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Autler–Townes Effect
In spectroscopy, the Autler–Townes effect (also known as AC Stark effect), is a dynamical Stark effect corresponding to the case when an oscillating electric field (e.g., that of a laser) is tuned in resonance (or close) to the transition frequency of a given spectral line, and resulting in a change of the shape of the absorption/ emission spectra of that spectral line. The AC Stark effect was discovered in 1955 by American physicists Stanley Autler and Charles Townes. It is the AC equivalent of the static Stark effect which splits the spectral lines of atoms and molecules in a constant electric field. Compared to its DC counterpart, the AC Stark effect is computationally more complex. While generally referring to atomic spectral shifts due to AC fields at any (single) frequency, the effect is more pronounced when the field frequency is close to that of a natural atomic or molecular dipole transition. In this case, the alternating field has the effect of splitting the two bar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectroscopy
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter waves and acoustic waves can also be considered forms of radiative energy, and recently gravitational waves have been associated with a spectral signature in the context of the Laser Interferometer Gravitational-Wave Observatory (LIGO) In simpler terms, spectroscopy is the precise study of color as generalized from visible light to all bands of the electromagnetic spectrum. Historically, spectroscopy originated as the study of the wavelength dependence of the absorption by gas phase matter of visible light dispersed by a prism. Spectroscopy, primarily in the electromagnetic spectrum, is a fundamental exploratory tool in the fields of astronomy, chemistry, materials science, and physics, allowing the composition, physical structure an ... [...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] |
Fourier Series
A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or ''period''), the number of components, and their amplitudes and phase parameters. With appropriate choices, one cycle (or ''period'') of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic). The number of components is theoretically infinite, in which case the other parameters can be chosen to cause the series to converge to almost any ''well behaved'' periodic function (see Pathological and Dirichlet–Jordan test). The components of a particular function are determined by ''analysis'' techniques described in this article. Sometimes the components are known first, and the unknown function is ''synthesized'' by a Fourier series. Such is the case of a discrete- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floquet's Theorem
Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the form :\dot = A(t) x, with \displaystyle A(t) a piecewise continuous periodic function with period T and defines the state of the stability of solutions. The main theorem of Floquet theory, Floquet's theorem, due to , gives a canonical form for each fundamental matrix solution of this common linear system. It gives a coordinate change \displaystyle y=Q^(t)x with \displaystyle Q(t+2T)=Q(t) that transforms the periodic system to a traditional linear system with constant, real coefficients. When applied to physical systems with periodic potentials, such as crystals in condensed matter physics, the result is known as Bloch's theorem. Note that the solutions of the linear differential equation form a vector space. A matrix \phi\,(t) is called a '' fundamental matrix solution'' if all columns are linearly independent solutio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous Differential Equation
A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written :f(x,y) \, dy = g(x,y) \, dx, where and are homogeneous functions of the same degree of and . In this case, the change of variable leads to an equation of the form :\frac = h(u) \, du, which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives. In the case of linear differential equations, this means that there are no constant terms. The solutions of any linear ordinary differential equation of any order may be deduced by integration from the solution of the homogeneous equation obtained by removing the constant term. History The term ''homogeneous'' was first applied to differential equations by Johann Bernoulli in section 9 of his 1726 article ''De integraionibus aequationum differentialium'' (On ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Differential Equation
In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y + a_1(x)y' + a_2(x)y'' \cdots + a_n(x)y^ = b(x) where and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of an unknown function of the variable . Such an equation is an ordinary differential equation (ODE). A ''linear differential equation'' may also be a linear partial differential equation (PDE), if the unknown function depends on several variables, and the derivatives that appear in the equation are partial derivatives. A linear differential equation or a system of linear equations such that the associated homogeneous equations have constant coefficients may be solved by quadrature, which means that the solutions may be expressed in terms of integrals. This is also true for a linear equation of order one, with non-co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schrödinger Equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject. The equation is named after Erwin Schrödinger, who postulated the equation in 1925, and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of a wave function, the quantum-mechanical characterization of an isolated physical system. The equation can be derived from the fact that the time-evolution operator must be unitary, and must therefore be generated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Potential
