Electromagnetically induced transparency

Last updated December 02, 2024

Electromagnetically induced transparency (EIT) is a coherent optical nonlinearity which renders a medium transparent within a narrow spectral range around an absorption line. Extreme 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.^[1]

Observation of EIT involves two optical fields (highly coherent light sources, such as lasers) which are tuned to interact with three quantum states 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 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 an optical lattice.^[3]

Medium requirements

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 $|3\rangle$ is especially important; ideally $|3\rangle$ should be a robust, metastable state.

Currently ^{[ when? ]} 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^[4] and optomechanical^[5] systems, where it is known as optomechanically induced transparency. Work is also being done in semiconductor nanostructures such as quantum wells,^[6] quantum wires and quantum dots.^[7]^[8]

Theory

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;^[9] 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 $|1\rangle$ to $|2\rangle$ . The fields can drive population from $|1\rangle$ - $|2\rangle$ directly or from $|1\rangle$ - $|2\rangle$ - $|3\rangle$ - $|2\rangle$ . The probability amplitudes for the different paths interfere destructively. If $|3\rangle$ has a comparatively long lifetime, then the result will be a transparent window completely inside of the $|1\rangle$ - $|2\rangle$ 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.

Slow light and stopped light

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.^[10] 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,^[11] achieving this by using quantum interference effects responsible for electromagnetically induced transparency (EIT).^[12] 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."^[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 thermal rubidium vapor.^[14]

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.^[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 cooling

EIT has been used to laser cool long strings of atoms to their motional ground state in an ion trap.^[18] To illustrate the cooling technique, consider a three level atom as shown with a ground state $|g\rangle$ , an excited state $|e\rangle$ , and a stable or metastable state $|m\rangle$ that lies in between them. The excited state $|e\rangle$ is dipole coupled to $|m\rangle$ and $|g\rangle$ . An intense "coupling" laser drives the $|m\rangle \rightarrow |e\rangle$ transition at detuning $\Delta _{m}$ above resonance. Due to the quantum interference of transition amplitudes, a weaker "cooling" laser driving the $|g\rangle \rightarrow |e\rangle$ transition at detuning $\Delta _{g}$ above resonance sees a Fano-like feature on the absorption profile. EIT cooling is realized when $\Delta _{g}=\Delta _{m}$ , such that the carrier transition $|g,n\rangle \rightarrow |e,n\rangle$ 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 $\Omega _{m}$ of the coupling laser is chosen such that the $|g,n\rangle \rightarrow |e,n-1\rangle$ "red" sideband lies on the narrow maximum of the Fano-like feature. Conversely the $|g,n\rangle \rightarrow |e,n+1\rangle$ "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).^[19]

$Absorption profile seen by the cooling laser as a function of detuning D g {\displaystyle \Delta _{g}} . The Rabi frequency O m {\displaystyle \Omega _{m}} is chosen so that the red sideband (red dashed line) lies on the narrow peak of the Fano-like feature and the blue sideband (blue dashed line) lies in a region of low probability. The carrier (black dashed line) lies on the dark resonance where the detunings are equal, i.e. D g = D m {\displaystyle \Delta _{g}=\Delta _{m}} , such that absorption is zero. Absorption of Cooling Laser versus Detuning of Cooling laser for EIT cooling.png$

Absorption profile seen by the cooling laser as a function of detuning

\Delta _{g}

. The Rabi frequency

\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.

\Delta _{g}=\Delta _{m}

, such that absorption is zero.

Related Research Articles

<span class="mw-page-title-main">Bose–Einstein condensate</span> State of matter

In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero, i.e., 0 K. Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which microscopic quantum-mechanical phenomena, particularly wavefunction interference, become apparent macroscopically. More generally, condensation refers to the appearance of macroscopic occupation of one or several states: for example, in BCS theory, a superconductor is a condensate of Cooper pairs. As such, condensation can be associated with phase transition, and the macroscopic occupation of the state is the order parameter.

