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is the frequency of the light. That energy possessed by a single photon corresponds exactly to the transition between discrete energy levels in an atom (or other system) that emitted the photon; material absorption of a photon is the reverse process. Einstein's explanation of
144:—i.e., research into principles, design and application of these devices—became an important field, and the quantum mechanics underlying the laser's principles was studied now with more emphasis on the properties of light, and the name
199:
et al. demonstrated a single atom emitting one photon at a time, further compelling evidence that light consists of photons. Previously unknown quantum states of light with characteristics unlike classical states, such as
995:
132:
as a whole. However, the subfields of quantum mechanics dealing with matter-light interaction were principally regarded as research into matter rather than into light; hence one rather spoke of
994:
48:, interact with atoms and molecules. It includes the study of the particle-like properties of photons. Photons have been used to test many of the counter-intuitive predictions of
151:
As laser science needed good theoretical foundations, and also because research into these soon proved very fruitful, interest in quantum optics rose. Following the work of
84:. Quantum optics studies the nature and effects of light as quantized photons. The first major development leading to that understanding was the correct modeling of the
223:) were found, and mechanical forces of light on matter were studied. The latter led to levitating and positioning clouds of atoms or even small biological samples in an
996:
293:, and much more. Topics classified under the term of quantum optics, especially as applied to engineering and technological innovation, often go under the modern term
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is fundamental to the concepts of quantum optics: light is described in terms of field operators for creation and annihilation of photons—i.e. in the language of
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applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the
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regularly takes quantum mechanics into account, and is usually concerned with electrons. Specific applications of quantum mechanics in
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320:"for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science".
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techniques—opened the way to the study of what became known as ultrafast processes. Applications for solid state research (e.g.
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can generate so-called 'twin beams', where (ideally) each photon of one beam is associated with a photon in the other beam.
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2003:
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508:. Other important quantum aspects are related to correlations of photon statistics between different beams. For example,
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541:. This is important for understanding how light is detected by solid-state devices, commonly used in experiments.
331:"for ground-breaking experimental methods that enable measuring & manipulation of individual quantum systems".
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operation, which is today studied as a topic in quantum optics. Usage of the term overlapped early work on the
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568:. Today, it is rarely considered a sub-field in its own right, and it has been absorbed by other fields.
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2060:
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1958:
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1601:
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589:
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1052:– a quantum physics wiki devoted to providing technical resources for practicing quantum physicists.
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in 1960. This state, which can be used to approximately describe the output of a single-frequency
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showed that the hypothesis of optical radiation being quantized corresponded to his theory of the
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1046:, with content on quantum optics (particularly quantum noise in lasers), by RĂĽdiger Paschotta.
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in 1899 under the hypothesis of light being emitted in discrete units of energy. The
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being driven by the absorption or emission of light according to
Einstein's theory.
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1058:– a free-content WWW resource in quantum information science that anyone can edit.
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as a concept that addressed variations between laser light, thermal light, exotic
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1988:
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is a term that was used mainly between the 1950s and 1970s to denote the area of
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1968:
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262:, a subject that partly emerged from quantum optics, partly from theoretical
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was created from a revision of this article dated 11 August 2009
285:, their application, and how to manipulate them (a sub-field often called
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in particular. The understanding of the interaction between light and
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294:
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1038:
698:(10th anniversary ed.). Cambridge: Cambridge University Press.
454:(and laser) many years later was dependent on a method to produce a
277:, even shorter (attosecond) light pulses, use of quantum optics for
269:
Today's fields of interest among quantum optics researchers include
3305:
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have been awarded for work in quantum optics. These were awarded:
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following these developments was crucial for the development of
100:
in a 1905 paper, a discovery for which he was to be awarded the
3309:
2805:
653:
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125:
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quantized according to an integer number of particles known as
73:
45:
239:, was the crucial technology needed to achieve the celebrated
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581:
481:
451:
447:
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2800:
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1055:
30:"Quantum electronics" redirects here. For the journal, see
410:
in vacuum. These particles should not be considered to be
96:
was further evidence of this quantization as explained by
72:
Light propagating in a restricted volume of space has its
2944:
2929:
806:
Brunner, Witlof; Radloff, Wolfgang; Junge, Klaus (1975).
