Semiconductor-luminescence Equations
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Semiconductor-luminescence Equations
The semiconductor luminescence equations (SLEs)Kira, M.; Jahnke, F.; Koch, S.; Berger, J.; Wick, D.; Nelson, T.; Galina Khitrova, Khitrova, G.; Gibbs, H. (1997). "Quantum Theory of Nonlinear Semiconductor Microcavity Luminescence Explaining "Boser" Experiments". ''Physical Review Letters'' 79 (25): 5170–5173. do10.1103/PhysRevLett.79.5170/ref>Kira, M.; Koch, S. W. (2011). ''Semiconductor Quantum Optics''. Cambridge University Press. . describe luminescence of semiconductors resulting from spontaneous Carrier generation and recombination, recombination of electronic excitations, producing a Luminous flux, flux of Spontaneous emission, spontaneously emitted light. This description established the first step toward semiconductor quantum optics because the SLEs simultaneously includes the quantized light–matter interaction and the Coulomb's law, Coulomb-interaction coupling among electronic excitations within a semiconductor. The SLEs are one of the most accurate methods to describe ...
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Galina Khitrova
Galina Khitrova (1959 – June 4, 2016) was a Russian-American physicist and optical scientist known for her research on cavity quantum electrodynamics, excitons, nonlinear optics, quantum dots, and vacuum Rabi oscillations. She was a professor of optical sciences at the University of Arizona. Education and career Khitrova was born in Saint Petersburg, and has degrees in physics from Yerevan State University, Brooklyn College, and New York University, where she completed her Ph.D. She came to the University of Arizona as a researcher in 1986, married Arizona professor Professor Hyatt M. Gibbs in 1986, was given tenure as an associate professor in 1997, and became full professor in 2002. Recognition Khitrova was named a Fellow of The Optical Society Optica (formerly known as The Optical Society (OSA) and before that as the Optical Society of America) is a professional society of individuals and companies with an interest in optics and photonics. It publishes journals and orga ...
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Quantum-optical Spectroscopy
Quantum-optical spectroscopyKira, M.; Koch, S. (2006). "Quantum-optical spectroscopy of semiconductors". ''Physical Review A'' 73 (1). doibr>10.1103/PhysRevA.73.013813 .Koch, S. W.; Kira, M.; Khitrova, G.; Gibbs, H. M. (2006). "Semiconductor excitons in new light". ''Nature Materials'' 5 (7): 523–531. doibr>10.1038/nmat1658 . is a quantum-optical generalization of laser spectroscopy where matter is excited and probed with a sequence of laser pulses. Classically, such pulses are defined by their spectral and temporal shape as well as phase and amplitude of the electromagnetic field. Besides these properties of light, the phase-amplitude aspects have intrinsic quantum fluctuations that are of central interest in quantum optics. In ordinary laser spectroscopy,Stenholm, S. (2005). ''Foundations of laser spectroscopy''. Dover Pubn. Inc. .Demtröder, W. (2008). ''Laser Spectroscopy: Vol. 1: Basic Principles''. Springer. .Demtröder, W. (2008). ''Laser Spectroscopy: Vol. 2: Experime ...
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Cluster-expansion Approach
The cluster-expansion approach is a technique in quantum mechanics that systematically truncates the BBGKY hierarchy problem that arises when quantum dynamics of interacting systems is solved. This method is well suited for producing a closed set of numerically computable equations that can be applied to analyze a great variety of many-body and/or quantum-optical problems. For example, it is widely applied in semiconductor quantum opticsKira, M.; Koch, S. W. (2011). ''Semiconductor Quantum Optics''. Cambridge University Press. and it can be applied to generalize the semiconductor Bloch equations and semiconductor luminescence equations. Background Quantum theory essentially replaces classically accurate values by a probabilistic distribution that can be formulated using, e.g., a wavefunction, a density matrix, or a phase-space distribution. Conceptually, there is always, at least formally, probability distribution behind each observable that is measured. Already in 1889, a lo ...
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Electron Hole
In physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is a quasiparticle which is the lack of an electron at a position where one could exist in an atom or atomic lattice. Since in a normal atom or crystal lattice the negative charge of the electrons is balanced by the positive charge of the atomic nuclei, the absence of an electron leaves a net positive charge at the hole's location. Holes in a metal or semiconductor crystal lattice can move through the lattice as electrons can, and act similarly to positively-charged particles. They play an important role in the operation of semiconductor devices such as transistors, diodes and integrated circuits. If an electron is excited into a higher state it leaves a hole in its old state. This meaning is used in Auger electron spectroscopy (and other x-ray techniques), in computational chemistry, and to explain the low electron-electron scattering-rate in crystals (metals, semiconduct ...
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Flux
Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface. Terminology The word ''flux'' comes from Latin: ''fluxus'' means "flow", and ''fluere'' is "to flow". As ''fluxion'', this term was introduced into differential calculus by Isaac Newton. The concept of heat flux was a key contribution of Joseph Fourier, in the analysis of heat transfer phenomena. His seminal treatise ''Théorie analytique de la chaleur'' (''The Analytical Theory of Heat''), defines ''fluxion'' as a central quantity and proceeds to derive the now well-known express ...
