A **quantum clock** is a type of atomic clock with laser cooled single ions confined together in an electromagnetic ion trap. Developed in 2010 by National Institute of Standards and Technology physicists, the clock was 37 times more precise than the then-existing international standard.^{[1]} The quantum logic clock is based on an aluminium spectroscopy ion with a logic atom.

Both the aluminium-based quantum clock and the mercury-based optical atomic clock track time by the ion vibration at an optical frequency using a UV laser, that is 100,000 times higher than the microwave frequencies used in NIST-F1 and other similar time standards around the world. Quantum clocks like this are able to be far more precise than microwave standards.

The NIST team are not able to measure clock ticks per second because the definition of a second is based on the NIST-F1 which cannot measure a more precise machine. However the aluminium ion clock's measured frequency to the current standard is 1121015393207857.4(7)Hz.^{[2]} NIST have attributed the clock's accuracy to the fact that it is insensitive to background magnetic and electric fields, and unaffected by temperature.^{[3]}

In March 2008, physicists at NIST described an experimental quantum logic clock based on individual ions of beryllium and aluminium. This clock was compared to NIST's mercury ion clock. These were the most accurate clocks that had been constructed, with neither clock gaining nor losing time at a rate that would exceed a second in over a billion years.^{[4]}

In February 2010, NIST physicists described a second, enhanced version of the quantum logic clock based on individual ions of magnesium and aluminium. Considered the world's most precise clock in 2010 with a fractional frequency inaccuracy of 8.6 × 10^{−18}, it offers more than twice the precision of the original.^{[5]}
^{[6]}
In terms of standard deviation, the quantum logic clock deviates one second every 3.68 billion (3.68 × 10^{9}) years, while the then current international standard NIST-F1 caesium fountain atomic clock uncertainty was about 3.1 × 10^{−16} expected to neither gain nor lose a second in more than 100 million (100 × 10^{6}) years.^{[7]}
^{[8]}

In 2010 an experiment placed two aluminium-ion quantum clocks close to each other, but with the second elevated 12 in (30.5 cm) compared to the first, making the gravitational time dilation effect visible in everyday lab scales.^{[9]}

The accuracy of quantum clocks has since been superseded by optical lattice clocks based on strontium-87 and ytterbium-171. An experimental optical lattice clock was described in a 2014 Nature paper.^{[10]}
In 2015 JILA evaluated the absolute frequency uncertainty of their latest strontium-87 optical lattice clock at 2.1 × 10^{−18}, which corresponds to a measurable gravitational time dilation for an elevation change of 2 cm (0.79 in) on planet Earth that according to JILA/NIST Fellow Jun Ye is "getting really close to being useful for relativistic geodesy".^{[11]}^{[12]}^{[13]}
At this frequency uncertainty, this JILA optical lattice optical clock is expected to neither gain nor lose a second in more than 15 billion (1.5 × 10^{10}) years.^{[14]}

