**Quantum optics** is a field of research in

physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, dealing with the application of

quantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

to phenomena involving

lightLight or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

and its interactions with

matterMatter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

.

## History of quantum optics

Light is made up of particles called photons and hence inherently is "grainy" (quantized). Quantum optics is the study of the nature and effects of light as quantized photons. The first indication that light might be quantized came from

Max PlanckMax Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...

in 1899 when he correctly modeled blackbody radiation. By assuming blackbody radiation is quantized,

BohrBohr may refer to:People:* Niels Bohr , Danish atomic physicist, Nobel Prize in physics 1922* Aage Bohr , Danish nuclear physicist, Nobel Prize in physics 1975, son of Niels Bohr...

showed that the atoms were also quantized, in the sense that they could only emit discrete amounts of energy. The understanding of the interaction between light and

matterMatter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

following these developments not only formed the basis of quantum optics but was also 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 scienceLaser science or laser physics is a branch of optics that describes the theory and practice of lasers.Laser science is principally concerned with quantum electronics, laser construction, optical cavity design, the physics of producing a population inversion in laser media, and the temporal...

—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. Following the work of

DiracPaul Adrien Maurice Dirac, OM, FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics...

in

quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

,

George SudarshanEnnackal Chandy George Sudarshan , also E.C.G. Sudarshan, is a prominent Indian American physicist, author, and professor at The University of Texas at Austin.-Early life:...

,

Roy J. GlauberRoy Jay Glauber is an American theoretical physicist. He is the Mallinckrodt Professor of Physics at Harvard University and Adjunct Professor of Optical Sciences at the University of Arizona...

, and

Leonard MandelLeonard Mandel was the Lee DuBridge Professor Emeritus of Physics and Optics at the University of Rochester when he died at the age of 73 at his home in Pittsford, New York. He contributed immensely to theoretical and experimental optics...

applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the

statisticsStatistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...

of light (see

degree of coherence). This led to the introduction of the

coherent stateIn quantum mechanics a coherent state is a specific kind of quantum state of the quantum harmonic oscillator whose dynamics most closely resembles the oscillating behaviour of a classical harmonic oscillator...

as a quantum description of laser light and the realization that some states of light could not be described with classical waves. In 1977,

KimbleH. Jeff Kimble is the William L. Valentine Professor and Professor of Physics at Caltech. His research is in quantum optics and is noted for groundbreaking experiments in physics including one of the first demonstrations of teleportation of a quantum state , quantum logic gate, and the development...

et al. demonstrated the first source of light which required a quantum description: a single atom that emitted one photon at a time. This was the first conclusive evidence that light was made up of photons. Another quantum state of light with certain advantages over any classical state,

squeezed light, was soon proposed. At the same time, development of short and

ultrashortIn optics, an ultrashort pulse of light is an electromagnetic pulse whose time duration is of the order of a femtosecond . Such pulses have a broadband optical spectrum, and can be created by mode-locked oscillators...

laser pulses—created by Q switching and

modelockingMode-locking is a technique in optics by which a laser can be made to produce pulses of light of extremely short duration, on the order of picoseconds or femtoseconds ....

techniques—opened the way to the study of unimaginably fast ("ultrafast") processes. Applications for solid state research (e.g.

Raman spectroscopyRaman spectroscopy is a spectroscopic technique used to study vibrational, rotational, and other low-frequency modes in a system.It relies on inelastic scattering, or Raman scattering, of monochromatic light, usually from a laser in the visible, near infrared, or near ultraviolet range...

) 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 tweezersOptical tweezers are scientific instruments that use a highly focused laser beam to provide an attractive or repulsive force , depending on the refractive index mismatch to physically hold and move microscopic dielectric objects...

by laser beam. This, along with

Doppler coolingDoppler cooling is a mechanism that can be used to trap and cool atoms. The term is sometimes used synonymously with laser cooling, though laser cooling includes other techniques.-History:...

was the crucial technology needed to achieve the celebrated Bose-Einstein condensation.

Other remarkable results are the

demonstration of quantum entanglementThe Bell test experiments serve to investigate the validity of the entanglement effect in quantum mechanics by using some kind of Bell inequality...

,

quantum teleportationQuantum teleportation, or entanglement-assisted teleportation, is a process by which a qubit can be transmitted exactly from one location to another, without the qubit being transmitted through the intervening space...

, 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 scienceComputer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...

.

Today's fields of interest among quantum optics researchers include parametric down-conversion,

parametric oscillationAn optical parametric oscillator is a parametric oscillator which oscillates at optical frequencies. It converts an input laser wave into two output waves of lower frequency by means of second order nonlinear optical interaction. The sum of the output waves frequencies is equal to the input wave...

