Localized molecular orbitals - Revision history

en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9985)

2014-03-14T07:52:26Z

WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9985)

← Older revision		Revision as of 09:52, 14 March 2014
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	~~A '''magnetic trap'''~~ is an apparatus which uses a magnetic field gradient to trap neutral particles with [[magnetic moment]]s. Although such traps have been employed for many purposes in physics research, they are best known as the ~~last stage in cooling atoms to achieve [[Bose-Einstein condensation]]. The magnetic trap (as a way of trapping very cold atoms) was first proposed by [[David E. Pritchard]].~~		Wilber Berryhill is the title his parents gave him and he totally digs that name. What me and my family members adore is to climb but I'm best psychic [[http://www.aseandate.com/index.php?m=member_profile&p=profile&id=13352970 www.aseandate.com]] considering on starting some thing new. For many years he's been living in Mississippi and he doesn't plan on changing it. My day job is an information officer but I've already applied for another 1.<br><br>Look at my page :: email [http://mybrandcp.com/xe/board_XmDx25/107997 best psychic] readings - [http://www.familysurvivalgroup.com/easy-methods-planting-looking-backyard/ www.familysurvivalgroup.com] -

	~~== Operating principle ==~~

	~~Many atoms have a magnetic moment; their energy shifts in a [[magnetic field]] according to the formula~~

	~~:<math>\Delta E = - \vec{\mu} \cdot \vec{B}</math>.~~

	~~According to the principles of [[quantum mechanics]] the magnetic moment of an atom will be [[Quantization (physics)\|quantized]];~~ that is, it will take on one of certain discrete values. If the atom is placed in a strong magnetic field, its magnetic moment will be aligned with the field. If a number of atoms are placed in the same field, they will be distributed over the various allowed values of magnetic quantum number for that atom.

	If a magnetic field gradient is superimposed on the uniform field, those atoms whose magnetic moments are aligned with the field will have lower energies in a higher field. Like a ball rolling down a hill, these atoms will tend to occupy locations with higher fields and are known as "high-field-seeking" atoms. ~~Conversely, those atoms with magnetic moments aligned opposite the field will have higher energies in a higher field, tend to occupy locations with lower fields,~~ and ~~are called "low-field-seeking" atoms.~~

	It is ~~impossible~~ to produce a local maximum of the magnetic-field magnitude in free space; however, a local minimum may be produced. This minimum can trap atoms which are low-field-seeking if they do not have enough kinetic energy to escape the minimum. Typically, magnetic traps have relatively shallow field minima and are only able to trap atoms whose kinetic energies correspond to temperatures of a fraction of a [[~~kelvin]]~~. ~~The field minima required for magnetic trapping can be produced in a variety of ways~~. ~~These include permanent magnet traps, Ioffe configuration traps, QUIC traps and others~~.

	==~~Microchip atom trap~~==

	~~[[Image:MicroChipAtomicTrap00.jpg\|100px\|right\|thumb\|Microchip atomic trap developed in [[Institute for Laser Science\|ILS]] in 2005]]~~
	~~The minimum magnitude of the magnetic field can be realized with the "atom microchip".<ref name="nakagawa2006">{{cite journal~~
	~~\| author= M~~.~~Horikoshi~~
	~~\| coauthors= K~~.~~Nakagawa~~
	~~\| title= Atom chip based fast production of Bose–Einstein condensate~~
	~~\| year=2006~~
	~~\| pages=363–366~~
	~~\| volume=82~~
	~~\| issue=3~~
	~~\| journal=[[Applied Physics B~~]]
	~~\| doi= 10.1007/s00340-005-2083-z~~
	~~}}</ref>~~
	~~One of the first microchip atomic traps is shown~~ on ~~the right~~. ~~The Z-shaped conductor (actually the golden Z-shaped strip painted on the Si surface) is placed into the uniform magnetic field (the field~~'s ~~source is not shown~~ in ~~the figure)~~. Only atoms with positive spin-field energy were trapped. To prevent the mixing of spin states, the external magnetic field was inclined in the plane of the chip, providing the adiabatic rotation of the spin at the movement of the atom. In the first approximation, magnitude (but ~~not orientation) of the magnetic field is responsible~~ for ~~effective energy of the trapped atom~~. The chip shown is 2 cm x 2 cm; this size was chosen for ease in manufacture. In principle, the size of such microchip traps can be drastically reduced. An array of such traps can be manufactured with conventional [~~[Lithography\|lithographic]] methods; such an array is considered a prototype of a q-bit [[Computer data storage\|memory cell]] for the [[quantum computer]]. Ways of transferring atoms and~~/~~or q-bits between traps are under development; the adiabatic optical (with off-resonant frequencies) and~~/~~or the electrical control (with additional electrodes) is assumed~~.