492:
interactions, a coherent state can be transformed into a
472:
A frequently encountered state of the light field is the
195:
describing the waves in the classical picture. In 1977,
421:
Each particle carries one quantum of energy, equal to
44:
dealing with how individual quanta of light, known as
414:, but as quantum mechanical particles described by a
1039:
An introduction to quantum optics of the light field
599:
496:, by applying a squeezing operator that can exhibit
2771:
805:
580:. The term also encompassed the basic processes of
564:in matter, together with their interactions with
3383:
2526:
390:, light may be considered not only to be as an
694:Nielsen, Michael A.; Chuang, Isaac L. (2010).
2512:
1705:
1434:
1096:
1082:
733:. Nobel Foundation. Retrieved 9 October 2012.
693:
1044:Encyclopedia of laser physics and technology
950:
450:rests. However, the actual invention of the
828:
696:Quantum computation and quantum information
515:Atoms are considered as quantum mechanical
2519:
2505:
1712:
1698:
1441:
1427:
1089:
1075:
829:Gerry, Christopher; Knight, Peter (2004).
721:. Nobel Foundation. Retrieved 9 June 2023.
526:, with the transitions between the energy
659:Quantization of the electromagnetic field
484:well above the laser threshold, exhibits
1448:
1022:, and does not reflect subsequent edits.
1005:
931:
504:photon statistics. Such light is called
3037:Continuous-variable quantum information
183:). This led to the introduction of the
27:Sub-field of quantum physics and optics
14:
3384:
1287:Atomic, molecular, and optical physics
619:Atomic, molecular, and optical physics
544:
510:spontaneous parametric down-conversion
488:photon number statistics. Via certain
42:atomic, molecular, and optical physics
2500:
1719:
1693:
1422:
1070:
533:For solid state matter, one uses the
258:. The latter are of much interest in
248:demonstration of quantum entanglement
867:Optical Coherence and Quantum Optics
812:Deutscher Verlag der Wissenschaften
24:
992:
853:
25:
3408:
973:
786:"The Nobel Prize in Physics 1997"
765:"The Nobel Prize in Physics 2001"
744:"The Nobel Prize in Physics 2005"
731:"The Nobel Prize in Physics 2012"
719:"The Nobel Prize in Physics 2022"
246:Other remarkable results are the
3366:
3365:
3356:
3355:
2481:
2480:
1004:
602:
442:also predicted the existence of
281:, manipulation of single atoms,
231:by laser beam. This, along with
110:quantized energy levels of atoms
60:, and are a useful resource for
1408:Timeline of physics discoveries
848:The Nobel Prize in Physics 2005
446:, the principle upon which the
2430:Relativistic quantum mechanics
1644:Hanbury Brown and Twiss effect
1062:Various Quantum Optics Reports
936:. Cambridge University Press.
932:Kira, M.; Koch, S. W. (2011).
904:Introduction to Quantum Optics
833:. Cambridge University Press.
831:Introduction to Quantum Optics
799:
778:
757:
736:
724:
712:
687:
204:were subsequently discovered.
62:quantum information processing
13:
1:
3032:Adiabatic quantum computation
2408:Quantum statistical mechanics
2185:Quantum differential calculus
2107:Delayed-choice quantum eraser
1875:Symmetry in quantum mechanics
926:Quantum Optics in Phase Space
822:
418:spread over a finite region.
