of cavity quantum electrodynamics (QED), including damped Rabi oscillations and the modification of atomic spontaneous emission rates. Finally, it demonstrates how STIRAP techniques can be used to create a deterministic source of single photons in a leaky cavity with a three-level atom.This section discusses the dynamics of a single-mode cavity field coupled to a reservoir of harmonic oscillators, focusing on the relaxation of the cavity field. The cavity field is described by creation and annihilation operators \(a^\dagger\) and \(a\), with a Hamiltonian \(\mathcal{H}^\mathrm{F} = \hbar \omega a^\dagger a\). The reservoir, composed of an infinite set of harmonic oscillators, is described by a Hamiltonian \(\mathcal{H}^\mathrm{R} = \sum_k \hbar \omega_k b_k^\dagger b_k\). The interaction between the cavity field and the reservoir is bilinear, represented by \(\mathcal{V} = \mathcal{A} \cdot \mathcal{B}\), where \(\mathcal{A} = \boldsymbol{\varphi} (a + a^\dagger)\) and \(\mathcal{B} = \sum_k \boldsymbol{\beta}_k = \mathrm{i} \sum_k \boldsymbol{\epsilon}_k (b_k^\dagger - b_k)\). The coupling matrix element \(\boldsymbol{\varphi}\) depends on the electric field transmission coefficient for transmission losses or the coupling with bound electrons for absorption losses. The section also introduces the master equation, Fokker–Planck equation, and Heisenberg–Langevin equations of motion for the cavity field, and discusses aspects of cavity quantum electrodynamics (QED), including damped Rabi oscillations and the modification of atomic spontaneous emission rates. Finally, it demonstrates how STIRAP techniques can be used to create a deterministic source of single photons in a leaky cavity with a three-level atom.