Ramsey spectroscopy is one of the most powerful techniques for precision frequency measurements in quantum optics. It is the basic operating principle behind atomic clocks. It rests on a simple yet profound idea: coherent control of a two-level system using two separated pulses.

A beam splitter is not merely an optical element in classical optics; in quantum optics, its action on photon modes is elegantly described by an SU(2) operator that linearly transforms the annihilation and creation operators of two modes.

Trapped-ion quantum computing relies on the controlled interaction between an ion’s internal two-level structure and its quantized motion in the trap. By driving the ion with laser fields near the carrier and motional sidebands, we can engineer spin-dependent forces and geometric phase evolutions that form the essential quantum gates.

A driven two-level atom exchanges energy with the field through stimulated absorption and emission, while spontaneous emission carries energy into the fluorescence and scattering channels. The rate-equation formalism provides an intuitive way to track population dynamics.

In time-dependent perturbation theory, the primary goal is to determine the time evolution of a perturbed quantum system, with a particular focus on calculating transition probabilities and modeling the irreversible decay of probability in a small quantum system coupled to a much larger system. The interaction picture will be employed to discuss time-dependent perturbations.

The Jaynes-Cummings model (sometimes abbreviated JCM) is a theoretical model in quantum optics. It describes the system of a two-level atom interacting with a quantized mode of an optical cavity (or a bosonic field).

Cavity quantum electrodynamics (cavity QED) is the study of the interaction between light confined in a reflective cavity and atoms or other particles, under conditions where the quantum nature of photons is significant.

The density operator provides a unified framework for describing quantum systems in both pure and mixed states, making it indispensable for analyzing open quantum systems. For a two-level system with dissipation, this description leads to the Optical Bloch Equations.

In this article, we introduce the basic concepts of trapping neutral atoms using optical dipole potentials created by far-detuned laser light. In this regime, optical excitation is strongly suppressed, and the radiation-pressure force from photon scattering becomes negligible compared to the dipole (gradient) force.

Semi-classical description of matter-light interaction means that treating atoms quantum mechanically while treating electromagnetic field classically.