Editing Electromagnetically induced transparency

{{Short description|Intereference effect in quantum optics}}
[[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]] within a narrow [[spectrum|spectral]] range around an [[absorption line]].  Extreme [[dispersion (optics)|dispersion]] is also created within this transparency "window" which leads to "[[slow light]]", described below.  It is in essence a quantum interference effect that permits the propagation of light through an otherwise opaque atomic medium.<ref>{{cite journal |doi=10.1038/35054017|pmid=11206540|title=Observation of coherent optical information storage in an atomic medium using halted light pulses|journal=Nature|volume=409|issue=6819|pages=490–493|year=2001|last1=Liu|first1=Chien|last2=Dutton|first2=Zachary|last3=Behroozi|first3=Cyrus H.|last4=Hau|first4=Lene Vestergaard|bibcode=2001Natur.409..490L|s2cid=1894748|url=http://nrs.harvard.edu/urn-3:HUL.InstRepos:3636968}}</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.

The quantum interference in EIT can be exploited to [[laser cooling|laser cool]] atomic particles, even down to the quantum mechanical ground state of motion.<ref>
{{cite journal
 | last = Morigi | first = Giovanna | author-link = Giovanna Morigi
 | year = 2000
 | title = Ground State Laser Cooling Using Electromagnetically Induced Transparency
 | journal = Physical Review Letters
 | volume = 85 | issue = 21 | pages = 4458–4461
 | doi = 10.1103/PhysRevLett.85.4458| pmid = 11082570
 | arxiv = quant-ph/0005009 |bibcode = 2000PhRvL..85.4458M
 | s2cid = 12580278
 }}</ref>  This was used in 2015 to directly image individual atoms trapped in an [[optical lattice]].<ref>{{Cite journal|title = Single-atom imaging of fermions in a quantum-gas microscope|journal = Nature Physics|pages = 738–742|volume = 11|issue = 9|doi = 10.1038/nphys3403|first1 = Elmar|last1 = Haller|first2 = James|last2 = Hudson|first3 = Andrew|last3 = Kelly|first4 = Dylan A.|last4 = Cotta|first5 = Bruno|last5 = Peaudecerf|first6 = Graham D.|last6 = Bruce|first7 = Stefan|last7 = Kuhr|arxiv = 1503.02005 |bibcode = 2015NatPh..11..738H |year = 2015|s2cid = 51991496}}</ref>

== 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 non-zero 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.

