formulasearchengine - User contributions [en]

Composite laminates

2014-10-28T00:36:50Z

131.243.163.94: Changed subscripts "33" to "66" in the equation for Q^*_{66}

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Hildebrand solubility parameter

2014-07-22T01:47:45Z

131.243.47.141: /* Uses and Limitations */

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Rigid rotor

2013-08-20T18:33:17Z

131.243.163.82: /* Quantum mechanical linear rigid rotor */ R was incorrectly labelled as "half the distance between the two atoms". In fact, R is the distance between the atoms.

[[Image:EIT spectrum.jpg|right|thumb|350px|The effect of EIT on a typical absorption line. A weak probe normally experiences absorption shown in blue. A second coupling beam induces EIT and creates a "window" in the absorption region (red). This plot is a computer simulation of EIT in an InAs/GaAs quantum dot]]
'''Electromagnetically induced transparency (EIT)''' is a [[coherence (physics)|coherent]] [[optics|optical]] [[Nonlinear optics|nonlinearity]] which renders a medium [[Transparency (optics)|transparent]] over a narrow [[spectrum|spectral]] range within an [[absorption line]]. Extreme [[dispersion (optics)|dispersion]] is also created within this transparency "window" which leads to "[[slow light]]", described below. Basically it "is a quantum interference effect that permits the propagation of light through an otherwise opaque atomic medium".<ref>[Observation of coherent optical information storage in an atomic medium using halted light pulses http://www.readcube.com/articles/10.1038/35054017]</ref>

Observation of EIT involves two optical fields (highly coherent light sources, such as [[laser]]s) which are tuned to interact with three [[quantum state]]s of a material. The "probe" field is tuned near resonance between two of the states and measures the [[absorption spectrum]] of the transition. A much stronger "coupling" field is tuned near resonance at a different transition. If the states are selected properly, the presence of the coupling field will create a spectral "window" of transparency which will be detected by the probe. The coupling laser is sometimes referred to as the "control" or "pump", the latter in analogy to incoherent optical nonlinearities such as [[spectral hole burning]] or saturation.

EIT is based on the destructive interference of the transition [[probability amplitude]] between atomic states. Closely related to EIT are [[coherent population trapping]] (CPT) phenomena.

== Medium requirements ==
[[Image:EIT schemes.jpg|left|thumb|350px|EIT level schemes can be sorted into three categories; vee, ladder, and lambda.]]

There are specific restrictions on the configuration of the three states. Two of the three possible transitions between the states must be "dipole allowed", i.e. the [[transition rule|transitions can be induced]] by an oscillating electric field. The third transition must be "dipole forbidden." One of the three states is connected to the other two by the two optical fields. The three types of EIT schemes are differentiated by the energy differences between this state and the other two. The schemes are the ladder, vee, and lambda. Any real material system may contain many triplets of states which could theoretically support EIT, but there are several practical limitations on which levels can actually be used.

Also important are the dephasing rates of the individual states. In any real system at finite temperature there are processes which cause a scrambling of the phase of the quantum states. In the gas phase, this means usually collisions. In solids, dephasing is due to interaction of the electronic states with the host lattice. The dephasing of state <math>|3\rangle</math> is especially important; ideally <math>|3\rangle</math> should be a robust, metastable state.

Current EIT research uses atomic systems in dilute gasses, solid solutions, or more exotic states such as [[Bose-Einstein condensate]]. Work is also being done in semiconductor nanostructures such as [[quantum well]]s, [[quantum wire]]s and [[quantum dots]].

== Theory ==
EIT was first proposed theoretically by professor Jakob Khanin and graduate student Olga Kocharovskaya at Gorky State University (present: Nizhnij Novgorod), Russia;<ref>{{cite web|url=http://www.spaceref.com/news/viewpr.html?pid=3722 |title=Texas A&M University physicists have devised a way to stop light | SpaceRef - Your Space Reference |publisher=SpaceRef |date=2001-01-31 |accessdate=2013-01-28}}</ref> there are now several different approaches to a theoretical treatment of EIT. One approach is to extend the [[density matrix]] treatment used to derive [[Rabi oscillation]] of a two-state, single field system. In this picture the [[probability amplitude]] for the system to transfer between states can [[Interference (wave propagation)#Quantum interference|interfere destructively]], preventing absorption. In this context, "interference" refers to interference between ''quantum events'' (transitions) and not optical interference of any kind. As a concrete example, consider the lambda scheme shown above. Absorption of the probe is defined by transition from <math>|1\rangle</math> to <math>|2\rangle</math>. The fields can drive population from <math>|1\rangle</math>-<math>|2\rangle</math> directly or from <math>|1\rangle</math>-<math>|2\rangle</math>-<math>|3\rangle</math>-<math>|2\rangle</math>. The probability amplitudes for the different paths interfere destructively. If <math>|3\rangle</math> has a comparatively long lifetime, then the result will be a transparent window completely inside of the <math>|1\rangle</math>-<math>|2\rangle</math> absorption line.

Another approach is the "[[Light dressed state|dressed state]]" picture, wherein the system + coupling field [[Hamiltonian (quantum mechanics)|Hamiltonian]] is diagonalized and the effect on the probe is calculated in the new basis. In this picture EIT resembles a combination of [[Autler-Townes splitting]] and [[Fano interference]] between the dressed states. Between the doublet peaks, in the center of the transparency window, the quantum probability amplitudes for the probe to cause a transition to either state cancel.

A [[polariton]] picture is particularly important in describing stopped light schemes. Here, the [[photons]] of the probe are coherently "transformed" into "dark state polaritons" which are [[excited state|excitations]] of the medium. These excitations exist (or can be "stored") for a length of time dependent only on the dephasing rates.