32:Quantum Electronics (journal)
3083:Topological quantum computer
956:Quantum Optics for Engineers
934:Semiconductor Quantum Optics
556:dealing with the effects of
7:
3361:Quantum information science
2528:Quantum information science
2210:Quantum stochastic calculus
2200:Quantum measurement problem
2122:Mach–Zehnder interferometer
1372:Quantum information science
595:
381:
10:
3413:
2756:quantum gate teleportation
1203:Classical electromagnetism
291:coherent perfect absorbers
271:parametric down-conversion
260:quantum information theory
241:Bose–Einstein condensation
67:
29:
3351:
3294:
3257:
3223:
3200:
3167:
3158:
3091:
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2885:Quantum Fourier transform
2830:
2781:Post-quantum cryptography
2724:Entanglement distillation
2697:
2606:
2534:
2476:
2438:
2390:
2270:Quantum complexity theory
2248:Quantum cellular automata
2223:
2155:
2089:
2002:
1951:
1938:Path integral formulation
1905:
1770:
1727:
1675:Creation and annihilation
1662:
1631:
1615:
1589:
1563:
1537:
1530:
1505:
1489:
1463:
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590:quantum cellular automata
283:Bose–Einstein condensates
207:Development of short and
3371:Quantum mechanics topics
3066:Quantum machine learning
3042:One-way quantum computer
2895:Quantum phase estimation
2796:Quantum key distribution
2729:Monogamy of entanglement
2337:Quantum machine learning
2317:Quantum key distribution
2307:Quantum image processing
2297:Quantum error correction
2147:Wheeler's delayed choice
1623:Transition dipole moment
1309:Condensed matter physics
680:
664:Two-state quantum system
412:classical billiard balls
211:laser pulses—created by
2978:Randomized benchmarking
2840:Amplitude amplification
2253:Quantum finite automata
1513:Anti-symmetric operator
1506:Operators for operators
494:squeezed coherent state
467:quantum electrodynamics
372:William Daniel Phillips
3078:Quantum Turing machine
3071:quantum neural network
2818:Quantum secret sharing
2357:Quantum neural network
1393:Nobel Prize in Physics
1255:Relativistic mechanics
1000:
980:Listen to this article
368:Claude Cohen-Tannoudji
275:parametric oscillation
193:electromagnetic fields
3150:Entanglement-assisted
3111:quantum convolutional
2786:Quantum coin flipping
2751:Quantum teleportation
2712:entanglement-assisted
2542:DiVincenzo's criteria
2382:Quantum teleportation
1895:Wave–particle duality
1398:Philosophy of physics
999:
902:and F. Soto-Eguibar,
578:semiconductor physics
576:is researched within
478:E.C. George Sudarshan
463:statistical mechanics
396:"stream" of particles
392:electro-magnetic wave
252:quantum teleportation
2961:processor benchmarks
2890:Quantum optimization
2773:Quantum cryptography
2584:physical vs. logical
2413:Quantum field theory
2342:Quantum metamaterial
2287:Quantum cryptography
2017:Consistent histories
1450:Operators in physics
1357:Mathematical physics
1031:More spoken articles
906:(Rinton Press 2011).
456:population inversion
440:spontaneous emission
402:, which travel with
157:quantum field theory
94:photoelectric effect
2674:Quantum speed limit
2569:Quantum programming
2564:Quantum information
2398:Quantum fluctuation
2367:Quantum programming
2327:Quantum logic gates
2312:Quantum information
2292:Quantum electronics
1752:Classical mechanics
1332:Atmospheric physics
1171:Classical mechanics
1099:branches of physics
644:Optical phase space
586:quantum Hall effect
570:Solid state physics
560:on the behavior of
550:Quantum electronics
545:Quantum electronics
539:solid state physics
476:, as introduced by
444:stimulated emission
279:quantum information
256:quantum logic gates
181:degree of coherence
138:quantum electronics
86:blackbody radiation
18:Quantum electronics
3323:Forest/Rigetti QCS
3059:quantum logic gate
2845:Bernstein–Vazirani
2832:Quantum algorithms
2707:Classical capacity
2591:Quantum processors
2574:Quantum simulation
2451:in popular culture
2233:Quantum algorithms
2081:Von Neumann–Wigner
2061:Objective collapse
1757:Old quantum theory
1649:Quantum correlator
1388:History of physics
1001:
629:Nonclassical light
354:Eric Allin Cornell
221:Raman spectroscopy
148:became customary.
118:discharge emission
3379:
3378:
3290:
3289:
3187:Linear optical QC
2968:Quantum supremacy
2922:complexity theory
2875:Quantum annealing
2826:
2825:
2763:Superdense coding
2552:Quantum computing
2494:
2493:
2468:Quantum mysticism
2446:Schrödinger's cat
2377:Quantum simulator
2347:Quantum metrology
2275:Quantum computing
2238:Quantum amplifier
2215:Quantum spacetime
2180:Quantum cosmology
2170:Quantum chemistry
1870:Scattering theory
1818:Zero-point energy
1813:Degenerate levels
1721:Quantum mechanics
1687:
1686:
1683:
1682:
1670:Casimir invariant
1526:
1525:
1416:
1415:
1403:Physics education
1352:Materials science
1319:Interdisciplinary
1277:Quantum mechanics
997:
958:. New York: CRC.
919:(Cambridge 1997).
869:(Cambridge 1995).
