### Quantum electronics

This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. (April 2009) |

**Quantum optics** is a field of research in physics,^{[1]} dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter.

## Contents

## History of quantum optics

Light propagating in a vacuum has its energy and momentum quantized according to an integer number of particles known as photons. Quantum optics studies the nature and effects of light as quantized photons. The first major development leading to that understanding was the correct modeling of the blackbody radiation spectrum by Max Planck in 1899 under the hypothesis of light being emitted in discrete units of energy. The photoelectric effect was further evidence of this quantization as explained by Einstein in a 1905 paper, a discovery for which he was to be awarded the Nobel Prize in 1921. Niels Bohr showed that the hypothesis of optical radiation being quantized corresponded to his theory of the quantized energy levels of atoms, and the spectrum of discharge emission from hydrogen in particular. The understanding of the interaction between light and matter following these developments was 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 into matter rather than into light; hence one rather spoke of atom physics and quantum electronics in 1960. 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^{[dubious – discuss]}, 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. Following the work of Dirac in quantum field theory, George Sudarshan, Roy J. Glauber, and Leonard Mandel applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the statistics of light (see degree of coherence). This led to the introduction of the coherent state as a concept which addressed variations between laser light, thermal light, exotic squeezed states, etc. as it became understood that light can not be fully described just referring to the electromagnetic fields describing the waves in the classical picture. In 1977, Kimble et al. demonstrated a single atom emitting one photon at a time, further compelling evidence that light consists of photons. Previously unknown quantum states of light with characteristics unlike classical states, such as squeezed light were subsequently discovered.

Development of short and ultrashort laser pulses—created by Q switching and modelocking techniques—opened the way to the study of what became known as 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 1995) 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), coherent perfect absorbers, and much more.

Topics classified under the term of quantum optics, especially as applied to technological innovation, often go under the modern term photonics.

## Concepts of quantum optics

According to quantum theory, 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 should not be considered to be classical billiard balls, but as quantum mechanical particles described by a wavefunction spread over a finite region.

Each particle carries one quantum of energy equal to *hf*, where h is Planck's constant and f is the frequency of the light. That energy possessed by a single photon which is created corresponds exactly to a transition between discrete energy levels in an atom (or other light emitting system); material absorption of a photon is the reverse process. Einstein explanation of spontaneous emission also predicted the existence of stimulated emission, the principle upon which the laser rests. However the actual invention of the maser (and laser) many years later was dependent on a method to produce a population inversion.

The use of statistical mechanics is fundamental to the 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 George Sudarshan in 1963. This state, which can be used to approximately describe the output of a single-frequency laser well above the laser threshold, exhibits Poissonian photon number statistics. Via certain nonlinear interactions, a coherent state can be transformed into a squeezed coherent state, which can exhibit super- or sub-Poissonian 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.

## Quantum electronics

This term was used for the area of physics dealing with the effects of quantum mechanics on the behavior of electrons in matter, and their interactions with photons. It is today rarely considered a sub-field in its own right, as it has been absorbed by other fields. Solid state physics regularly takes quantum mechanics into account, and is usually concerned with electrons. Specific application to electronics is researched within semiconductor physics. The term also encompassed the basic processes of laser operation where photons are interacting with electrons: absorption, spontaneous emission, and stimulated emission. The term was mainly used between the 1950s and the 1970s. Today, the research output of this field is mainly used in quantum optics, especially for the part of it that draws not from atomic physics but from solid-state physics. Its usage overlapped Quantum Hall effect and Quantum cellular automata.

## See also

## Notes

## References

## Further reading

- L. Mandel, E. Wolf
*Optical Coherence and Quantum Optics*(Cambridge 1995) - D. F. Walls and G. J. Milburn
*Quantum Optics*(Springer 1994) - C. W. Gardiner and Peter Zoller,
*Quantum Noise*, (Springer 2004). - H.M. Moya-Cessa and F. Soto-Eguibar,
*Introduction to Quantum Optics*(Rinton Press 2011). - M. O. Scully and M. S. Zubairy
*Quantum Optics*(Cambridge 1997) - W. P. Schleich
*Quantum Optics in Phase Space*(Wiley 2001) -

## External links

**Listen to this article**(info/dl)

- An introduction to quantum optics of the light field
- Encyclopedia of laser physics and technology, with content on quantum optics (particularly quantum noise in lasers), by Rüdiger Paschotta.
- Qwiki - A quantum physics wiki devoted to providing technical resources for practicing quantum physicists.
- Quantiki - a free-content WWW resource in quantum information science that anyone can edit.
- Various Quantum Optics Reports

Template:Physics operator