Currently {{When|date=December 2018}} EIT research uses atomic systems in dilute gases, solid solutions, or more exotic states such as [[Bose–Einstein condensate]].  EIT has been demonstrated in electromechanical<ref>{{Cite journal |doi = 10.1038/nature09898|pmid = 21390127|title = Circuit cavity electromechanics in the strong-coupling regime|journal = Nature|volume = 471|issue = 7337|pages = 204–208|year = 2011|last1 = Teufel|first1 = J. D.|last2 = Li|first2 = Dale|last3 = Allman|first3 = M. S.|last4 = Cicak|first4 = K.|last5 = Sirois|first5 = A. J.|last6 = Whittaker|first6 = J. D.|last7 = Simmonds|first7 = R. W.|bibcode = 2011Natur.471..204T|arxiv = 1011.3067|s2cid = 4418446}}</ref> and optomechanical<ref>{{Cite journal |doi = 10.1038/nature09933|pmid = 21412237|title = Electromagnetically induced transparency and slow light with optomechanics|journal = Nature|volume = 472|issue = 7341|pages = 69–73|year = 2011|last1 = Safavi-Naeini|first1 = A. H.|last2 = Alegre|first2 = T. P. Mayer|last3 = Chan|first3 = J.|last4 = Eichenfield|first4 = M.|last5 = Winger|first5 = M.|last6 = Lin|first6 = Q.|last7 = Hill|first7 = J. T.|last8 = Chang|first8 = D. E.|last9 = Painter|first9 = O.|bibcode = 2011Natur.472...69S|arxiv = 1012.1934|s2cid = 4428942}}</ref> systems, where it is known as [[optomechanically induced transparency]]. Work is also being done in semiconductor nanostructures such as [[quantum well]]s,<ref name="SerapigliaPaspalakis2000">{{cite journal|last1=Serapiglia|first1=G. B.|last2=Paspalakis|first2=E.|last3=Sirtori|first3=C.|last4=Vodopyanov|first4=K. L.|last5=Phillips|first5=C. C.|title=Laser-Induced Quantum Coherence in a Semiconductor Quantum Well|journal=Physical Review Letters|volume=84|issue=5|year=2000|pages=1019–1022|issn=0031-9007|doi=10.1103/PhysRevLett.84.1019|pmid=11017430|bibcode=2000PhRvL..84.1019S }}</ref> [[quantum wire]]s and [[quantum dot]]s.<ref name="XuSun2008">{{cite journal|last1=Xu|first1=Xiaodong|last2=Sun|first2=Bo|last3=Berman|first3=Paul R.|last4=Steel|first4=Duncan G.|last5=Bracker|first5=Allan S.|last6=Gammon|first6=Dan|last7=Sham|first7=L. J.|title=Coherent population trapping of an electron spin in a single negatively charged quantum dot|journal=Nature Physics|volume=4|issue=9|year=2008|pages=692–695|issn=1745-2473|doi=10.1038/nphys1054|arxiv=0805.2074 |bibcode=2008NatPh...4..692X |s2cid=8098743|doi-access=free}}</ref><ref name="BrunnerGerardot2009">{{cite journal|last1=Brunner|first1=Daniel|last2=Gerardot|first2=Brian D.|last3=Dalgarno|first3=Paul A.|last4=Wüst|first4=Gunter|last5=Karrai|first5=Khaled|last6=Stoltz|first6=Nick G.|last7=Petroff|first7=Pierre M.|last8=Warburton|first8=Richard J.|title=A Coherent Single-Hole Spin in a Semiconductor|journal=Science|volume=325|issue=5936|year=2009|pages=70–72|issn=0036-8075|doi=10.1126/science.1173684|pmid=19574387|bibcode=2009Sci...325...70B |s2cid=31505564}}</ref>