**^**Ghose, Tia (5 February 2010). "Ultra-Precise Quantum-Logic Clock Puts Old Atomic Clock to Shame".*Wired*. Retrieved 2010-02-07.**^**"Frequency Ratio of Al+ and Hg+ Single-ion Optical Clocks; Metrology at the 17th Decimal Place" (PDF). sciencemag.org. 28 March 2008. Retrieved 2013-07-31.**^**"Quantum Clock Proves to be as Accurate as World's Most Accurate Clock". azonano.com. 7 March 2008. Retrieved 2012-11-06.**^**Swenson, Gayle (7 June 2010). "Press release: NIST 'Quantum Logic Clock' Rivals Mercury Ion as World's Most Accurate Clock". NIST.**^**NIST's Second 'Quantum Logic Clock' Based on Aluminum Ion is Now World's Most Precise Clock, NIST, 4 February 2010**^**C.W Chou; D. Hume; J.C.J. Koelemeij; D.J. Wineland & T. Rosenband (17 February 2010). "Frequency Comparison of Two High-Accuracy Al+ Optical Clocks" (PDF).*NIST*. Retrieved 9 February 2011.**^**"NIST's Second 'Quantum Logic Clock' Based on Aluminum Ion is Now World's Most Precise Clock" (Press release). National Institute of Standards and Technology. 4 February 2010. Retrieved 2012-11-04.**^**"NIST-F1 Cesium Fountain Atomic Clock: The Primary Time and Frequency Standard for the United States". NIST. August 26, 2009. Retrieved 2 May 2011.**^**"Einstein's time dilation apparent when obeying the speed limit" (Press release). Ars Technica. 24 September 2010. Retrieved 2015-04-10.**^**Bloom, B. J.; Nicholson, T. L.; Williams, J. R.; Campbell, S. L.; Bishof, M.; Zhang, X.; Zhang, W.; Bromley, S. L.; Ye, J. (22 January 2014). "An optical lattice clock with accuracy and stability at the 10−18 level".*Nature*.**506**(7486): 71–5. arXiv:1309.1137. Bibcode:2014Natur.506...71B. doi:10.1038/nature12941. PMID 24463513.**^**T.L. Nicholson; S.L. Campbell; R.B. Hutson; G.E. Marti; B.J. Bloom; R.L. McNally; W. Zhang; M.D. Barrett; M.S. Safronova; G.F. Strouse; W.L. Tew; J. Ye (21 April 2015). "Systematic evaluation of an atomic clock at 2 × 10^{−18}total uncertainty".*Nature Communications 6, Article Number:6896, 21 April 2015*.**6**: 6896. arXiv:1412.8261. Bibcode:2015NatCo...6E6896N. doi:10.1038/ncomms7896. PMC 4411304. PMID 25898253.**^**JILA Scientific Communications (21 April 2015). "About Time". Retrieved 27 June 2015.**^**Laura Ost (21 April 2015). "Getting Better All the Time: JILA Strontium Atomic Clock Sets New Record".*National Institute of Standards and Technology*. Retrieved 17 October 2015.**^**James Vincent (22 April 2015). "The most accurate clock ever built only loses one second every 15 billion years".*The Verge*. Retrieved 26 June 2015.

Aluminium (also spelled aluminum) is a chemical element with the symbol Al and atomic number 13. It is a silvery-white, soft, paramagnetic and ductile metal in the boron group. By mass, aluminium makes up about 8% of the Earth's crust; it is the third most abundant element after oxygen and silicon and the most abundant metal in the crust, though it is less common in the mantle below. The chief ore of aluminium is bauxite. Aluminium metal is so chemically reactive that native specimens are rare and limited to extreme reducing environments. Instead, it is found combined in over 270 different minerals.Aluminium is remarkable for its low density and its ability to resist corrosion through the phenomenon of passivation. Aluminium and its alloys are vital to the aerospace industry and important in transportation and building industries, such as building facades and window frames. The oxides and sulfates are the most useful compounds of aluminium.Despite its prevalence in the environment, no known form of life uses aluminium salts metabolically, but aluminium is well tolerated by plants and animals. Because of these salts' abundance, the potential for a biological role for them is of continuing interest, and studies continue.

Atomic clockAn atomic clock is a clock device that uses a hyperfine transition frequency in the microwave, or electron transition frequency in the optical, or ultraviolet region of the electromagnetic spectrum of atoms as a frequency standard for its timekeeping element. Atomic clocks are the most accurate time and frequency standards known, and are used as primary standards for international time distribution services, to control the wave frequency of television broadcasts, and in global navigation satellite systems such as GPS.

The principle of operation of an atomic clock is based on atomic physics; it measures the electromagnetic signal that electrons in atoms emit when they change energy levels. Early atomic clocks were based on masers at room temperature. Since 2004, more accurate atomic clocks first cool the atoms to near absolute zero temperature by slowing them with lasers and probing them in atomic fountains in a microwave-filled cavity. An example of this is the NIST-F1 atomic clock, one of the national primary time and frequency standards of the United States.

The accuracy of an atomic clock depends on two factors. The first factor is temperature of the sample atoms—colder atoms move much more slowly, allowing longer probe times. The second factor is the frequency and intrinsic linewidth of the electronic or hyperfine transition. Higher frequencies and narrow lines increase the precision.

National standards agencies in many countries maintain a network of atomic clocks which are intercompared and kept synchronized to an accuracy of 10−9 seconds per day (approximately 1 part in 1014). These clocks collectively define a continuous and stable time scale, the International Atomic Time (TAI). For civil time, another time scale is disseminated, Coordinated Universal Time (UTC). UTC is derived from TAI, but has added leap seconds from UT1, to account for variations in the rotation of the Earth with respect to the solar time.

