Electromagnetically induced transparency (EIT) is acoherentopticalnonlinearity which renders a mediumtransparent within a narrowspectral range around anabsorption line. Extremedispersion 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.^[1]

Observation of EIT involves two optical fields (highly coherent light sources, such aslasers) which are tuned to interact with threequantum states of a material. The "probe" field is tuned near resonance between two of the states and measures theabsorption 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 asspectral hole burning or saturation.

EIT is based on the destructive interference of the transitionprobability amplitude between atomic states. Closely related to EIT arecoherent population trapping (CPT) phenomena.

The quantum interference in EIT can be exploited tolaser cool atomic particles, even down to the quantum mechanical ground state of motion.^[2] This was used in 2015 to directly image individual atoms trapped in anoptical lattice.^[3]

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. thetransitions 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${\displaystyle |3⟩}$ is especially important; ideally${\displaystyle |3⟩}$ should be a robust, metastable state.

Currently^[when?] EIT research uses atomic systems in dilute gases, solid solutions, or more exotic states such asBose–Einstein condensate. EIT has been demonstrated in electromechanical^[4] and optomechanical^[5] systems, where it is known asoptomechanically induced transparency. Work is also being done in semiconductor nanostructures such asquantum wells,^[6]quantum wires andquantum dots.^[7][8]

EIT was first proposed theoretically by professor Jakob Khanin and graduate studentOlga Kocharovskaya atGorky State University (renamed to Nizhny Novgorod in 1990), Russia;^[9] there are now several different approaches to a theoretical treatment of EIT. One approach is to extend thedensity matrix treatment used to driveRabi oscillation of a two-state, single field system. In this picture theprobability amplitude for the system to transfer between states caninterfere destructively, preventing absorption. In this context, "interference" refers to interference betweenquantum 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${\displaystyle |1⟩}$ to${\displaystyle |2⟩}$. The fields can drive population from${\displaystyle |1⟩}$-${\displaystyle |2⟩}$ directly or from${\displaystyle |1⟩}$-${\displaystyle |2⟩}$-${\displaystyle |3⟩}$-${\displaystyle |2⟩}$. The probability amplitudes for the different paths interfere destructively. If${\displaystyle |3⟩}$ has a comparatively long lifetime, then the result will be a transparent window completely inside of the${\displaystyle |1⟩}$-${\displaystyle |2⟩}$ absorption line.

Another approach is the "dressed state" picture, wherein the system + coupling fieldHamiltonian is diagonalized and the effect on the probe is calculated in the new basis. In this picture EIT resembles a combination ofAutler-Townes splitting andFano 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.

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

EIT is only one of many diverse mechanisms which can produceslow light. TheKramers–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 andpositive change in refractive index produces an extremely lowgroup velocity.^[10] The first experimental observation of the low group velocity produced by EIT was by Boller,İmamoğlu, and Harris at Stanford University in 1991 instrontium. In 1999Lene Hau reported slowing light in a medium of ultracoldsodium atoms,^[11] achieving this by using quantum interference effects responsible for electromagnetically induced transparency (EIT).^[12] Her group performed copious research regarding EIT withStephen 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."^[13] 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 thermalrubidium vapor.^[14]

Stopped light, in the context of an EIT medium, refers to thecoherent transfer of photons to the quantum system and back again. In principle, this involves switchingoff the coupling beam in anadiabatic fashion while the probe pulse is still inside of the EIT medium. There is experimental evidence of trapped pulses in EIT medium. Authors created astationary light pulse inside the atomic coherent media.^[15] In 2009 researchers from Harvard University and MIT demonstrated a few-photon optical switch for quantum optics based on the slow light ideas.^[16]Lene Hau and a team from Harvard University were the first to demonstrate stopped light.^[17]

EIT has been used tolaser cool long strings of atoms to their motional ground state in anion trap.^[18] To illustrate the cooling technique, consider a three level atom as shown with a ground state${\displaystyle |g⟩}$, an excited state${\displaystyle |e⟩}$, and a stable or metastable state${\displaystyle |m⟩}$ that lies in between them. The excited state${\displaystyle |e⟩}$ is dipole coupled to${\displaystyle |m⟩}$ and${\displaystyle |g⟩}$. An intense "coupling" laser drives the${\displaystyle |m⟩\to |e⟩}$ transition at detuning${\displaystyle {\mathrm{\Delta }}_m}$ above resonance. Due to the quantum interference of transition amplitudes, a weaker "cooling" laser driving the${\displaystyle |g⟩\to |e⟩}$ transition at detuning${\displaystyle {\mathrm{\Delta }}_g}$ above resonance sees aFano-like feature on the absorption profile. EIT cooling is realized when${\displaystyle {\mathrm{\Delta }}_g={\mathrm{\Delta }}_m}$, such that the carrier transition${\displaystyle |g,n⟩\to |e,n⟩}$ lies on the dark resonance of theFano-like feature, where${\displaystyle n}$ is used to label thequantized motional state of the atom. TheRabi frequency${\displaystyle {\mathrm{\Omega }}_m}$ of the coupling laser is chosen such that the${\displaystyle |g,n⟩\to |e,n-1⟩}$ "red" sideband lies on the narrow maximum of theFano-like feature. Conversely the${\displaystyle |g,n⟩\to |e,n+1⟩}$ "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 todoppler orsideband cooling (assuming the same cooling rate).^[19]

• Atomic coherence
• Electromagnetically Induced Grating

• O.Kocharovskaya, Ya.I.Khanin, Sov. Phys. JETP,63, p945 (1986)
• K.J. Boller,A. İmamoğlu,S. E. Harris, Physical Review Letters66, 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 Letters86, p783 (2001)
• Naomi S. Ginsberg,Sean R. Garner,Lene Vestergaard Hau, Nature445, 623 (2007)

• Harris, Steve (July, 1997).Electromagnetically Induced TransparencyArchived 2012-07-16 at theWayback Machine.Physics Today, 50 (7), pp. 36–42 (PDF Format)
• Zachary Dutton,Naomi S. Ginsberg,Christopher Slowe, andLene Vestergaard Hau (2004)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), "Electromagnetically induced transparency: Optics in Coherent Media", Reviews Modern Physics,77, 633

• Wave mechanics
• Molecular physics
• Lasers
• Quantum optics

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