**Quantum optics** is a field of research in physics, dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter.

## History of quantum optics

Light is made up of particles and hence inherently "grainy"; quantum optics is the study of the nature and effects of this. The fundamental ideas of quantum optics, namely Albert Einstein's 1905 theory of the photoelectric effect and all the understanding of the interaction between light and matter following from it not only form the basis of quantum optics but also were crucial for the development of quantum mechanics as a whole. However, the subfields of quantum mechanics dealing with matter-light interaction were principally regarded as research in matter rather than in light and hence, one rather spoke of atom physics and quantum electronics.

This changed with the invention of the laser in 1950. Laser science—i.e., research into principles, design and application of these devices—became an important field, and the quantum mechanics underlying the laser's principles was studied now with more emphasis on the properties of light, and the name *quantum optics* became customary.

As laser science needed good theoretical foundations, and also because research into these soon proved very fruitful, interest in quantum optics rose. A clearer understanding of the statistics of light was gained, with the introduction of the concepts of coherent states, squeezed light etc. being the successes of the 1970s and 1980s, as well as the development of short and ultrashort laser pulses created by Q switching and modelocking techniques, opening the way to the study of unimaginably fast ("ultrafast") processes. Applications for solid state research (e.g. Raman spectroscopy) were found, and mechanical forces of light on matter were studied. The latter led to levitating and positioning clouds of atoms or even small biological samples in an optical trap or optical tweezers by laser beam. This, along with Doppler cooling was the crucial technology needed to achieve the celebrated Bose-Einstein condensation.

Other remarkable results are the demonstration of quantum entanglement, quantum teleportation and (recently, in 2004) quantum logic gates. The latter are of much interest in quantum information theory, a subject which partly emerged from quantum optics, partly from theoretical computer science.

Today's fields of interest among quantum optics researchers include parametric down-conversion, parametric oscillation , even shorter (attosecond) light pulses, use of quantum optics for quantum information, manipulation of single atoms, Bose-Einstein condensates, their application, and how to manipulate them (a sub-field often called atom optics ), and much more.

Research into quantum optics, which aims to bring photons to use for information transfer and computation, is now often called photonics to emphasize the claim that photons and photonics will take the role that electrons and electronics now have.

## Concepts of quantum optics

According to quantum mechanics, light may be considered not only as an electro-magnetic wave but also as a "stream" of particles called photons which travel with *c*, the vacuum speed of light. These particles are not considered as billiard balls, but as moving fuzzy regions having an elementary excitation amplitude. If you put an piece of matter into a region that is visited by a certain number of photons, there is a certain probability that your piece of matter has absorbed up to those quanta of energy. The postulation of the quantization of light by Max Planck in 1899 and the discovery of the general validity of this idea in Albert Einstein's 1905 explanation of the photoelectric effect soon led physicists to realize the possibility of population inversion and the possibility of the laser.

This kind of use of statistical mechanics is the fundament of most concepts of quantum optics: Light is described in terms of field operators for creation and annihilation of photons—i.e. in the language of quantum electrodynamics.

A frequently encountered state of the light field is the coherent state as introduced by R. J. Glauber in 1963. This state, which can be used to approximately describe the output of a single-frequency laser well above the laser threshold, exhibits Poissonean photon number statistics. Via certain nonlinear interactions, a coherent state can be transformed into a squeezed coherent state, which can exhibit super- or sub-Poissonean photon statistics. Such light is called squeezed light . Other important quantum aspects are related to correlations of photon statistics between different beams. For example, parametric nonlinear processes can generate so-called twin beams, where ideally each photon of one beam is associated with a photon in the other beam.

Atoms are considered as quantum mechanical oscillators with a discrete energy spectrum with the transitions between the energy eigenstates being driven by the absorption or emission of light according to Einstein's theory with the oscillator strength depending on the quantum numbers of the states.

For solid state matter one uses the energy band models of solid state physics. This is important as understanding how light is detected (typically by a solid-state device that absorbs it) is crucial for understanding experiments.

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