<span class="mw-page-title-main">Laser cooling</span> Cooling technique in atomic physics

Laser cooling includes several techniques where atoms, molecules, and small mechanical systems are cooled with laser light. The directed energy of lasers is often associated with heating materials, e.g. laser cutting, so it can be counterintuitive that laser cooling often results in sample temperatures approaching absolute zero. It is a routine step in many atomic physics experiments where the laser-cooled atoms are then subsequently manipulated and measured, or in technologies, such as atom-based quantum computing architectures. Laser cooling relies on the change in momentum when an object, such as an atom, absorbs and re-emits a photon. For example, if laser light illuminates a warm cloud of atoms from all directions and the laser's frequency is tuned below an atomic resonance, the atoms will be cooled. This common type of laser cooling relies on the Doppler effect where individual atoms will preferentially absorb laser light from the direction opposite to the atom's motion. The absorbed light is re-emitted by the atom in a random direction. After repeated emission and absorption of light the net effect on the cloud of atoms is that they will expand more slowly. The slower expansion reflects a decrease in the velocity distribution of the atoms, which corresponds to a lower temperature and therefore the atoms have been cooled. For an ensemble of particles, their thermodynamic temperature is proportional to the variance in their velocity, therefore the lower the distribution of velocities, the lower temperature of the particles.

Coherence expresses the potential for two waves to interfere. Two monochromatic beams from a single source always interfere. Wave sources are not strictly monochromatic: they may be partly coherent. Beams from different sources are mutually incoherent.

In physics, a squeezed coherent state is a quantum state that is usually described by two non-commuting observables having continuous spectra of eigenvalues. Examples are position $and momentum of a particle, and the (dimension-less) electric field in the amplitude and in the mode of a light wave. The product of the standard deviations of two such operators obeys the uncertainty principle:$

Resolved sideband cooling is a laser cooling technique allowing cooling of tightly bound atoms and ions beyond the Doppler cooling limit, potentially to their motional ground state. Aside from the curiosity of having a particle at zero point energy, such preparation of a particle in a definite state with high probability (initialization) is an essential part of state manipulation experiments in quantum optics and quantum computing.

Lene Vestergaard Hau is a Danish physicist and educator. She is the Mallinckrodt Professor of Physics and of Applied Physics at Harvard University.

In physics, atomic coherence is the induced coherence between levels of a multi-level atomic system and an electromagnetic field.

A trapped-ion quantum computer is one proposed approach to a large-scale quantum computer. Ions, or charged atomic particles, can be confined and suspended in free space using electromagnetic fields. Qubits are stored in stable electronic states of each ion, and quantum information can be transferred through the collective quantized motion of the ions in a shared trap. Lasers are applied to induce coupling between the qubit states or coupling between the internal qubit states and the external motional states.

<span class="mw-page-title-main">Optical lattice</span> Atomic-scale structure formed through the Stark shift by opposing beams of light

An optical lattice is formed by the interference of counter-propagating laser beams, creating a spatially periodic polarization pattern. The resulting periodic potential may trap neutral atoms via the Stark shift. Atoms are cooled and congregate at the potential extrema. The resulting arrangement of trapped atoms resembles a crystal lattice and can be used for quantum simulation.

In optics, slow light is the propagation of an optical pulse or other modulation of an optical carrier at a very low group velocity. Slow light occurs when a propagating pulse is substantially slowed by the interaction with the medium in which the propagation takes place.

In spectroscopy, the Autler–Townes effect, is a dynamical Stark effect corresponding to the case when an oscillating electric field is tuned in resonance to the transition frequency of a given spectral line, and resulting in a change of the shape of the absorption/emission spectra of that spectral line. The AC Stark effect was discovered in 1955 by American physicists Stanley Autler and Charles Townes.

Cavity quantum electrodynamics is the study of the interaction between light confined in a reflective cavity and atoms or other particles, under conditions where the quantum nature of photons is significant. It could in principle be used to construct a quantum computer.

Electromagnetically induced grating (EIG) is an optical interference phenomenon where an interference pattern is used to build a dynamic spatial diffraction grating in matter. EIGs are dynamically created by light interference on optically resonant materials and rely on population inversion and/or optical coherence properties of the material. They were first demonstrated with population gratings on atoms. EIGs can be used for purposes of atomic/molecular velocimetry, to probe the material optical properties such as coherence and population life-times, and switching and routing of light. Related but different effects are thermally induced gratings and photolithography gratings.

