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Mandel Q Parameter
The Mandel Q parameter measures the departure of the occupation number distribution from Poissonian statistics. It was introduced in quantum optics by Leonard Mandel. It is a convenient way to characterize non-classical states with negative values indicating a sub-Poissonian statistics, which have no classical analog. It is defined as the normalized variance of the boson distribution: : Q=\frac = \frac -1 = \langle \hat \rangle \left(g^(0)-1 \right) where \hat is the photon number operator and g^ is the normalized second-order correlation function as defined by Glauber. Non-classical value Negative values of Q corresponds to state which variance of photon number is less than the mean (equivalent to sub-Poissonian statistics). In this case, the phase space distribution cannot be interpreted as a classical probability distribution. : -1\leq Q < 0 \Leftrightarrow 0\leq \langle (\Delta \hat)^2 \rangle \leq \langle \hat \rangle The minimal value |
Poisson Distribution
In 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 or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson (; ). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume. For instance, a call center receives an average of 180 calls per hour, 24 hours a day. The calls are independent; receiving one does not change the probability of when the next one will arrive. The number of calls received during any minute has a Poisson probability distribution with mean 3: the most likely numbers are 2 and 3 but 1 and 4 are also likely and there is a small probability of it being as low as zero and a very small probability it could be 10. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Optics
Quantum optics is a branch of atomic, molecular, and optical physics dealing with how individual quanta of light, known as photons, interact with atoms and molecules. It includes the study of the particle-like properties of photons. Photons have been used to test many of the counter-intuitive predictions of quantum mechanics, such as entanglement and teleportation, and are a useful resource for quantum information processing. History Light propagating in a restricted volume of space 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 Albert Einstein in a 1905 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonard Mandel
Leonard Mandel (May 9, 1927 – February 9, 2001) was an American physicist who contributed to the development of theoretical and experimental modern optics and is widely considered one of the founding fathers of the field of quantum optics. With Emil Wolf he published the highly regarded book ''Optical Coherence and Quantum Optics.'' Life Mandel was born in Berlin, Germany, where his father, Robert (Naftali) Mandel, had emigrated from Eastern Europe. He received a BSc degree in mathematics and physics in 1947 and a PhD degree in nuclear physics in 1951 from Birkbeck College, University of London, in the United Kingdom. He became a technical officer at Imperial Chemical Industries Ltd in Welwyn, UK, in 1951. In 1955, he became a lecturer and, later, senior lecturer at Imperial College London, University of London. He remained at Imperial until 1964, when he joined the University of Rochester as a professor of physics. Mandel became Lee DuBridge Professor Emeritus of Phys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fock State
In quantum mechanics, a Fock state or number state is a quantum state that is an element of a Fock space with a well-defined number of particles (or quanta). These states are named after the Soviet physicist Vladimir Fock. Fock states play an important role in the second quantization formulation of quantum mechanics. The particle representation was first treated in detail by Paul Dirac for bosons and by Pascual Jordan and Eugene Wigner for fermions. The Fock states of bosons and fermions obey useful relations with respect to the Fock space creation and annihilation operators. Definition One specifies a multiparticle state of N non-interacting identical particles by writing the state as a sum of tensor products of N one-particle states. Additionally, depending on the integrality of the particles' spin, the tensor products must be alternating (anti-symmetric) or symmetric products of the underlying one-particle Hilbert space. Specifically: * Fermions, having half-integer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roy J
Roy is a masculine given name and a family surname with varied origin. In Anglo-Norman England, the name derived from the Norman ''roy'', meaning "king", while its Old French cognate, ''rey'' or ''roy'' (modern ''roi''), likewise gave rise to Roy as a variant in the Francophone world. In India, Roy is a variant of the surname '' Rai'',. likewise meaning "king".. It also arose independently in Scotland, an anglicisation from the Scottish Gaelic nickname ''ruadh'', meaning "red". Given name * Roy Acuff (1903–1992), American country music singer and fiddler * Roy Andersen (born 1955), runner * Roy Andersen (South Africa) (born 1948), South African businessman and military officer * Roy Anderson (American football) (born 1980), American football coach * Sir Roy M. Anderson (born 1947), British scientific adviser * Roy Andersson (born 1943), Swedish film director * Roy Andersson (footballer) (born 1949), footballer from Sweden * Roy Chapman Andrews (1884–1960), American ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Space