808:Quantenelektronik
558:quantum mechanics
350:Wolfgang Ketterle
336:Theodor W. Hänsch
329:David J. Wineland
130:quantum mechanics
50:quantum mechanics
16:(Redirected from
3404:
3369:
3368:
3359:
3358:
3165:
3164:
3095:error correction
3024:computing models
2990:Relaxation times
2880:Quantum counting
2769:
2768:
2717:quantum capacity
2664:No-teleportation
2649:No-communication
2521:
2514:
2507:
2498:
2497:
2484:
2483:
2195:Quantum geometry
2190:Quantum dynamics
2047:Superdeterminism
1979:Rarita–Schwinger
1928:Matrix mechanics
1783:Bra–ket notation
1714:
1707:
1700:
1691:
1690:
1663:Particle physics
1616:Electromagnetism
1590:Angular momentum
1535:
1534:
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1429:
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1342:Chemical physics
1282:Particle physics
1208:Classical optics
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1084:
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1068:
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1021:
1019:
1008:
1007:
998:
988:
986:
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896:(Springer 2004).
886:Crispin Gardiner
882:(Springer 1994).
844:
816:
815:
803:
797:
796:
794:
793:
788:. Nobelprize.org
782:
776:
775:
773:
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767:. Nobelprize.org
761:
755:
754:
752:
751:
746:. Nobelprize.org
740:
734:
728:
722:
716:
710:
709:
691:
612:
607:
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264:computer science
237:Sisyphus cooling
229:optical tweezers
165:George Sudarshan
21:
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3405:
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3259:Superconducting
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3219:
3210:Neutral atom QC
3202:Ultracold atoms
3196:
3161:implementations
3160:
3154:
3094:
3087:
3054:Quantum circuit
3022:
3016:
3010:
3000:
2960:
2954:
2921:
2914:
2870:Hidden subgroup
2822:
2811:other protocols
2767:
2744:quantum network
2739:Quantum channel
2699:
2693:
2639:No-broadcasting
2629:Gottesman–Knill
2602:
2530:
2525:
2495:
2490:
2472:
2458:Wigner's friend
2434:
2425:Quantum gravity
2386:
2372:Quantum sensing
2352:Quantum network
2332:Quantum machine
2302:Quantum imaging
2265:Quantum circuit
2260:Quantum channel
2219:
2165:Quantum biology
2151:
2127:Elitzur–Vaidman
2102:Davisson–Germer
2085:
2037:Hidden-variable
2027:de Broglie–Bohm
2004:Interpretations
1998:
1947:
1901:
1788:Complementarity
1766:
1723:
1718:
1688:
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1658:
1627:
1611:
1585:
1559:
1522:
1518:Ladder operator
1501:
1485:
1452:
1447:
1417:
1412:
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1362:Medical physics
1313:
1272:Nuclear physics
1241:
1235:Non-equilibrium
1157:
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1101:
1095:
1035:
1034:
1023:
1017:
1015:
1012:This audio file
1009:
1002:
993:
990:
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983:
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900:H.M. Moya-Cessa
856:
854:Further reading
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683:
678:
649:Optical physics
639:Quantum control
608:
601:
598:
547:
524:energy spectrum
431:Planck constant
384:
318:Anton Zeilinger
233:Doppler cooling
189:squeezed states
161:John R. Klauder
98:Albert Einstein
70:
40:is a branch of
35:
28:
23:
22:
15:
12:
11:
5:
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3392:Quantum optics
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3343:many others...