== Slow light and stopped light==
[[Image:EIT dispersion.jpg|thumb|275px|right|Rapid change of index of refraction (blue) in a region of rapidly changing absorption (gray) associated with EIT. The steep and positive linear region of the refractive index in the center of the transparency window gives rise to slow light]]
It is important to realize that EIT is only one of many diverse mechanisms which can produce [[slow light]]. The [[Kramers–Kronig relation]]s dictate that a change in absorption (or gain) over a narrow spectral range must be accompanied by a change in refractive index over a similarly narrow region. This rapid and ''positive'' change in refractive index produces an extremely low [[group velocity]]. See for this the comprehensive review on this subject in.<ref>Matsko A.B., Kocharovskaya O., Rostovtsev Y., Welch G.R., Zibrov A.S., Scully M.O., "Slow, ultraslow, stored, and frozen light", ADVANCES IN ATOMIC, MOLECULAR, AND OPTICAL PHYSICS, VOL 46, 191-242, (2001)</ref> The first experimental observation of the low group velocity produced by EIT was by Boller, [[Atac Imamoglu|Imamoglu]], and Harris at Stanford University in 1991 in [[strontium]]. The current record for slow light in an EIT medium is held by Budker, Kimball, Rochester, and Yashchuk at U.C. Berkeley in 1999. Group velocities as low as 8 m/s were measured in a warm thermal [[rubidium]] vapor.<ref>D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear Magneto-optics and Reduced Group Velocity of Light in Atomic Vapor with Slow Ground State Relaxation", Phys. Rev. Lett. 83, pg. 1767-1770 (1999)</ref>

''Stopped'' light, in the context of an EIT medium, refers to the ''coherent'' transfer of photons to the quantum system and back again. In principle, this involves switching ''off'' the coupling beam in an [[adiabatic process (quantum mechanics)|adiabatic]] fashion while the probe pulse is still inside of the EIT medium. There is experimental evidence of trapped pulses in EIT medium. In <ref>Bajcsy M, Zibrov A.S, Lukin M.D., "Stationary pulses of light in an atomic medium", NATURE, '''426''', 638-641, (2003)</ref> authors created a [[stationary light pulse]] inside the atomic coherent media. In 2009 researchers from Harvard University and MIT demonstrated a few-photon optical switch for quantum optics based on the slow light ideas.<ref>Bajcsy M , Hofferberth S, Balic V, Peyronel T, Hafezi M , Zibrov A.S , Vuletic V , Lukin M.D., "All-Optical Switching Using Slow Light within a Hollow Fiber", Phys. Rev. Lett., '''102''', 20390, (2009)</ref> [[Lene Hau]] and a team from Harvard University were the first to demonstrate stopped light,<ref>{{cite web|author=Nature |url=http://www.nature.com/nature/journal/v445/n7128/abs/nature05493.html |title=Coherent control of optical information with matter wave dynamics : Abstract |publisher=Nature |date= |accessdate=2013-01-28}}</ref> and then light that could be converted to matter, then back into light once more, research with enormous potential for [[quantum encryption]] and [[quantum computing]].

==See also==
*[[Atomic coherence]]
*[[Electromagnetically Induced Grating]]

==References==
{{reflist}}

===Primary work===
* O.Kocharovskaya, Ya.I.Khanin, Sov. Phys. JETP, '''63''', p945 (1986)
* K.J. Boller, A. Imamoglu, [[S. E. Harris]], Physical Review Letters '''66''', p2593 (1991)
* Eberly, J. H., M. L. Pons, and H. R. Haq, Phys. Rev. Lett. '''72''', 56 (1994)
* D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, Physical Review Letters, '''83''', p1767 (1999)
* [[Lene Vestergaard Hau]], [[Stephen E. Harris|S.E. Harris]], [[Zachary Dutton]], Cyrus H. Behroozi, Nature v.397, p594 (1999)
* D.F. Phillips, A. Fleischhauer, A. Mair, R.L. Walsworth, M.D. Lukin, Physical Review Letters '''86''', p783 (2001)
* [[Naomi Ginsberg|Naomi S. Ginsberg]], [[Sean R. Garner]], [[Lene Vestergaard Hau]], Nature '''445''', 623 (2007)

===Review===
* [[Stephen E. Harris|Harris, Steve]] (July, 1997). [http://www.stanford.edu/group/harrisgroup/PAPERS/review.pdf Electromagnetically Induced Transparency]. ''Physics Today'', 50 (7), pp. 36–42 (PDF Format)
* [[Zachary Dutton]], [[Naomi Ginsberg|Naomi S. Ginsberg]], [[Christopher Slowe]], and [[Lene Vestergaard Hau]] (2004) [http://www.europhysicsnews.org/articles/epn/pdf/2004/02/epn04201.pdf The art of taming light: ultra-slow and stopped light]. ''Europhysics News'' Vol. 35 No. 2
* M. Fleischhauer, A. Imamoglu, and J. P. Marangos (2005), "[http://link.aps.org/abstract/RMP/v77/p633 Electromagnetically induced transparency: Optics in Coherent Media]", Reviews Modern Physics, '''77''', 633

===Сriticism===
* Evgenii B Aleksandrov and Valerii S Zapasskii Phys.-Usp. "[http://iopscience.iop.org/1063-7869/47/10/A04]" '''47''', 1033 (2004)

{{DEFAULTSORT:Electromagnetically Induced Transparency}}
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[[Category:Quantum mechanics]]
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