|
Photon Antibunching
Photon antibunching generally refers to a light field with photons more equally spaced than a coherent laser field, a signature being a measured two-time correlation suppressed below that of a coherent laser field. 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 ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sub-Poissonian
In mathematics, a super-Poissonian distribution is a probability distribution that has a larger variance than a Poisson distribution with the same mean. Conversely, a sub-Poissonian distribution has a smaller variance. An example of super-Poissonian distribution is negative binomial distribution. The Poisson distribution is a result of a process where the time (or an equivalent measure) between events has an exponential distribution, representing a memoryless process. Mathematical definition In probability theory it is common to say a distribution, ''D'', is a sub-distribution of another distribution ''E'' if ''D'' 's moment-generating function, is bounded by ''E'' 's up to a constant. In other words : E_ exp(t X)\le E_ exp(C t X) for some ''C > 0''. This implies that if X_1 and X_2 are both from a sub-E distribution, then so is X_1+X_2. A distribution is ''strictly sub-'' if ''C ≤ 1''. From this definition a distribution, ''D'', is sub-Poissonian if : E_ exp(t X)\le E_ exp(t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 if these events occur with a known constant mean rate and independently of the time since the last event. It can also be used for the number of events in other types of intervals than time, and in dimension greater than 1 (e.g., number of events in a given area or volume). The Poisson distribution is named after French mathematician Siméon Denis Poisson. It plays an important role for discrete-stable distributions. Under a Poisson distribution with the expectation of ''λ'' events in a given interval, the probability of ''k'' events in the same interval is: :\frac . For instance, consider a call center which receives an average of ''λ ='' 3 calls per minute at all times of day. If the calls are independent, receiving one does not change the probability of when the next on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black-body Radiation
Black-body radiation is the thermal radiation, 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 that depends only on the body's temperature., Chapter 13. A perfectly-insulated enclosure which is in thermal equilibrium internally contains blackbody 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 blackbody 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, blackbody radiation is still a good first approximation for the energy they emit. The term ''black body'' was introduced by Gustav Kirchhoff in 1860. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Super-Poissonian
In mathematics, a super-Poissonian distribution is a probability distribution that has a larger variance than a Poisson distribution with the same mean. Conversely, a sub-Poissonian distribution has a smaller variance. An example of super-Poissonian distribution is negative binomial distribution. The Poisson distribution is a result of a process where the time (or an equivalent measure) between events has an exponential distribution, representing a memoryless process. Mathematical definition In probability theory it is common to say a distribution, ''D'', is a sub-distribution of another distribution ''E'' if ''D'' 's moment-generating function, is bounded by ''E'' 's up to a constant. In other words : E_ exp(t X)\le E_ exp(C t X) for some ''C > 0''. This implies that if X_1 and X_2 are both from a sub-E distribution, then so is X_1+X_2. A distribution is ''strictly sub-'' if ''C ≤ 1''. From this definition a distribution, ''D'', is sub-Poissonian if : E_ exp(t X)\le E_ exp(t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hanbury Brown And Twiss Effect
In physics, the Hanbury Brown and Twiss (HBT) effect is any of a variety of correlation and anti-correlation effects in the intensity (physics), 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 appl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degree Of Coherence
In quantum optics, correlation functions are used to characterize the statistical and Coherence (physics), coherence properties – the ability of waves to interfere – of electromagnetic radiation, like optical light. Higher order coherence or ''n''-th order coherence (for any positive integer ''n''>1) extends the concept of coherence to quantum optics and coincidence experiments. It is used to differentiate between optics experiments that require a Quantum electrodynamics, quantum mechanical description from those for which classical fields suffice. Classical optical experiments like Young's interference experiment, Young's double slit experiment and Mach–Zehnder interferometer, Mach-Zehnder interferometry are characterized only by the first order coherence. The 1956 Hanbury Brown and Twiss effect, Hanbury Brown and Twiss experiment brought to light a different kind of correlation between fields, namely the correlation of intensities, which correspond to second order coheren ... [...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 |
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 The University of Rochester is a private university, private research unive ... [...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 Natural frequency, measured in terms of '' eigenfrequency'', is the rate at which an oscillatory system tends to oscillate in the absence of disturbance. A foundational example pertains to simple harmonic oscillators, such as an idealized spring ... 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 ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy–Schwarz Inequality
The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is an upper bound on the absolute value of the inner product between two vectors in an inner product space in terms of the product of the vector norms. It is considered one of the most important and widely used inequalities in mathematics. Inner products of vectors can describe finite sums (via finite-dimensional vector spaces), infinite series (via vectors in sequence spaces), and integrals (via vectors in Hilbert spaces). 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 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 ... [...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, ''signal'' and ''idler'' photons) of lower energy, in accordance with the laws of law of conservation of energy, energy conservation and law of conservation of momentum, momentum conservation. It is an important process in quantum optics, for the generation of photon entanglement, entangled photon pairs and of single photons. Description A Nonlinear optics, nonlinear crystal is used to produce pairs of photons from a photon beam. In accordance with conservations of energy and momentum, the pairs need to have combined energies and momenta equal to the energy and momentum of the original photon. Because the index of refraction changes with frequency (Dispersion (optics), dispersion), only certain triplets of frequencies will be phase ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