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3292:
3291:
3288:
3287:
3285:
3284:
3279:
3274:
3269:
3263:
3261:
3255:
3254:
3252:
3251:
3246:
3241:
3236:
3230:
3228:
3221:
3220:
3218:
3217:
3215:Trapped-ion QC
3212:
3206:
3204:
3198:
3197:
3195:
3194:
3189:
3184:
3179:
3173:
3171:
3169:Quantum optics
3162:
3156:
3155:
3153:
3152:
3147:
3146:
3145:
3138:
3133:
3128:
3123:
3118:
3113:
3108:
3099:
3097:
3089:
3088:
3086:
3085:
3080:
3075:
3074:
3073:
3063:
3062:
3061:
3051:
3050:
3049:
3039:
3034:
3028:
3026:
3018:
3017:
3015:
3014:
3013:
3012:
3008:
3002:
2998:
2987:
2986:
2985:
2975:
2973:Quantum volume
2970:
2964:
2962:
2956:
2955:
2953:
2952:
2947:
2942:
2937:
2932:
2926:
2924:
2916:
2915:
2913:
2912:
2907:
2902:
2897:
2892:
2887:
2882:
2877:
2872:
2867:
2862:
2857:
2852:
2850:Boson sampling
2847:
2842:
2836:
2834:
2828:
2827:
2824:
2823:
2821:
2820:
2815:
2814:
2813:
2808:
2803:
2793:
2788:
2783:
2777:
2775:
2766:
2765:
2760:
2759:
2758:
2748:
2747:
2746:
2736:
2731:
2726:
2721:
2720:
2719:
2714:
2703:
2701:
2695:
2694:
2692:
2691:
2686:
2684:Solovay–Kitaev
2681:
2676:
2671:
2666:
2661:
2656:
2651:
2646:
2641:
2636:
2631:
2626:
2621:
2616:
2610:
2608:
2604:
2603:
2601:
2600:
2599:
2598:
2588:
2587:
2586:
2576:
2571:
2566:
2561:
2560:
2559:
2549:
2544:
2538:
2536:
2532:
2531:
2524:
2523:
2516:
2509:
2501:
2492:
2491:
2489:
2488:
2477:
2474:
2473:
2471:
2470:
2465:
2460:
2455:
2454:
2453:
2442:
2440:
2436:
2435:
2433:
2432:
2427:
2422:
2421:
2420:
2410:
2405:
2403:Casimir effect
2400:
2394:
2392:
2388:
2387:
2385:
2384:
2379:
2374:
2369:
2364:
2362:Quantum optics
2359:
2354:
2349:
2344:
2339:
2334:
2329:
2324:
2319:
2314:
2309:
2304:
2299:
2294:
2289:
2284:
2283:
2282:
2272:
2267:
2262:
2257:
2256:
2255:
2245:
2240:
2235:
2229:
2227:
2221:
2220:
2218:
2217:
2212:
2207:
2202:
2197:
2192:
2187:
2182:
2177:
2172:
2167:
2161:
2159:
2153:
2152:
2150:
2149:
2144:
2139:
2137:Quantum eraser
2134:
2129:
2124:
2119:
2114:
2109:
2104:
2099:
2093:
2091:
2087:
2086:
2084:
2083:
2078:
2073:
2068:
2063:
2058:
2053:
2052:
2051:
2050:
2049:
2034:
2029:
2024:
2019:
2014:
2008:
2006:
2000:
1999:
1997:
1996:
1991:
1986:
1981:
1976:
1971:
1966:
1961:
1955:
1953:
1949:
1948:
1946:
1945:
1940:
1935:
1930:
1925:
1920:
1915:
1909:
1907:
1903:
1902:
1900:
1899:
1898:
1897:
1892:
1882:
1877:
1872:
1867:
1862:
1857:
1852:
1847:
1842:
1837:
1832:
1827:
1822:
1821:
1820:
1815:
1810:
1805:
1795:
1793:Density matrix
1790:
1785:
1780:
1774:
1772:
1768:
1767:
1765:
1764:
1759:
1754:
1749:
1748:
1747:
1737:
1731:
1729:
1725:
1724:
1717:
1716:
1709:
1702:
1694:
1685:
1684:
1681:
1680:
1678:
1677:
1672:
1666:
1664:
1660:
1659:
1657:
1656:
1651:
1646:
1641:
1635:
1633:
1629:
1628:
1626:
1625:
1619:
1617:
1613:
1612:
1610:
1609:
1604:
1599:
1593:
1591:
1587:
1586:
1584:
1583:
1581:Kinetic energy
1578:
1573:
1567:
1565:
1561:
1560:
1558:
1557:
1552:
1547:
1541:
1539:
1532:
1528:
1527:
1524:
1523:
1521:
1520:
1515:
1509:
1507:
1503:
1502:
1500:
1499:
1493:
1491:
1487:
1486:
1484:
1483:
1478:
1473:
1467:
1465:
1464:Space and time