In atomic physics, Raman cooling is a sub-recoil cooling technique that allows the cooling of atoms using optical methods below the limitations of Doppler cooling, Doppler cooling being limited by the recoil energy of a photon given to an atom. This scheme can be performed in simple optical molasses or in molasses where an optical lattice has been superimposed, which are called respectively free space Raman cooling and Raman sideband cooling. Both techniques make use of Raman scattering of laser light by the atoms.

<span class="mw-page-title-main">Stephen E. Harris</span> American physicist (born 1936)

Stephen Ernest Harris is an American physicist known for his contributions to electromagnetically induced transparency (EIT), modulation of single photons, and x-ray emission.

Quantum-optical spectroscopy is a quantum-optical generalization of laser spectroscopy where matter is excited and probed with a sequence of laser pulses.

Cavity optomechanics is a branch of physics which focuses on the interaction between light and mechanical objects on low-energy scales. It is a cross field of optics, quantum optics, solid-state physics and materials science. The motivation for research on cavity optomechanics comes from fundamental effects of quantum theory and gravity, as well as technological applications.

Gray molasses is a method of sub-Doppler laser cooling of atoms. It employs principles from Sisyphus cooling in conjunction with a so-called "dark" state whose transition to the excited state is not addressed by the resonant lasers. Ultracold atomic physics experiments on atomic species with poorly-resolved hyperfine structure, like isotopes of lithium and potassium, often utilize gray molasses instead of Sisyphus cooling as a secondary cooling stage after the ubiquitous magneto-optical trap (MOT) to achieve temperatures below the Doppler limit. Unlike a MOT, which combines a molasses force with a confining force, a gray molasses can only slow but not trap atoms; hence, its efficacy as a cooling mechanism lasts only milliseconds before further cooling and trapping stages must be employed.

In quantum computing, quantum memory is the quantum-mechanical version of ordinary computer memory. Whereas ordinary memory stores information as binary states, quantum memory stores a quantum state for later retrieval. These states hold useful computational information known as qubits. Unlike the classical memory of everyday computers, the states stored in quantum memory can be in a quantum superposition, giving much more practical flexibility in quantum algorithms than classical information storage.

Quantum logic spectroscopy (QLS) is an ion control scheme that maps quantum information between two co-trapped ion species. Quantum logic operations allow desirable properties of each ion species to be utilized simultaneously. This enables work with ions and molecular ions that have complex internal energy level structures which preclude laser cooling and direct manipulation of state. QLS was first demonstrated by NIST in 2005. QLS was first applied to state detection in diatomic molecules in 2016 by Wolf et al, and later applied to state manipulation and detection of diatomic molecules by the Liebfried group at NIST in 2017