, even shorter (attosecond) light pulses, use of quantum optics for

quantum informationIn quantum mechanics, quantum information is physical information that is held in the "state" of a quantum system. The most popular unit of quantum information is the qubit, a two-level quantum system...

, manipulation of single atoms, Bose-Einstein condensates, their application, and how to manipulate them (a sub-field often called

atom opticsAtom optics is the area of physics which deals with beams of cold, slowly moving neutral atoms, as a special case of a particle beam....

),

coherent perfect absorberA Coherent perfect absorber , or anti-laser, is a device which absorbs coherent light and converts it to some form of internal energy such as heat or electrical energy. It is the time reversed counterpart of a laser. The concept was first published in the July 26, 2010, issue of Physical Review...

s, and much more.

Research into quantum optics that aims to bring photons into use for information transfer and computation is now often called

photonicsThe science of photonics includes the generation, emission, transmission, modulation, signal processing, switching, amplification, detection and sensing of light. The term photonics thereby emphasizes that photons are neither particles nor waves — they are different in that they have both particle...

to emphasize the claim that photons and photonics will take the role that

electronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s and

electronicsElectronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

now have.

## 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 lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

. These particles should not be considered to be classical billiard balls, but as quantum mechanical particles described by a

wavefunctionNot to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...

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. The postulation of the

quantizationIn physics, quantization is the process of explaining a classical understanding of physical phenomena in terms of a newer understanding known as "quantum mechanics". It is a procedure for constructing a quantum field theory starting from a classical field theory. This is a generalization of the...

of light by

Max PlanckMax Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...

in 1899 and the discovery of the general validity of this idea in

Albert EinsteinAlbert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

's 1905 explanation of the

photoelectric effectIn the photoelectric effect, electrons are emitted from matter as a consequence of their absorption of energy from electromagnetic radiation of very short wavelength, such as visible or ultraviolet light. Electrons emitted in this manner may be referred to as photoelectrons...

soon led physicists to realize the possibility of

population inversionIn physics, specifically statistical mechanics, a population inversion occurs when a system exists in state with more members in an excited state than in lower energy states...

and the possibility of the

laserA laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

.

This kind of use of

statistical mechanicsStatistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...

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 electrodynamicsQuantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

.

A frequently encountered state of the light field is the

coherent stateIn quantum mechanics a coherent state is a specific kind of quantum state of the quantum harmonic oscillator whose dynamics most closely resembles the oscillating behaviour of a classical harmonic oscillator...

as introduced by

George SudarshanEnnackal Chandy George Sudarshan , also E.C.G. Sudarshan, is a prominent Indian American physicist, author, and professor at The University of Texas at Austin.-Early life:...

in 1963. This state, which can be used to approximately describe the output of a single-frequency

laserA laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

well above the laser threshold, exhibits

PoissonianIn probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since...

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

discreteIn topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points are "isolated" from each other in a certain sense.- Definitions :Given a set X:...

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 numberQuantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...

s 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

physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

dealing with the effects of

quantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

on the behavior of

electronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s in matter, and their interactions with

photonIn physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s. 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

electronicsElectronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

is researched within

semiconductorA semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...

physics. The term also encompassed the basic processes of

laserA laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...

operation where photons are interacting with electrons: absorption,

spontaneous emissionSpontaneous emission is the process by which a light source such as an atom, molecule, nanocrystal or nucleus in an excited state undergoes a transition to a state with a lower energy, e.g., the ground state and emits a photon...

, and

stimulated emissionIn optics, stimulated emission is the process by which an atomic electron interacting with an electromagnetic wave of a certain frequency may drop to a lower energy level, transferring its energy to that field. A photon created in this manner has the same phase, frequency, polarization, and...

. 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 physicsAtomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and...

but from solid-state physics. Its usage overlapped

Quantum Hall effect and

Quantum cellular automataQuantum Cellular Automata refers to models of quantum computation, which have been devised in analogy to conventional models of cellular automata introduced by von Neumann...

.

## See also

- Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

- Optical phase space
In quantum optics, an optical phase space is a phase space in which all quantum states of an optical system are described. Each point in the optical phase space corresponds to a unique state of an optical system. For any such system, a plot of the quadratures against each other, possibly as...

- Optical physics
Optical physics, or optical science, is a subfield of atomic, molecular, and optical physics. It is the study of the generation of electromagnetic radiation, the properties of that radiation, and the interaction of that radiation with matter, especially its manipulation and control...

- Nonclassical light
Nonclassical light is any state of light that cannot be described using classical electromagnetism; its characteristics are described by the quantised electromagnetic field and quantum mechanics...

## External links