In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a ''scalar potential'', which is a scalar field whose gradient is a given vector field. Formally, given a vector field v, a ''vector potential'' is a C^2 vector field A such that \mathbf = \nabla \times \mathbf. Consequence If a vector field v admits a vector potential A, then from the equality \nabla \cdot (\nabla \times \mathbf) = 0 (divergence of the curl is zero) one obtains \nabla \cdot \mathbf = \nabla \cdot (\nabla \times \mathbf) = 0, which implies that v must be a solenoidal vector field. Theorem Let \mathbf : \R^3 \to \R^3 be a solenoidal vector field which is twice continuously differentiable. Assume that decreases at least as fast as 1/\, \mathbf\, for \, \mathbf\, \to \infty . Define \mathbf (\mathbf) = \frac \int_ \frac \, d^3\mathbf. Then, A is a vector potential for , that is, \nabla \times \mathbf =\mathbf. Here, \nabla_y \time ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiclassical Physics
Semiclassical physics, or simply semiclassical refers to a theory in which one part of a system is described quantum mechanically whereas the other is treated classically. For example, external fields will be constant, or when changing will be classically described. In general, it incorporates a development in powers of Planck's constant, resulting in the classical physics of power 0, and the first nontrivial approximation to the power of (−1). In this case, there is a clear link between the quantum-mechanical system and the associated semi-classical and classical approximations, as it is similar in appearance to the transition from physical optics to geometric optics. Instances Some examples of a semiclassical approximation include: * WKB approximation: electrons in classical external electromagnetic fields. * semiclassical gravity: quantum field theory within a classical curved gravitational background (see general relativity). * quantum chaos; quantization of class ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carbonyl Sulfide
Carbonyl sulfide is the chemical compound with the linear formula OCS. It is a colorless flammable gas with an unpleasant odor. It is a linear molecule consisting of a carbonyl group double bonded to a sulfur atom. Carbonyl sulfide can be considered to be intermediate between carbon dioxide and carbon disulfide, both of which are valence isoelectronic with it. Occurrence Carbonyl sulfide is the most abundant sulfur compound naturally present in the atmosphere, at , because it is emitted from oceans, volcanoes and deep sea vents. As such, it is a significant compound in the global sulfur cycle. Measurements on the Antarctica ice cores and from air trapped in snow above glaciers ( firn air) have provided a detailed picture of OCS concentrations from 1640 to the present day and allow an understanding of the relative importance of anthropogenic and non-anthropogenic sources of this gas to the atmosphere. Some carbonyl sulfide that is transported into the stratospheric sulfate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massachusetts Institute Of Technology
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the most prestigious and highly ranked academic institutions in the world. Founded in response to the increasing industrialization of the United States, MIT adopted a European polytechnic university model and stressed laboratory instruction in applied science and engineering. MIT is one of three private land grant universities in the United States, the others being Cornell University and Tuskegee University. The institute has an urban campus that extends more than a mile (1.6 km) alongside the Charles River, and encompasses a number of major off-campus facilities such as the MIT Lincoln Laboratory, the Bates Center, and the Haystack Observatory, as well as affiliated laboratories such as the Broad and Whitehead Institutes. , 98 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MIT Lincoln Laboratory
The MIT Lincoln Laboratory, located in Lexington, Massachusetts, is a United States Department of Defense federally funded research and development center chartered to apply advanced technology to problems of national security. Research and development activities focus on long-term technology development as well as rapid system prototyping and demonstration. Its core competencies are in sensors, integrated sensing, signal processing for information extraction, decision-making support, and communications. These efforts are aligned within ten mission areas. The laboratory also maintains several field sites around the world. The laboratory transfers much of its advanced technology to government agencies, industry, and academia, and has launched more than 100 start-ups. History Origins At the urging of the United States Air Force, the Lincoln Laboratory was created in 1951 at the Massachusetts Institute of Technology (MIT) as part of an effort to improve the U.S. air defense syst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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