Davisson–Germer experimentThe Davisson–Germer experiment was a 1923-7 experiment by Clinton Davisson and Lester Germer at Western Electric (later Bell Labs), in which electrons, scattered by the surface of a crystal of nickel metal, displayed a diffraction pattern. This confirmed the hypothesis, advanced by Louis de Broglie in 1924, of wave-particle duality, and was an experimental milestone in the creation of quantum mechanics.

Fractional quantum mechanicsIn physics, fractional quantum mechanics is a generalization of standard quantum mechanics, which naturally comes out when the Brownian-like quantum paths substitute with the Lévy-like ones in the Feynman path integral. This concept was discovered by Nick Laskin who coined the term fractional quantum mechanics.

Klein–Gordon equationThe Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation. It is second-order in space and time and manifestly Lorentz-covariant. It is a quantized version of the relativistic energy–momentum relation. Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. Its theoretical relevance is similar to that of the Dirac equation. Electromagnetic interactions can be incorporated, forming the topic of scalar electrodynamics, but because common spinless particles like the pions are unstable and also experience the strong interaction (with unknown interaction term in the Hamiltonian,) the practical utility is limited.

The equation can be put into the form of a Schrödinger equation. In this form it is expressed as two coupled differential equations, each of first order in time. The solutions have two components, reflecting the charge degree of freedom in relativity. It admits a conserved quantity, but this is not positive definite. The wave function cannot therefore be interpreted as a probability amplitude. The conserved quantity is instead interpreted as electric charge, and the norm squared of the wave function is interpreted as a charge density. The equation describes all spinless particles with positive, negative, and zero charge.

Any solution of the free Dirac equation is, component-wise, a solution of the free Klein–Gordon equation.

The equation does not form the basis of a consistent quantum relativistic one-particle theory. There is no known such theory for particles of any spin. For full reconciliation of quantum mechanics with special relativity, quantum field theory is needed, in which the Klein–Gordon equation reemerges as the equation obeyed by the components of all free quantum fields. In quantum field theory, the solutions of the free (noninteracting) versions of the original equations still play a role. They are needed to build the Hilbert space (Fock space) and to express quantum field by using complete sets (spanning sets of Hilbert space) of wave functions.

List of laser articlesThis is a list of laser topics.

Planck time

In quantum mechanics, the **Planck time** (`t`_{P}) is the unit of time in the system of natural units known as Planck units. A Planck time unit is the time required for light to travel a distance of 1 Planck length in a vacuum, which is a time interval of approximately 5.39 × 10 ^{−44} s. The unit is named after Max Planck, who was the first to propose it.

The Planck time is defined as:

where:

`ħ`= ^{h}⁄_{2π}is the reduced Planck constant (sometimes h is used instead of ħ in the definition)- G = gravitational constant
- c = speed of light in vacuum

Using the known values of the constants, the approximate equivalent value in terms of the SI unit, the second, is

where the two digits between parentheses denote the standard error of the approximated value.

QCSQCS may refer to:

Queensland Core Skills Test

Queen's Colour Squadron

Quantum Clock Synchronization

Quantum calculus**Quantum calculus**, sometimes called **calculus without limits**, is equivalent to traditional infinitesimal calculus without the notion of limits. It defines "q-calculus" and "h-calculus", where h ostensibly stands for Planck's constant while *q* stands for quantum. The two parameters are related by the formula

where is the reduced Planck constant.

Quantum chaosQuantum chaos is a branch of physics which studies how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship between quantum mechanics and classical chaos?" The correspondence principle states that classical mechanics is the classical limit of quantum mechanics, specifically in the limit as the ratio of Planck's constant to the action of the system tends to zero. If this is true, then there must be quantum mechanisms underlying classical chaos (although this may not be a fruitful way of examining classical chaos). If quantum mechanics does not demonstrate an exponential sensitivity to initial conditions, how can exponential sensitivity to initial conditions arise in classical chaos, which must be the correspondence principle limit of quantum mechanics? In seeking to address the basic question of quantum chaos, several approaches have been employed:

Development of methods for solving quantum problems where the perturbation cannot be considered small in perturbation theory and where quantum numbers are large.