== Theory ==
EIT was first proposed theoretically by professor Jakob Khanin and graduate student [[Olga Kocharovskaya]] at [[N. I. Lobachevsky State University of Nizhny Novgorod|Gorky State University]] (renamed to Nizhny Novgorod in 1990), 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 &#124; SpaceRef – Your Space Reference |publisher=SpaceRef |date=2001-01-31 |access-date=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 drive [[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 specific 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 <u>positive</u> linear region of the refractive index in the center of the transparency window gives rise to slow light]]
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]].<ref>{{Cite journal |doi = 10.1364/OPN.13.6.000044|title = Slow, Ultraslow, Stored, and Frozen Light|journal = Optics and Photonics News|volume = 13|issue = 6|pages = 44|year = 2002|last1 = Rostovtsev|first1 = Yuri|last2 = Kocharovskaya|first2 = Olga|last3 = Welch|first3 = George R.|last4 = Scully|first4 = Marlan O.}}</ref> The first experimental observation of the low group velocity produced by EIT was by Boller, [[Ataç İmamoğlu|İmamoğlu]], and Harris at Stanford University in 1991 in [[strontium]]. In 1999 [[Lene Hau]] reported slowing light in a medium of ultracold [[sodium]] atoms,<ref>{{cite web|url=http://www.physicscentral.com/explore/people/hau.cfm |title=Lene Hau |publisher=Physicscentral.com |access-date=2013-01-28}}</ref> achieving this by using quantum interference effects responsible for electromagnetically induced transparency (EIT).<ref>{{Cite web |url=http://uw.physics.wisc.edu/~timbie/P325/Cohen_stopping_light.pdf |title=Stopping Light |author=Alex Cohen |date=2006 |access-date=2013-01-28 |archive-url=https://web.archive.org/web/20100611004540/http://uw.physics.wisc.edu/~timbie/P325/Cohen_stopping_light.pdf |archive-date=2010-06-11 |url-status=dead}}</ref> Her group performed copious research regarding EIT with [[Stephen E. Harris]]. "Using detailed numerical simulations, and analytical theory, we study properties of micro-cavities which incorporate materials that exhibit Electro-magnetically Induced Transparency (EIT) or Ultra Slow Light (USL). We find that such systems, while being miniature in size (order wavelength), and integrable, can have some outstanding properties. In particular, they could have lifetimes orders of magnitude longer than other existing systems, and could exhibit non-linear all-optical switching at single photon power levels. Potential applications include miniature atomic clocks, and all-optical quantum information processing."<ref>{{cite book |doi=10.1117/12.562304|chapter=Electromagnetically induced transparency in microcavities|title=Photonics for Space Environments IX|volume=5554|pages=174|year=2004|last1=Soljacic|first1=Marin |last2=Lidorikis|first2=Elefterios |last3=Joannopoulos|first3=John D.|last4=Hau|first4=Lene V.|editor1-first=Edward W.|editor1-last=Taylor|series=Proceedings of SPIE|s2cid=137523967}}</ref>  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&nbsp;m/s were measured in a warm thermal [[rubidium]] vapor.<ref>{{Cite journal | doi=10.1103/PhysRevLett.83.1767|title = Nonlinear Magneto-optics and Reduced Group Velocity of Light in Atomic Vapor with Slow Ground State Relaxation| journal=Physical Review Letters| volume=83| issue=9| pages=1767–1770|year = 1999|last1 = Budker|first1 = D.| last2=Kimball| first2=D. F.| last3=Rochester| first3=S. M.| last4=Yashchuk| first4=V. V.| bibcode=1999PhRvL..83.1767B}}</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. Authors created a [[stationary light pulse]] inside the atomic coherent media.<ref>{{Cite journal |doi = 10.1038/nature02176|pmid = 14668857|title = Stationary pulses of light in an atomic medium|journal = Nature|volume = 426|issue = 6967|pages = 638–641|year = 2003|last1 = Bajcsy|first1 = M.|last2 = Zibrov|first2 = A. S.|last3 = Lukin|first3 = M. D.|bibcode = 2003Natur.426..638B|arxiv = quant-ph/0311092|s2cid = 4320280}}</ref> In 2009 researchers from Harvard University and MIT demonstrated a few-photon optical switch for quantum optics based on the slow light ideas.<ref>{{Cite journal | doi=10.1103/PhysRevLett.102.203902| pmid=19519028|title = Efficient All-Optical Switching Using Slow Light within a Hollow Fiber| journal=Physical Review Letters| volume=102| issue=20| pages=203902|year = 2009|last1 = Bajcsy|first1 = M.| last2=Hofferberth| first2=S.| last3=Balic| first3=V.| last4=Peyronel| first4=T.| last5=Hafezi| first5=M.| last6=Zibrov| first6=A. S.| last7=Vuletic| first7=V.| last8=Lukin| first8=M. D.| bibcode=2009PhRvL.102t3902B| arxiv=0901.0336| s2cid=5504022}}</ref> [[Lene Hau]] and a team from Harvard University were the first to  demonstrate stopped light.<ref>{{cite journal |doi=10.1038/nature05493 |pmid=17287804|title=Coherent control of optical information with matter wave dynamics|journal=Nature|volume=445|issue=7128|pages=623–626|year=2007|last1=Ginsberg|first1=Naomi S.|last2=Garner|first2=Sean R.|last3=Hau|first3=Lene Vestergaard|s2cid=4324343|url=http://nrs.harvard.edu/urn-3:HUL.InstRepos:3636963}}</ref>

== EIT cooling ==

[[Image:Three Level Atom.png|right|thumb|350px|Three level lambda structure that is used for EIT cooling, with the [[Rabi frequency|Rabi frequencies]] <math>\displaystyle \Omega_g, \Omega_m</math> and detunings <math>\Delta_g, \Delta_m</math> of the cooling and coupling laser, respectively.]]