In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. It is the outer product of direct space and reciprocal space. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs. Introduction In a phase space, every degree of freedom or parameter of the system is represented as an axis of a multidimensional space; a one-dimensional system is called a phase line, while a two-dimensional system is called a phase plane. For every possible state of the system or allowed combination of values of the system's parameters, a point is included in the multidimensional space. The system's evolving state over time traces a path (a phase-space trajectory for the sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black-body Radiation
Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spectrum of wavelengths, inversely related to intensity, that depend only on the body's temperature, which is assumed, for the sake of calculations and theory, to be uniform and constant., Chapter 13. A perfectly insulated enclosure which is in thermal equilibrium internally contains black-body radiation, and will emit it through a hole made in its wall, provided the hole is small enough to have a negligible effect upon the equilibrium. The thermal radiation spontaneously emitted by many ordinary objects can be approximated as black-body radiation. Of particular importance, although planets and stars (including the Earth and Sun) are neither in thermal equilibrium with their surroundings nor perfect black bodies, black-body radiation is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Distribution
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma is its standard deviation. The variance of the distribution is \sigma^2. A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution converges to a normal dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bose–Einstein Statistics
In quantum statistics, Bose–Einstein statistics (B–E statistics) describes one of two possible ways in which a collection of non-interacting, indistinguishable particles may occupy a set of available discrete energy states at thermodynamic equilibrium. The aggregation of particles in the same state, which is a characteristic of particles obeying Bose–Einstein statistics, accounts for the cohesive streaming of laser light and the frictionless creeping of superfluid helium. The theory of this behaviour was developed (1924–25) by Satyendra Nath Bose, who recognized that a collection of identical and indistinguishable particles can be distributed in this way. The idea was later adopted and extended by Albert Einstein in collaboration with Bose. The Bose–Einstein statistics applies only to the particles not limited to single occupancy of the same state – that is, particles that do not obey the Pauli exclusion principle restrictions. Such particles have integer values of s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coherent States
In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state which has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator. It was the first example of quantum dynamics when Erwin Schrödinger derived it in 1926, while searching for solutions of the Schrödinger equation that satisfy the correspondence principle. The quantum harmonic oscillator (and hence the coherent states) arise in the quantum theory of a wide range of physical systems.J.R. Klauder and B. Skagerstam, ''Coherent States'', World Scientific, Singapore, 1985. For instance, a coherent state describes the oscillating motion of a particle confined in a quadratic potential well (for an early reference, see e.g. Schiff's textbook). The coherent state describes a state in a system for which the ground-state wavepacket is displaced from the origin of the system. This state can be rela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emil Wolf
Emil Wolf (July 30, 1922 – June 2, 2018) was a Czech-born American physicist who made advancements in physical optics, including diffraction, coherence properties of optical fields, spectroscopy of partially coherent radiation, and the theory of direct scattering and inverse scattering. He was also the author of numerous other contributions to optics. Life and career Wolf was born into a Jewish family in Prague, Czechoslovakia. He was forced to leave his native country when the Germans invaded. After brief periods in Italy and France (where he worked for the Czech government in exile), he moved to the United Kingdom in 1940. He received his B.Sc. in Mathematics and Physics (1945), and Ph.D. in Mathematics from Bristol University, England, in 1948. Between 1951 and 1954 he worked at the University of Edinburgh with Max Born, writing the famous textbook Principles of Optics now usually known simply as '' Born and Wolf''. After a period on the Faculty of the University of Manches ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
