electromagnetically induced transparency

Image:EIT schemes.jpg

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 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 $|3\backslash rangle$ is especially important; ideally $|3\backslash rangle$ 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{{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}} and optomechanical{{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}} systems, where it is known as optomechanically induced transparency. Work is also being done in semiconductor nanostructures such as quantum wells,{{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 }} quantum wires and quantum dots.{{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}}{{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}}

EIT was first proposed theoretically by professor Jakob Khanin and graduate student Olga Kocharovskaya at Gorky State University (renamed to Nizhny Novgorod in 1990), Russia;{{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 |access-date=2013-01-28}} 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 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 $|1\backslash rangle$ to $|2\backslash rangle$. The fields can drive population from $|1\backslash rangle$-$|2\backslash rangle$ directly or from $|1\backslash rangle$-$|2\backslash rangle$-$|3\backslash rangle$-$|2\backslash rangle$. The probability amplitudes for the different paths interfere destructively. If $|3\backslash rangle$ has a comparatively long lifetime, then the result will be a transparent window completely inside of the $|1\backslash rangle$-$|2\backslash rangle$ absorption line.

Another approach is the "dressed state" picture, wherein the system + coupling field 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 excitations of the medium. These excitations exist (or can be "stored") for a length of time dependent only on the dephasing rates.

Image:EIT dispersion.jpg

EIT is only one of many diverse mechanisms which can produce slow light. The Kramers–Kronig relations 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.{{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.}} The first experimental observation of the low group velocity produced by EIT was by Boller, İmamoğlu, and Harris at Stanford University in 1991 in strontium. In 1999 Lene Hau reported slowing light in a medium of ultracold sodium atoms,{{cite web|url=http://www.physicscentral.com/explore/people/hau.cfm |title=Lene Hau |publisher=Physicscentral.com |access-date=2013-01-28}} achieving this by using quantum interference effects responsible for electromagnetically induced transparency (EIT).{{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}} 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."{{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}} 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.{{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}}

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 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.{{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}} In 2009 researchers from Harvard University and MIT demonstrated a few-photon optical switch for quantum optics based on the slow light ideas.{{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}} Lene Hau and a team from Harvard University were the first to demonstrate stopped light.{{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}}

Image:Three Level Atom.png $\backslash displaystyle\; \backslash Omega\_g,\; \backslash Omega\_m$ and detunings $\backslash Delta\_g,\; \backslash Delta\_m$ of the cooling and coupling laser, respectively.]]

EIT has been used to laser cool long strings of atoms to their motional ground state in an ion trap.{{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 }} To illustrate the cooling technique, consider a three level atom as shown with a ground state $|g\backslash rangle$, an excited state $|e\backslash rangle$, and a stable or metastable state $|m\backslash rangle$ that lies in between them. The excited state $|e\backslash rangle$ is dipole coupled to $|m\backslash rangle$ and $|g\backslash rangle$. An intense "coupling" laser drives the $|m\; \backslash rangle\; \backslash rightarrow\; |e\backslash rangle$ transition at detuning $\backslash Delta\_m$ above resonance. Due to the quantum interference of transition amplitudes, a weaker "cooling" laser driving the $|g\; \backslash rangle\; \backslash rightarrow\; |e\backslash rangle$ transition at detuning $\backslash Delta\_g$ above resonance sees a Fano-like feature on the absorption profile. EIT cooling is realized when $\backslash Delta\_g\; =\; \backslash Delta\_m$, such that the carrier transition $|g,n\; \backslash rangle\; \backslash rightarrow\; |e,\; n\backslash rangle$ lies on the dark resonance of the Fano-like feature, where $n$ is used to label the quantized motional state of the atom. The Rabi frequency $\backslash Omega\_m$ of the coupling laser is chosen such that the $|g,n\; \backslash rangle\; \backslash rightarrow\; |e,\; n-1\backslash rangle$ "red" sideband lies on the narrow maximum of the Fano-like feature. Conversely the $|g,n\; \backslash rangle\; \backslash rightarrow\; |e,\; n+1\backslash rangle$ "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 or sideband cooling (assuming the same cooling rate).{{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 }}

Image:Absorption of Cooling Laser versus Detuning of Cooling laser for EIT cooling.png $\backslash Omega\_m$ 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. $\backslash Delta\_g\; =\; \backslash Delta\_m$, such that absorption is zero.]]

• Atomic coherence
• Electromagnetically Induced Grating

{{Reflist}}

• O.Kocharovskaya, Ya.I.Khanin, Sov. Phys. JETP, 63, p945 (1986)
• K.J. Boller, 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, 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 S. Ginsberg, Sean R. Garner, Lene Vestergaard Hau, Nature 445, 623 (2007)

• 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. 36–42 (PDF Format)
• Zachary Dutton, 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. 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

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