EIT has been used to [[laser cooling|laser cool]] long strings of atoms to their motional ground state in an [[ion trap]].<ref>{{cite journal | doi=10.1103/PhysRevA.93.053401 | last1=Lechner |first1=Regina |last2=Maier| first2=Christine | last3=Hempell | first3=Cornelius | last4=Jurcevic | first4=Petar| last5=Lanyon | first5=Ben| last6=Monz | first6=Thomas| last7=Brownnutt | first7=Michael| last8=Blatt | first8=Rainer| last9=Roos | first9=Christian | title=Electromagnetically-induced-transparency ground-state cooling of long ion strings |journal=Physical Review A |date=2016 |volume=93 |issue=5 | page=053401 | arxiv=1603.05568 | bibcode=2016PhRvA..93e3401L | url=https://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.053401| hdl=10722/248563 | s2cid=227665214 | hdl-access=free }}</ref> To illustrate the cooling technique, consider a three level atom as shown with a ground state <math>|g\rangle</math>, an excited state <math>|e\rangle</math>, and a stable or metastable state <math>|m\rangle</math> that lies in between them. The excited state <math>|e\rangle</math> is dipole coupled to <math>|m\rangle</math> and <math>|g\rangle</math>. An intense "coupling" laser drives the <math>|m \rangle \rightarrow |e\rangle</math> transition at detuning <math>\Delta_m</math> above resonance. Due to the quantum interference of transition amplitudes, a weaker "cooling" laser driving the <math>|g \rangle \rightarrow |e\rangle</math> transition at detuning <math>\Delta_g</math> above resonance sees a [[Fano interference|Fano-like]] feature on the absorption profile. EIT cooling is realized when <math>\Delta_g = \Delta_m</math>, such that the carrier transition <math>|g,n \rangle \rightarrow |e, n\rangle</math> lies on the dark resonance of the [[Fano interference|Fano-like]] feature, where <math>n</math> is used to label the [[Quantum harmonic oscillator|quantized motional state]] of the atom. The [[Rabi frequency]] <math>\Omega_m</math> of the coupling laser is chosen such that the <math>|g,n \rangle \rightarrow |e, n-1\rangle</math> "red" sideband lies on the narrow maximum of the [[Fano interference|Fano-like]] feature. Conversely the <math>|g,n \rangle \rightarrow |e, n+1\rangle</math> "blue" sideband lies in a region of low excitation probability, as shown in the figure below. Due to the large ratio of the excitation probabilities, the cooling limit is lowered in comparison to [[Doppler cooling|doppler]] or [[Resolved sideband cooling|sideband]] cooling (assuming the same cooling rate).<ref>{{cite journal | doi=10.1103/PhysRevLett.85.4458 | last1=Morigi |first1=Giovanna | author1-link = Giovanna Morigi |last2=Eschner |first2=Jurgen |last3=Christoph |first3=Keitel |title=Ground State Laser Cooling Using Electromagnetically Induced Transparency |journal=Physical Review Letters |date=2000 |volume=85 |issue=21 | pages=4458–4461 | pmid=11082570 | url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.85.4458|arxiv=quant-ph/0005009 | bibcode=2000PhRvL..85.4458M | s2cid=12580278 }}</ref>

[[Image:Absorption of Cooling Laser versus Detuning of Cooling laser for EIT cooling.png|right|thumb|350px|Absorption profile seen by the cooling laser as a function of detuning <math>\Delta_g</math>.  The [[Rabi frequency]] <math>\Omega_m</math> is chosen so that the red sideband (red dashed line) lies on the narrow peak of the Fano-like feature and the blue sideband (blue dashed line) lies in a region of low probability. The carrier (black dashed line) lies on the dark resonance where the detunings are equal, ''i.e.'' <math>\Delta_g = \Delta_m</math>, such that absorption is zero.]]

==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, [[Ataç İmamoğlu|A. İmamoğlu]], [[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] {{Webarchive|url=https://web.archive.org/web/20120716183257/http://www.stanford.edu/group/harrisgroup/PAPERS/review.pdf |date=2012-07-16 }}. ''Physics Today'', 50 (7), pp.&nbsp;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, [[Ataç İmamoğlu|A. İmamoğlu]], 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

{{DEFAULTSORT:Electromagnetically Induced Transparency}}
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