A beam splitter or beamsplitter is an optical device that splits a beam of light into a transmitted and a reflected beam. It is a crucial part of many optical experimental and measurement systems, such as interferometers, also finding widespread application in fibre optic telecommunications.

The passage introduces the fundamental theory of trapped-ion quantum computing.

Atomic spectra are defined as the spectrum of the electromagnetic radiation emitted or absorbed by an electron during transitions between different energy levels within an atom.

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.

Density Operator is a generalization of the more usual state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent mixed states. Mixed states arise in quantum mechanics in two different situations: first when the preparation of the system is not fully known, and thus one must deal with a statistical ensemble of possible preparations, and second when one wants to describe a physical system which is entangled with another, without describing their combined state.

Semi-classical description of matter-light interaction means that we shall present the fundamental features of the interaction of an atom, which will be treated quantum mechanically, with a classical electromagnetic field, that is an electromagnetic field described by real electric and magnetic vectors obeying Maxwell’s equations.

In a calculation on a digital computer, information is processed in the form of so-called binary digits or bits, representing its smallest unit. Each bit can have the value 0 or 1, corresponding to two discrete states. Moving the processing of information itself into the quantum mechanical domain, one can identify a two-level system now called quantum bit, or qubit that is based on two distinguishable quantum states. Therefore, it is necessary to look on two-level system specifically.

In time-dependent perturbation theory the main goal is to determine the time-evolution of a perturbed quantum system, with particular emphasis on calculating transition probabilities and modeling the irreversible decay of probability from a small quantum system coupled to a very large quantum system. The interaction picture will be used to discuss time-dependent perturbation.

Interaction Picture Interaction Picture Perturbation Hamiltonian HS=H0S+HintS(t)H^S = H^S_0 + H^S_\text{int} (t)HS=H0S​...