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Photon Antibunching
Photon antibunching generally refers to a light field with photons more equally spaced than a coherent laser field, a signature being signals at appropriate detectors which are anticorrelated. More specifically, it can refer to sub-Poissonian photon statistics, that is a photon number distribution for which the variance is less than the mean. A coherent state, as output by a laser far above threshold, has Poissonian statistics yielding random photon spacing; while a thermal light field has super-Poissonian statistics and yields bunched photon spacing. In the thermal (bunched) case, the number of fluctuations is larger than a coherent state; for an antibunched source they are smaller. Explanation The variance of the photon number distribution is : V_n=\langle \Delta n^2\rangle=\langle n^2\rangle-\langle n\rangle^2= \left\langle \left(a^a\right)^2\right\rangle-\langle a^a\rangle ^2. Using commutation relations, this can be written as : V_n=\langle )^2a^2 \rangle+\langle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Photon Bunching
In physics, the Hanbury Brown and Twiss (HBT) effect is any of a variety of correlation and anti-correlation effects in the intensities received by two detectors from a beam of particles. HBT effects can generally be attributed to the wave–particle duality of the beam, and the results of a given experiment depend on whether the beam is composed of fermions or bosons. Devices which use the effect are commonly called intensity interferometers and were originally used in astronomy, although they are also heavily used in the field of quantum optics. History In 1954, Robert Hanbury Brown and Richard Q. Twiss introduced the intensity interferometer concept to radio astronomy for measuring the tiny angular size of stars, suggesting that it might work with visible light as well. Soon after they successfully tested that suggestion: in 1956 they published an in-lab experimental mockup using blue light from a mercury-vapor lamp, and later in the same year, they applied this technique to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resonance Fluorescence
Resonance fluorescence is the process in which a two-level atom system interacts with the quantum electromagnetic field if the field is driven at a frequency near to the natural frequency of the atom. General theory Typically the photon contained electromagnetic field is applied to the two-level atom through the use of a monochromatic laser. A two-level atom is a specific type of two-state system in which the atom can be found in the two possible states. The two possible states are if an electron is found in its ground state or the excited state. In many experiments an atom of lithium is used because it can be closely modeled to a two-level atom as the excited states of the singular electron are separated by large enough energy gaps to significantly reduce the possibility of the electron jumping to a higher excited state. Thus it allows for easier frequency tuning of the applied laser as frequencies further off resonance can be used while still driving the electron to jump to on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Squeezed Coherent State
In physics, a squeezed coherent state is a quantum state that is usually described by two non-commuting observables having continuous spectra of eigenvalues. Examples are position x and momentum p of a particle, and the (dimension-less) electric field in the amplitude X (phase 0) and in the mode Y (phase 90°) of a light wave (the wave's quadratures). The product of the standard deviations of two such operators obeys the uncertainty principle: :\Delta x \Delta p \geq \frac2\; and \;\Delta X \Delta Y \geq \frac4 , respectively. Trivial examples, which are in fact not squeezed, are the ground state , 0\rangle of the quantum harmonic oscillator and the family of coherent states , \alpha\rangle. These states saturate the uncertainty above and have a symmetric distribution of the operator uncertainties with \Delta x_g = \Delta p_g in "natural oscillator units" and \Delta X_g = \Delta Y_g = 1/2. (In literature different normalizations for the quadrature amplitudes are u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hong–Ou–Mandel Effect
The Hong–Ou–Mandel effect is a two-photon interference effect in quantum optics that was demonstrated in 1987 by three physicists from the University of Rochester: Chung Ki Hong (홍정기), Zheyu Ou (区泽宇), and Leonard Mandel. The effect occurs when two identical single-photon waves enter a 1:1 beam splitter, one in each input port. When the temporal overlap of the photons on the beam splitter is perfect, the two photons will always exit the beam splitter together in the same output mode, meaning that there is zero chance that they will exit separately with one photon in each of the two outputs giving a coincidence event. The photons have a 50:50 chance of exiting (together) in either output mode. If they become more distinguishable (e.g. because they arrive at different times or with different wavelength), the probability of them each going to a different detector will increase. In this way, the interferometer coincidence signal can accurately measure bandwidth, path l ... [...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 spin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correlation Does Not Imply Causation
The phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two events or variables solely on the basis of an observed association or correlation between them. The idea that "correlation implies causation" is an example of a questionable-cause logical fallacy, in which two events occurring together are taken to have established a cause-and-effect relationship. This fallacy is also known by the Latin phrase ''cum hoc ergo propter hoc'' ('with this, therefore because of this'). This differs from the fallacy known as ''post hoc ergo propter hoc'' ("after this, therefore because of this"), in which an event following another is seen as a necessary consequence of the former event, and from conflation, the errant merging of two events, ideas, databases, etc., into one. As with any logical fallacy, identifying that the reasoning behind an argument is flawed does not necessarily imply that the resulting con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spontaneous Parametric Down-conversion
Spontaneous parametric down-conversion (also known as SPDC, parametric fluorescence or parametric scattering) is a nonlinear instant optical process that converts one photon of higher energy (namely, a pump photon), into a pair of photons (namely, a signal photon, and an idler photon) of lower energy, in accordance with the law of conservation of energy and law of conservation of momentum. It is an important process in quantum optics, for the generation of entangled photon pairs, and of single photons. Basic process A nonlinear crystal is used to produce pairs of photons from a photon beam. In accordance with the law of conservation of energy and law of conservation of momentum, the pairs have combined energies and momenta equal to the energy and momentum of the original photon. Because the index of refraction changes with frequency (dispersion), only certain triplets of frequencies will be phase-matched so that simultaneous energy and momentum conservation can be achieved. P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy–Schwarz Inequality
The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is considered one of the most important and widely used inequalities in mathematics. The inequality for sums was published by . The corresponding inequality for integrals was published by and . Schwarz gave the modern proof of the integral version. Statement of the inequality The Cauchy–Schwarz inequality states that for all vectors \mathbf and \mathbf of an inner product space it is true that where \langle \cdot, \cdot \rangle is the inner product. Examples of inner products include the real and complex dot product; see the examples in inner product. Every inner product gives rise to a norm, called the or , where the norm of a vector \mathbf is denoted and defined by: \, \mathbf\, := \sqrt so that this norm and the inner product are related by the defining condition \, \mathbf\, ^2 = \langle \mathbf, \mathbf \rangle, where \langle \mathbf, \mathbf \rangle is always a non-negative ... [...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 Physics a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correlation And Dependence
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are ''linearly'' related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. However ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 |
Degree Of Coherence
In quantum optics, correlation functions are used to characterize the statistical and coherence properties of an electromagnetic field. The degree of coherence is the normalized correlation of electric fields; in its simplest form, termed g^. It is useful for quantifying the coherence between two electric fields, as measured in a Michelson or other linear optical interferometer. The correlation between pairs of fields, g^, typically is used to find the statistical character of intensity fluctuations. First order correlation is actually the amplitude-amplitude correlation and the second order correlation is the intensity-intensity correlation. It is also used to differentiate between states of light that require a quantum mechanical description and those for which classical fields are sufficient. Analogous considerations apply to any Bose field in subatomic physics, in particular to mesons (cf. Bose–Einstein correlations). Degree of first-order coherence The normalized ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