	~~== Applications in Bose-Einstein condensation ==~~

	[[Bose-Einstein condensation]] (BEC) requires conditions of very high density and very low temperature in a gas of atoms. [[Laser cooling]] in a [[magneto-optical trap]] (MOT) is typically used to cool atoms down to the microkelvin range. However, laser cooling is limited by the momentum recoils an atom receives from single photons. Achieving BEC requires cooling the atoms beyond the limits of laser cooling, which means the lasers used in the MOT must be turned off and a new method of trapping devised. Magnetic traps have been used to hold very cold atoms, while [[evaporative cooling]] has reduced the temperature of the atoms enough to reach BEC.

	~~== References ==~~
	~~{{reflist}}~~

	~~==Sources==~~
	*{{cite journal \| doi = 10.1103/PhysRevLett.51.1336 \| title = Cooling Neutral Atoms in a Magnetic Trap for Precision Spectroscopy \| year = 1983 \| last1 = Pritchard \| first1 = David E. \| journal = Physical Review Letters \| volume = 51 \| issue = 15 \| pages = 1336 }}
	*{{cite journal \| doi = 10.1126/~~science.269.5221.198 \| title = Observation of Bose~~-Einstein Condensation in a Dilute Atomic Vapor \| year = 1995 \| last1 = Anderson \| first1 = M. H. \| last2 = Ensher \| first2 = J. R. \| last3 = Matthews \| first3 = M. R. \| last4 = Wieman \| first4 = C. E. \| last5 = Cornell \| first5 = E. A. \| journal = Science \| volume = 269 \| issue = 5221 \| pages = 198–201 \| pmid = 17789847 }}

	~~==External links==~~
	*[http://www.~~uibk~~.~~ac.at~~/~~exphys~~/~~ultracold/atomtraps~~.~~html Research groups working with atom traps]~~

	~~{{DEFAULTSORT:Magnetic Trap (Atoms)}}~~
	~~[[Category:Atomic physics]~~]

en>Susilehtola: /* Pipek-Mezey */

2013-10-20T19:04:38Z

Pipek-Mezey

← Older revision		Revision as of 21:04, 20 October 2013
Line 1:		Line 1:
	~~The author~~'s ~~title~~ is ~~Christy~~. ~~For~~ a ~~while I've been~~ in ~~Mississippi but now I'm considering other choices~~. ~~Invoicing~~ is ~~my occupation~~. ~~Doing ballet~~ is ~~some thing she would never give up~~.<br><br>~~My blog: phone psychic~~ [[http://www.~~sirudang~~.~~com~~/~~siroo_Notice~~/~~2110 visit the following web site~~]]		A '''magnetic trap''' is an apparatus which uses a magnetic field gradient to trap neutral particles with [[magnetic moment]]s. Although such traps have been employed for many purposes in physics research, they are best known as the last stage in cooling atoms to achieve [[Bose-Einstein condensation]]. The magnetic trap (as a way of trapping very cold atoms) was first proposed by [[David E. Pritchard]].

			== Operating principle ==

			Many atoms have a magnetic moment; their energy shifts in a [[magnetic field]] according to the formula

			:<math>\Delta E = - \vec{\mu} \cdot \vec{B}</math>.

			According to the principles of [[quantum mechanics]] the magnetic moment of an atom will be [[Quantization (physics)\|quantized]]; that is, it will take on one of certain discrete values. If the atom is placed in a strong magnetic field, its magnetic moment will be aligned with the field. If a number of atoms are placed in the same field, they will be distributed over the various allowed values of magnetic quantum number for that atom.

			If a magnetic field gradient is superimposed on the uniform field, those atoms whose magnetic moments are aligned with the field will have lower energies in a higher field. Like a ball rolling down a hill, these atoms will tend to occupy locations with higher fields and are known as "high-field-seeking" atoms. Conversely, those atoms with magnetic moments aligned opposite the field will have higher energies in a higher field, tend to occupy locations with lower fields, and are called "low-field-seeking" atoms.