References

↑ Liu, Chien; Dutton, Zachary; Behroozi, Cyrus H.; Hau, Lene Vestergaard (2001). "Observation of coherent optical information storage in an atomic medium using halted light pulses". Nature. 409 (6819): 490–493. Bibcode:2001Natur.409..490L. doi:10.1038/35054017. PMID 11206540. S2CID 1894748.
↑ Morigi, Giovanna (2000). "Ground State Laser Cooling Using Electromagnetically Induced Transparency". Physical Review Letters. 85 (21): 4458–4461. arXiv: quant-ph/0005009 . Bibcode:2000PhRvL..85.4458M. doi:10.1103/PhysRevLett.85.4458. PMID 11082570. S2CID 12580278.
↑ Haller, Elmar; Hudson, James; Kelly, Andrew; Cotta, Dylan A.; Peaudecerf, Bruno; Bruce, Graham D.; Kuhr, Stefan (2015). "Single-atom imaging of fermions in a quantum-gas microscope". Nature Physics. 11 (9): 738–742. arXiv: 1503.02005 . Bibcode:2015NatPh..11..738H. doi:10.1038/nphys3403. S2CID 51991496.
↑ Teufel, J. D.; Li, Dale; Allman, M. S.; Cicak, K.; Sirois, A. J.; Whittaker, J. D.; Simmonds, R. W. (2011). "Circuit cavity electromechanics in the strong-coupling regime". Nature. 471 (7337): 204–208. arXiv: 1011.3067 . Bibcode:2011Natur.471..204T. doi:10.1038/nature09898. PMID 21390127. S2CID 4418446.
↑ Safavi-Naeini, A. H.; Alegre, T. P. Mayer; Chan, J.; Eichenfield, M.; Winger, M.; Lin, Q.; Hill, J. T.; Chang, D. E.; Painter, O. (2011). "Electromagnetically induced transparency and slow light with optomechanics". Nature. 472 (7341): 69–73. arXiv: 1012.1934 . Bibcode:2011Natur.472...69S. doi:10.1038/nature09933. PMID 21412237. S2CID 4428942.
↑ Serapiglia, G. B.; Paspalakis, E.; Sirtori, C.; Vodopyanov, K. L.; Phillips, C. C. (2000). "Laser-Induced Quantum Coherence in a Semiconductor Quantum Well". Physical Review Letters. 84 (5): 1019–1022. Bibcode:2000PhRvL..84.1019S. doi:10.1103/PhysRevLett.84.1019. ISSN 0031-9007. PMID 11017430.
↑ Xu, Xiaodong; Sun, Bo; Berman, Paul R.; Steel, Duncan G.; Bracker, Allan S.; Gammon, Dan; Sham, L. J. (2008). "Coherent population trapping of an electron spin in a single negatively charged quantum dot". Nature Physics. 4 (9): 692–695. arXiv: 0805.2074 . Bibcode:2008NatPh...4..692X. doi: 10.1038/nphys1054 . ISSN 1745-2473. S2CID 8098743.
↑ Brunner, Daniel; Gerardot, Brian D.; Dalgarno, Paul A.; Wüst, Gunter; Karrai, Khaled; Stoltz, Nick G.; Petroff, Pierre M.; Warburton, Richard J. (2009). "A Coherent Single-Hole Spin in a Semiconductor". Science. 325 (5936): 70–72. Bibcode:2009Sci...325...70B. doi:10.1126/science.1173684. ISSN 0036-8075. PMID 19574387. S2CID 31505564.
↑ "Texas A&M University physicists have devised a way to stop light | SpaceRef – Your Space Reference". SpaceRef. 2001-01-31. Retrieved 2013-01-28.
↑ Rostovtsev, Yuri; Kocharovskaya, Olga; Welch, George R.; Scully, Marlan O. (2002). "Slow, Ultraslow, Stored, and Frozen Light". Optics and Photonics News. 13 (6): 44. doi:10.1364/OPN.13.6.000044.
↑ "Lene Hau". Physicscentral.com. Retrieved 2013-01-28.
↑ Alex Cohen (2006). "Stopping Light" (PDF). Archived from the original (PDF) on 2010-06-11. Retrieved 2013-01-28.
↑ Soljacic, Marin; Lidorikis, Elefterios; Joannopoulos, John D.; Hau, Lene V. (2004). "Electromagnetically induced transparency in microcavities". In Taylor, Edward W. (ed.). Photonics for Space Environments IX. Proceedings of SPIE. Vol. 5554. p. 174. doi:10.1117/12.562304. S2CID 137523967.
↑ Budker, D.; Kimball, D. F.; Rochester, S. M.; Yashchuk, V. V. (1999). "Nonlinear Magneto-optics and Reduced Group Velocity of Light in Atomic Vapor with Slow Ground State Relaxation". Physical Review Letters. 83 (9): 1767–1770. Bibcode:1999PhRvL..83.1767B. doi:10.1103/PhysRevLett.83.1767.
↑ Bajcsy, M.; Zibrov, A. S.; Lukin, M. D. (2003). "Stationary pulses of light in an atomic medium". Nature. 426 (6967): 638–641. arXiv: quant-ph/0311092 . Bibcode:2003Natur.426..638B. doi:10.1038/nature02176. PMID 14668857. S2CID 4320280.
↑ Bajcsy, M.; Hofferberth, S.; Balic, V.; Peyronel, T.; Hafezi, M.; Zibrov, A. S.; Vuletic, V.; Lukin, M. D. (2009). "Efficient All-Optical Switching Using Slow Light within a Hollow Fiber". Physical Review Letters. 102 (20): 203902. arXiv: 0901.0336 . Bibcode:2009PhRvL.102t3902B. doi:10.1103/PhysRevLett.102.203902. PMID 19519028. S2CID 5504022.
↑ Ginsberg, Naomi S.; Garner, Sean R.; Hau, Lene Vestergaard (2007). "Coherent control of optical information with matter wave dynamics". Nature. 445 (7128): 623–626. doi:10.1038/nature05493. PMID 17287804. S2CID 4324343.
↑ Lechner, Regina; Maier, Christine; Hempell, Cornelius; Jurcevic, Petar; Lanyon, Ben; Monz, Thomas; Brownnutt, Michael; Blatt, Rainer; Roos, Christian (2016). "Electromagnetically-induced-transparency ground-state cooling of long ion strings". Physical Review A. 93 (5): 053401. arXiv: 1603.05568 . Bibcode:2016PhRvA..93e3401L. doi:10.1103/PhysRevA.93.053401. hdl: 10722/248563 . S2CID 227665214.
↑ Morigi, Giovanna; Eschner, Jurgen; Christoph, Keitel (2000). "Ground State Laser Cooling Using Electromagnetically Induced Transparency". Physical Review Letters. 85 (21): 4458–4461. arXiv: quant-ph/0005009 . Bibcode:2000PhRvL..85.4458M. doi:10.1103/PhysRevLett.85.4458. PMID 11082570. S2CID 12580278.