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Light-emitting Diodes
A light-emitting diode (LED) is a semiconductor device that emits light when current flows through it. Electrons in the semiconductor recombine with electron holes, releasing energy in the form of photons. The color of the light (corresponding to the energy of the photons) is determined by the energy required for electrons to cross the band gap of the semiconductor. White light is obtained by using multiple semiconductors or a layer of light-emitting phosphor on the semiconductor device. Appearing as practical electronic components in 1962, the earliest LEDs emitted low-intensity infrared (IR) light. Infrared LEDs are used in remote-control circuits, such as those used with a wide variety of consumer electronics. The first visible-light LEDs were of low intensity and limited to red. Early LEDs were often used as indicator lamps, replacing small incandescent bulbs, and in seven-segment displays. Later developments produced LEDs available in visible, ultraviolet (UV), ...
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Quasi-stationary Distribution
In probability a quasi-stationary distribution is a random process that admits one or several absorbing states that are reached almost surely, but is initially distributed such that it can evolve for a long time without reaching it. The most common example is the evolution of a population: the only equilibrium is when there is no one left, but if we model the number of people it is likely to remain stable for a long period of time before it eventually collapses. Formal definition We consider a Markov process (Y_t)_ taking values in \mathcal. There is a measurable set \mathcal^of absorbing states and \mathcal^a = \mathcal \setminus \mathcal^. We denote by T the hitting time of \mathcal^, also called killing time. We denote by \ the family of distributions where \operatorname_x has original condition Y_0 = x \in \mathcal. We assume that \mathcal^ is almost surely reached, i.e. \forall x \in \mathcal, \operatorname_x(T t) = \nu(B)where \operatorname_\nu = \int_ \operatorname_x \, ...
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Expectation Value (quantum Mechanics)
In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the ''most'' probable value of a measurement; indeed the expectation value may have zero probability of occurring (e.g. measurements which can only yield integer values may have a non-integer mean). It is a fundamental concept in all areas of quantum physics. Operational definition Consider an operator A. The expectation value is then \langle A \rangle = \langle \psi , A , \psi \rangle in Dirac notation with , \psi \rangle a normalized state vector. Formalism in quantum mechanics In quantum theory, an experimental setup is described by the observable A to be measured, and the state \sigma of the system. The expectation value of A in the state \sigma is denoted as \langle A \rangle_\sigma. Mathematically, A is a ...
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Photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always move at the speed of light in vacuum, (or about ). The photon belongs to the class of bosons. As with other elementary particles, photons are best explained by quantum mechanics and exhibit wave–particle duality, their behavior featuring properties of both waves and particles. The modern photon concept originated during the first two decades of the 20th century with the work of Albert Einstein, who built upon the research of Max Planck. While trying to explain how matter and electromagnetic radiation could be in thermal equilibrium with one another, Planck proposed that the energy stored within a material object should be regarded as composed of an integer number of discrete, equal-sized parts. To explain the photoelectric effect, Eins ...
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Creation And Annihilation Operators
Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator (usually denoted \hat) lowers the number of particles in a given state by one. A creation operator (usually denoted \hat^\dagger) increases the number of particles in a given state by one, and it is the adjoint of the annihilation operator. In many subfields of physics and chemistry, the use of these operators instead of wavefunctions is known as second quantization. They were introduced by Paul Dirac. Creation and annihilation operators can act on states of various types of particles. For example, in quantum chemistry and many-body theory the creation and annihilation operators often act on electron states. They can also refer specifically to the ladder operators for the quantum harmonic oscillator. In the latter case, the raising operator is in ...
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Boson
In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spin (,, ...). Every observed subatomic particle is either a boson or a fermion. Bosons are named after physicist Satyendra Nath Bose. Some bosons are elementary particles and occupy a special role in particle physics unlike that of fermions, which are sometimes described as the constituents of "ordinary matter". Some elementary bosons (for example, gluons) act as force carriers, which give rise to forces between other particles, while one (the Higgs boson) gives rise to the phenomenon of mass. Other bosons, such as mesons, are composite particles made up of smaller constituents. Outside the realm of particle physics, superfluidity arises because composite bosons (bose particles), such as low temperature helium-4 atoms, follow Bose–E ...
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Second Quantization
Second quantization, also referred to as occupation number representation, is a formalism used to describe and analyze quantum many-body systems. In quantum field theory, it is known as canonical quantization, in which the fields (typically as the wave functions of matter) are thought of as field operators, in a manner similar to how the physical quantities (position, momentum, etc.) are thought of as operators in first quantization. The key ideas of this method were introduced in 1927 by Paul Dirac, and were later developed, most notably, by Pascual Jordan and Vladimir Fock. In this approach, the quantum many-body states are represented in the Fock state basis, which are constructed by filling up each single-particle state with a certain number of identical particles. The second quantization formalism introduces the creation and annihilation operators to construct and handle the Fock states, providing useful tools to the study of the quantum many-body theory. Quantum many-body ...
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