			It is impossible to produce a local maximum of the magnetic-field magnitude in free space; however, a local minimum may be produced. This minimum can trap atoms which are low-field-seeking if they do not have enough kinetic energy to escape the minimum. Typically, magnetic traps have relatively shallow field minima and are only able to trap atoms whose kinetic energies correspond to temperatures of a fraction of a [[kelvin]]. The field minima required for magnetic trapping can be produced in a variety of ways. These include permanent magnet traps, Ioffe configuration traps, QUIC traps and others.

			==Microchip atom trap==

			[[Image:MicroChipAtomicTrap00.jpg\|100px\|right\|thumb\|Microchip atomic trap developed in [[Institute for Laser Science\|ILS]] in 2005]]
			The minimum magnitude of the magnetic field can be realized with the "atom microchip".<ref name="nakagawa2006">{{cite journal
			\| author= M.Horikoshi
			\| coauthors= K.Nakagawa
			\| title= Atom chip based fast production of Bose–Einstein condensate
			\| year=2006
			\| pages=363–366
			\| volume=82
			\| issue=3
			\| journal=[[Applied Physics B]]
			\| doi= 10.1007/s00340-005-2083-z
			}}</ref>
			One of the first microchip atomic traps is shown on the right. The Z-shaped conductor (actually the golden Z-shaped strip painted on the Si surface) is placed into the uniform magnetic field (the field's source is not shown in the figure). Only atoms with positive spin-field energy were trapped. To prevent the mixing of spin states, the external magnetic field was inclined in the plane of the chip, providing the adiabatic rotation of the spin at the movement of the atom. In the first approximation, magnitude (but not orientation) of the magnetic field is responsible for effective energy of the trapped atom. The chip shown is 2 cm x 2 cm; this size was chosen for ease in manufacture. In principle, the size of such microchip traps can be drastically reduced. An array of such traps can be manufactured with conventional [[Lithography\|lithographic]] methods; such an array is considered a prototype of a q-bit [[Computer data storage\|memory cell]] for the [[quantum computer]]. Ways of transferring atoms and/or q-bits between traps are under development; the adiabatic optical (with off-resonant frequencies) and/or the electrical control (with additional electrodes) is assumed.

			== Applications in Bose-Einstein condensation ==

			[[Bose-Einstein condensation]] (BEC) requires conditions of very high density and very low temperature in a gas of atoms. [[Laser cooling]] in a [[magneto-optical trap]] (MOT) is typically used to cool atoms down to the microkelvin range. However, laser cooling is limited by the momentum recoils an atom receives from single photons. Achieving BEC requires cooling the atoms beyond the limits of laser cooling, which means the lasers used in the MOT must be turned off and a new method of trapping devised. Magnetic traps have been used to hold very cold atoms, while [[evaporative cooling]] has reduced the temperature of the atoms enough to reach BEC.

			== References ==
			{{reflist}}

			==Sources==
			*{{cite journal \| doi = 10.1103/PhysRevLett.51.1336 \| title = Cooling Neutral Atoms in a Magnetic Trap for Precision Spectroscopy \| year = 1983 \| last1 = Pritchard \| first1 = David E. \| journal = Physical Review Letters \| volume = 51 \| issue = 15 \| pages = 1336 }}
			*{{cite journal \| doi = 10.1126/science.269.5221.198 \| title = Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor \| year = 1995 \| last1 = Anderson \| first1 = M. H. \| last2 = Ensher \| first2 = J. R. \| last3 = Matthews \| first3 = M. R. \| last4 = Wieman \| first4 = C. E. \| last5 = Cornell \| first5 = E. A. \| journal = Science \| volume = 269 \| issue = 5221 \| pages = 198–201 \| pmid = 17789847 }}

			==External links==
			*[http://www.uibk.ac.at/exphys/ultracold/atomtraps.html Research groups working with atom traps]

			{{DEFAULTSORT:Magnetic Trap (Atoms)}}
			[[Category:Atomic physics]]

en>Sirjasonr: /* Edmiston-Ruedenberg */

2012-08-10T03:49:58Z

Edmiston-Ruedenberg

New page

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