Correlating statistical descriptions of eigenvalues (energy levels) with the classical behavior of the same Hamiltonian (system).

Semiclassical methods such as periodic-orbit theory connecting the classical trajectories of the dynamical system with quantum features.

Direct application of the correspondence principle.

Quantum cosmologyQuantum cosmology is the attempt in theoretical physics to develop a quantum theory of the Universe. This approach attempts to answer open questions of classical physical cosmology, particularly those related to the first phases of the universe.

The classical cosmology is based on Albert Einstein's general theory of relativity (GTR or simply GR). It describes the evolution of the universe very well, as long as you do not approach the Big Bang. It is the gravitational singularity and the Planck time where relativity theory fails to provide what must be demanded of a final theory of space and time. Therefore, a theory is needed that integrates relativity theory and quantum theory. Such an approach is attempted for instance with the loop quantum gravity, the string theory and the causal set theory.

Quantum cryptographyQuantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution which offers an information-theoretically secure solution to the key exchange problem. The advantage of quantum cryptography lies in the fact that it allows the completion of various cryptographic tasks that are proven or conjectured to be impossible using only classical (i.e. non-quantum) communication. For example, it is impossible to copy data encoded in a quantum state. If one attempts to read the encoded data, the quantum state will be changed (no-cloning theorem). This could be used to detect eavesdropping in quantum key distribution.

Quantum geometryIn theoretical physics, quantum geometry is the set of mathematical concepts generalizing the concepts of geometry whose understanding is necessary to describe the physical phenomena at distance scales comparable to Planck length. At these distances, quantum mechanics has a profound effect on physical phenomena.

Quantum informationIn physics and computer science, quantum information is the information of the state of a quantum system; it is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information, like classical information, can be processed using digital computers, transmitted from one location to another, manipulated with algorithms, and analyzed with the computer science mathematics. While the fundamental unit of classical information is the bit, the most basic unit of quantum information is the qubit.

Quantum probabilityQuantum probability was developed in the 1980s as a noncommutative analog of the Kolmogorovian theory of stochastic processes. One of its aims is to clarify the mathematical foundations of quantum theory and its statistical interpretation.A significant recent application to physics is the dynamical solution of the quantum measurement problem, by giving constructive models of quantum observation processes which resolve many famous paradoxes of quantum mechanics.

Some recent advances are based on quantum filtering and feedback control theory as applications of quantum stochastic calculus.

Quantum technologyQuantum technology is an emerging field of physics and engineering, which is about creating practical applications -- such as quantum computing, quantum sensors, quantum cryptography, quantum simulation, quantum metrology and quantum imaging -- based on properties of quantum mechanics, especially quantum entanglement, quantum superposition and quantum tunnelling.

Rydberg formulaIn atomic physics, the Rydberg formula calculates the wavelengths of a spectral line in many chemical elements. The formula was primarily presented as a generalization of the Balmer series for all atomic electron transitions of hydrogen. It was first empirically stated in 1888 by the Swedish physicist Johannes Rydberg, then theoretically by Niels Bohr in 1913, who used a primitive form of quantum mechanics. The formula directly generalizes the equations used to calculate the wavelengths of the hydrogen spectral series.

Scattering theoryIn mathematics and physics, scattering theory is a framework for studying and understanding the scattering of waves and particles. Wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunlight scattered by rain drops to form a rainbow. Scattering also includes the interaction of billiard balls on a table, the Rutherford scattering (or angle change) of alpha particles by gold nuclei, the Bragg scattering (or diffraction) of electrons and X-rays by a cluster of atoms, and the inelastic scattering of a fission fragment as it traverses a thin foil. More precisely, scattering consists of the study of how solutions of partial differential equations, propagating freely "in the distant past", come together and interact with one another or with a boundary condition, and then propagate away "to the distant future". The direct scattering problem is the problem of determining the distribution of scattered radiation/particle flux basing on the characteristics of the scatterer. The inverse scattering problem is the problem of determining the characteristics of an object (e.g., its shape, internal constitution) from measurement data of radiation or particles scattered from the object.

Since its early statement for radiolocation, the problem has found vast number of applications, such as echolocation, geophysical survey, nondestructive testing, medical imaging and quantum field theory, to name just a few.

Wave interferenceIn physics, interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive interference result from the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves. The resulting images or graphs are called interferograms.

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