Primary work

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)

Review

Harris, Steve (July, 1997). Electromagnetically Induced Transparency Archived 2012-07-16 at the Wayback Machine . Physics Today, 50 (7), pp. 36–42 (PDF Format)
Zachary Dutton, Naomi S. Ginsberg, Christopher Slowe, and Lene 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

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[1] Liu, Chien; Dutton, Zachary; Behroozi, Cyrus H.; Hau, Lene Vestergaard (2001). "Observation of coherent optical information storage in an atomic medium using halted light pulses". Nature. 409 (6819): 490–493. Bibcode:2001Natur.409..490L. doi:10.1038/35054017. PMID 11206540. S2CID 1894748.

[2] Morigi, Giovanna (2000). "Ground State Laser Cooling Using Electromagnetically Induced Transparency". Physical Review Letters. 85 (21): 4458–4461. arXiv: quant-ph/0005009 . Bibcode:2000PhRvL..85.4458M. doi:10.1103/PhysRevLett.85.4458. PMID 11082570. S2CID 12580278.

[3] Haller, Elmar; Hudson, James; Kelly, Andrew; Cotta, Dylan A.; Peaudecerf, Bruno; Bruce, Graham D.; Kuhr, Stefan (2015). "Single-atom imaging of fermions in a quantum-gas microscope". Nature Physics. 11 (9): 738–742. arXiv: 1503.02005 . Bibcode:2015NatPh..11..738H. doi:10.1038/nphys3403. S2CID 51991496.

[4] Teufel, J. D.; Li, Dale; Allman, M. S.; Cicak, K.; Sirois, A. J.; Whittaker, J. D.; Simmonds, R. W. (2011). "Circuit cavity electromechanics in the strong-coupling regime". Nature. 471 (7337): 204–208. arXiv: 1011.3067 . Bibcode:2011Natur.471..204T. doi:10.1038/nature09898. PMID 21390127. S2CID 4418446.

[5] Safavi-Naeini, A. H.; Alegre, T. P. Mayer; Chan, J.; Eichenfield, M.; Winger, M.; Lin, Q.; Hill, J. T.; Chang, D. E.; Painter, O. (2011). "Electromagnetically induced transparency and slow light with optomechanics". Nature. 472 (7341): 69–73. arXiv: 1012.1934 . Bibcode:2011Natur.472...69S. doi:10.1038/nature09933. PMID 21412237. S2CID 4428942.

[SerapigliaPaspalakis2000-6] Serapiglia, G. B.; Paspalakis, E.; Sirtori, C.; Vodopyanov, K. L.; Phillips, C. C. (2000). "Laser-Induced Quantum Coherence in a Semiconductor Quantum Well". Physical Review Letters. 84 (5): 1019–1022. Bibcode:2000PhRvL..84.1019S. doi:10.1103/PhysRevLett.84.1019. ISSN 0031-9007. PMID 11017430.

[XuSun2008-7] Xu, Xiaodong; Sun, Bo; Berman, Paul R.; Steel, Duncan G.; Bracker, Allan S.; Gammon, Dan; Sham, L. J. (2008). "Coherent population trapping of an electron spin in a single negatively charged quantum dot". Nature Physics. 4 (9): 692–695. arXiv: 0805.2074 . Bibcode:2008NatPh...4..692X. doi: 10.1038/nphys1054 . ISSN 1745-2473. S2CID 8098743.

[BrunnerGerardot2009-8] Brunner, Daniel; Gerardot, Brian D.; Dalgarno, Paul A.; Wüst, Gunter; Karrai, Khaled; Stoltz, Nick G.; Petroff, Pierre M.; Warburton, Richard J. (2009). "A Coherent Single-Hole Spin in a Semiconductor". Science. 325 (5936): 70–72. Bibcode:2009Sci...325...70B. doi:10.1126/science.1173684. ISSN 0036-8075. PMID 19574387. S2CID 31505564.

[9] "Texas A&M University physicists have devised a way to stop light | SpaceRef – Your Space Reference". SpaceRef. 2001-01-31. Retrieved 2013-01-28.

[10] Rostovtsev, Yuri; Kocharovskaya, Olga; Welch, George R.; Scully, Marlan O. (2002). "Slow, Ultraslow, Stored, and Frozen Light". Optics and Photonics News. 13 (6): 44. doi:10.1364/OPN.13.6.000044.

[11] "Lene Hau". Physicscentral.com. Retrieved 2013-01-28.

[12] Alex Cohen (2006). "Stopping Light" (PDF). Archived from the original (PDF) on 2010-06-11. Retrieved 2013-01-28.

[13] Soljacic, Marin; Lidorikis, Elefterios; Joannopoulos, John D.; Hau, Lene V. (2004). "Electromagnetically induced transparency in microcavities". In Taylor, Edward W. (ed.). Photonics for Space Environments IX. Proceedings of SPIE. Vol. 5554. p. 174. doi:10.1117/12.562304. S2CID 137523967.

[14] Budker, D.; Kimball, D. F.; Rochester, S. M.; Yashchuk, V. V. (1999). "Nonlinear Magneto-optics and Reduced Group Velocity of Light in Atomic Vapor with Slow Ground State Relaxation". Physical Review Letters. 83 (9): 1767–1770. Bibcode:1999PhRvL..83.1767B. doi:10.1103/PhysRevLett.83.1767.

[15] Bajcsy, M.; Zibrov, A. S.; Lukin, M. D. (2003). "Stationary pulses of light in an atomic medium". Nature. 426 (6967): 638–641. arXiv: quant-ph/0311092 . Bibcode:2003Natur.426..638B. doi:10.1038/nature02176. PMID 14668857. S2CID 4320280.

[16] Bajcsy, M.; Hofferberth, S.; Balic, V.; Peyronel, T.; Hafezi, M.; Zibrov, A. S.; Vuletic, V.; Lukin, M. D. (2009). "Efficient All-Optical Switching Using Slow Light within a Hollow Fiber". Physical Review Letters. 102 (20): 203902. arXiv: 0901.0336 . Bibcode:2009PhRvL.102t3902B. doi:10.1103/PhysRevLett.102.203902. PMID 19519028. S2CID 5504022.

[17] Ginsberg, Naomi S.; Garner, Sean R.; Hau, Lene Vestergaard (2007). "Coherent control of optical information with matter wave dynamics". Nature. 445 (7128): 623–626. doi:10.1038/nature05493. PMID 17287804. S2CID 4324343.

[18] Lechner, Regina; Maier, Christine; Hempell, Cornelius; Jurcevic, Petar; Lanyon, Ben; Monz, Thomas; Brownnutt, Michael; Blatt, Rainer; Roos, Christian (2016). "Electromagnetically-induced-transparency ground-state cooling of long ion strings". Physical Review A. 93 (5): 053401. arXiv: 1603.05568 . Bibcode:2016PhRvA..93e3401L. doi:10.1103/PhysRevA.93.053401. hdl: 10722/248563 . S2CID 227665214.

[19] Morigi, Giovanna; Eschner, Jurgen; Christoph, Keitel (2000). "Ground State Laser Cooling Using Electromagnetically Induced Transparency". Physical Review Letters. 85 (21): 4458–4461. arXiv: quant-ph/0005009 . Bibcode:2000PhRvL..85.4458M. doi:10.1103/PhysRevLett.85.4458. PMID 11082570. S2CID 12580278.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]