1458:
1454:
1453:
1446:
1445:
1438:
1431:
1423:
1414:
1413:
1411:
1410:
1405:
1400:
1395:
1390:
1384:
1382:
1378:
1377:
1375:
1374:
1369:
1364:
1359:
1354:
1349:
1344:
1339:
1334:
1329:
1323:
1321:
1315:
1314:
1312:
1311:
1306:
1305:
1304:
1299:
1294:
1284:
1279:
1274:
1269:
1268:
1267:
1262:
1251:
1249:
1243:
1242:
1240:
1239:
1238:
1237:
1232:
1225:Thermodynamics
1222:
1221:
1220:
1215:
1205:
1200:
1195:
1194:
1193:
1188:
1183:
1178:
1167:
1165:
1159:
1158:
1156:
1155:
1154:
1153:
1143:
1137:
1135:
1131:
1130:
1128:
1127:
1126:
1125:
1115:
1109:
1107:
1103:
1102:
1094:
1093:
1086:
1079:
1071:
1065:
1064:
1059:
1053:
1047:
1041:
1024:
1010:
1003:
991:
978:
977:
975:
974:External links
972:
971:
970:
965:978-1439888537
964:
948:
943:978-0521875097
942:
929:
923:W. P. Schleich
920:
917:Quantum Optics
907:
897:
883:
880:Quantum Optics
870:
855:
852:
851:
850:
845:
839:
824:
821:
818:
817:
798:
777:
756:
735:
723:
711:
705:978-1107002173
704:
685:
684:
682:
679:
677:
676:
671:
669:Spinplasmonics
666:
661:
656:
651:
646:
641:
636:
631:
626:
621:
615:
614:
613:
610:Physics portal
597:
594:
546:
543:
506:squeezed light
502:sub-Poissonian
474:coherent state
408:speed of light
394:but also as a
388:quantum theory
383:
380:
379:
378:
360:
346:
340:Roy J. Glauber
332:
321:
202:squeezed light
185:coherent state
179:of light (see
173:Leonard Mandel
169:Roy J. Glauber
146:quantum optics
69:
66:
38:Quantum optics
26:
9:
6:
4:
3:
2:
3409:
3398:
3395:
3393:
3390:
3389:
3387:
3372:
3364:
3362:
3354:
3353:
3350:
3344:
3341:
3339:
3336:
3334:
3331:
3329:
3326:
3324:
3320:
3317:
3315:
3311:
3307:
3304:
3303:
3301:
3299:
3293:
3283:
3280:
3278:
3275:
3273:
3270:
3268:
3265:
3264:
3262:
3260:
3256:
3250:
3247:
3245:
3242:
3240:
3239:Spin qubit QC
3237:
3235:
3232:
3231:
3229:
3226:
3222:
3216:
3213:
3211:
3208:
3207:
3205:
3203:
3199:
3193:
3190:
3188:
3185:
3183:
3180:
3178:
3175:
3174:
3172:
3170:
3166:
3163:
3157:
3151:
3148:
3144:
3143:
3139:
3137:
3134:
3132:
3129:
3127:
3124:
3122:
3119:
3117:
3114:
3112:
3109:
3107:
3104:
3103:
3101:
3100:
3098:
3096:
3090:
3084:
3081:
3079:
3076:
3072:
3069:
3068:
3067:
3064:
3060:
3057:
3056:
3055:
3052:
3048:
3047:cluster state
3045:
3044:
3043:
3040:
3038:
3035:
3033:
3030:
3029:
3027:
3025:
3019:
3011:
3007:
3003:
3001:
2997:
2993:
2992:
2991:
2988:
2984:
2981:
2980:
2979:
2976:
2974:
2971:
2969:
2966:
2965:
2963:
2957:
2951:
2948:
2946:
2943:
2941:
2938:
2936:
2933:
2931:
2928:
2927:
2925:
2923:
2917:
2911:
2908:
2906:
2903:
2901:
2898:
2896:
2893:
2891:
2888:
2886:
2883:
2881:
2878:
2876:
2873:
2871:
2868:
2866:
2863:
2861:
2858:
2856:
2855:Deutsch–Jozsa
2853:
2851:
2848:
2846:
2843:
2841:
2838:
2837:
2835:
2833:
2829:
2819:
2816:
2812:
2809:
2807:
2804:
2802:
2799:
2798:
2797:
2794:
2792:
2791:Quantum money
2789:
2787:
2784:
2782:
2779:
2778:
2776:
2774:
2770:
2764:
2761:
2757:
2754:
2753:
2752:
2749:
2745:
2742:
2741:
2740:
2737:
2735:
2732:
2730:
2727:
2725:
2722:
2718:
2715:
2713:
2710:
2709:
2708:
2705:
2704:
2702:
2700:communication
2696:
2690:
2687:
2685:
2682:
2680:
2677:
2675:
2672:
2670:
2667:
2665:
2662:
2660:
2657:
2655:
2652:
2650:
2647:
2645:
2642:
2640:
2637:
2635:
2632:
2630:
2627:
2625:
2622:
2620:
2617:
2615:
2612:
2611:
2609:
2605:
2597:
2594:
2593:
2592:
2589:
2585:
2582:
2581:
2580:
2577:
2575:
2572:
2570:
2567:
2565:
2562:
2558:
2555:
2554:
2553:
2550:
2548:
2545:
2543:
2540:
2539:
2537:
2533:
2529:
2522:
2517:
2515:
2510:
2508:
2503:
2502:
2499:
2487:
2479:
2478:
2475:
2469:
2466:
2464:
2461:
2459:
2456:
2452:
2449:
2448:
2447:
2444:
2443:
2441:
2437:
2431:
2428:
2426:
2423:
2419:
2416:
2415:
2414:
2411:
2409:
2406:
2404:
2401:
2399:
2396:
2395:
2393:
2389:
2383:
2380:
2378:
2375:
2373:
2370:
2368:
2365:
2363:
2360:
2358:
2355:
2353:
2350:
2348:
2345:
2343:
2340:
2338:
2335:
2333:
2330:
2328:
2325:
2323:
2322:Quantum logic
2320:
2318:
2315:
2313:
2310:
2308:
2305:
2303:
2300:
2298:
2295:
2293:
2290:
2288:
2285:
2281:
2278:
2277:
2276:
2273:
2271:
2268:
2266:
2263:
2261:
2258:
2254:
2251:
2250:
2249:
2246:
2244:
2241:
2239:
2236:
2234:
2231:
2230:
2228:
2226:
2222:
2216:
2213:
2211:
2208:
2206:
2203:
2201:
2198:
2196:
2193:
2191:
2188:
2186:
2183:
2181:
2178:
2176:
2175:Quantum chaos
2173:
2171:
2168:
2166:
2163:
2162:
2160:
2158:
2154:
2148:
2145:
2143:
2142:Stern–Gerlach
2140:
2138:
2135:
2133:
2130:
2128:
2125:
2123:
2120:
2118:
2115:
2113:
2110:
2108:
2105:
2103:
2100:
2098:
2095:
2094:
2092:
2088:
2082:
2079:
2077:
2076:Transactional
2074:
2072:
2069:
2067:
2066:Quantum logic
2064:
2062:
2059:
2057:
2054:
2048:
2045:
2044:
2043:
2040:
2039:
2038:
2035:
2033:
2030:
2028:
2025:
2023:
2020:
2018:
2015:
2013:
2010:
2009:
2007:
2005:
2001:
1995:
1992:
1990:
1987:
1985:
1982:
1980:
1977:
1975:
1972:
1970:
1967:
1965:
1962:
1960:
1957:
1956:
1954:
1950:
1944:
1941:
1939:
1936:
1934:
1931:
1929:
1926:
1924:
1921:
1919:
1916:
1914:
1911:
1910:
1908:
1904:
1896:
1893:
1891:
1888:
1887:
1886:
1885:Wave function
1883:
1881:
1878:
1876:
1873:
1871:
1868:
1866:
1863:
1861:
1860:Superposition
1858:
1856:
1855:Quantum state
1853:
1851:
1848:
1846:
1843:
1841:
1838:
1836:
1833:
1831:
1828:
1826:
1823:
1819:
1816:
1814:
1811:
1809:
1808:Excited state
1806:
1804:
1801:
1800:
1799:
1796:
1794:
1791:
1789:
1786:
1784:
1781:
1779:
1776:
1775:
1773:
1769:
1763:
1760:
1758:
1755:
1753:
1750:
1746:
1743:
1742:
1741:
1738:
1736:
1733:
1732:
1730:
1726:
1722:
1715:
1710:
1708:
1703:
1701:
1696:
1695:
1692:
1676:
1673:
1671:
1668:
1667:
1665:
1661:
1655:
1652:
1650:
1647:
1645:
1642:
1640:
1637:
1636:
1634:
1630:
1624:
1621:
1620:
1618:
1614:
1608:
1605:
1603:
1600:
1598:
1595:
1594:
1592:
1588:
1582:
1579:
1577:
1574:
1572:
1569:
1568:
1566:
1562:
1556:
1553:
1551:
1548:
1546:
1543:
1542:
1540:
1536:
1533:
1529:
1519:
1516:
1514:
1511:
1510:
1508:
1504:
1498:
1495:
1494:
1492:
1488:
1482:
1479:
1477:
1474:
1472:
1471:d'Alembertian
1469:
1468:
1466:
1462:
1459:
1455:
1451:
1444:
1439:
1437:
1432:
1430:
1425:
1424:
1421:
1409:
1406:
1404:
1401:
1399:
1396:
1394:
1391:
1389:
1386:
1385:
1383:
1379:
1373:
1370:
1368:
1367:Ocean physics
1365:
1363:
1360:
1358:
1355:
1353:
1350:
1348:
1345:
1343:
1340:
1338:
1335:
1333:
1330:
1328:
1325:
1324:
1322:
1320:
1316:
1310:
1307:
1303:
1302:Modern optics
1300:
1298:
1295:
1293:
1290:
1289:
1288:
1285:
1283:
1280:
1278:
1275:
1273:
1270:
1266:
1263:
1261:
1258:
1257:
1256:
1253:
1252:
1250:
1248:
1244:
1236:
1233:
1231:
1228:
1227:
1226:
1223:
1219:
1216:
1214:
1211:
1210:
1209:
1206:
1204:
1201:
1199:
1196:
1192:
1189:
1187:
1184:
1182:
1179:
1177:
1174:
1173:
1172:
1169:
1168:
1166:
1164:
1160:
1152:
1151:Computational
1149:
1148:
1147:
1144:
1142:
1139:
1138:
1136:
1132:
1124:
1121:
1120:
1119:
1116:
1114:
1111:
1110:
1108:
1104:
1100:
1092:
1087:
1085:
1080:
1078:
1073:
1072:
1069:
1063:
1060:
1057:
1054:
1051:
1048:
1045:
1042:
1040:
1037:
1036:
1032:
1028:
1013:
967:
961:
957:
953:
949:
945:
939:
935:
930:
928:(Wiley 2001).
927:
924:
921:
918:
915:
914:M. S. Zubairy
911:
908:
905:
901:
898:
895:
894:Quantum Noise
891:
887:
884:
881:
878:
877:G. J. Milburn
874:
871:
868:
865:
861:
858:
857:
849:
846:
842:
836:
832:
827:
826:
813:
810:(in German).
809:
802:
787:
781:
766:
760:
745:
739:
732:
727:
720:
715:
707:
701:
697:
690:
686:
675:
674:Valleytronics
672:
670:
667:
665:
662:
660:
657:
655:
652:
650:
647:
645:
642:
640:
637:
635:
634:Optomechanics
632:
630:
627:
625:
622:
620:
617:
616:
611:
605:
600:
593:
591:
587:
583:
579:
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3192:KLM protocol
3168:
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3005:
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2689:Purification
2619:Eastin–Knill
2361:
2205:Quantum mind
2117:Franck–Hertz
1959:Klein–Gordon
1913:Formulations
1906:Formulations
1835:Interference
1825:Entanglement
1803:Ground state
1798:Energy level
1771:Fundamentals
1735:Introduction
1639:Displacement
1571:Total energy
1327:Astrophysics
1141:Experimental
955:
952:F. J. Duarte
933:
925:
916:
910:M. O. Scully
903:
893:
890:Peter Zoller
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314:John Clauser
310:Alain Aspect
302:Nobel prizes
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268:
245:
225:optical trap
206:
150:
145:
134:atom physics
71:
54:entanglement
37:
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3298:programming
3277:Phase qubit
3182:Circuit QED
2654:No-deleting
2596:cloud-based
2463:EPR paradox
2243:Quantum bus
2112:Double-slit
2090:Experiments
2056:Many-worlds
1994:Schrödinger
1943:Phase space
1933:Schrödinger
1923:Interaction
1880:Uncertainty
1850:Nonlocality
1845:Measurement
1840:Decoherence
1830:Hamiltonian
1576:Hamiltonian
1538:Fundamental
1230:Statistical
1146:Theoretical
1123:Engineering
873:D. F. Walls
624:Attophysics
574:electronics
535:energy band
528:eigenstates
517:oscillators
461:The use of
358:Carl Wieman
287:atom optics
217:modelocking
213:Q switching
102:Nobel Prize
3386:Categories
3338:libquantum
3272:Flux qubit
3177:Cavity QED
3126:Bacon–Shor
3116:stabilizer
2644:No-cloning
2391:Extensions
2225:Technology
2071:Relational
2022:Copenhagen
1918:Heisenberg
1865:Tunnelling
1728:Background
1497:C-symmetry
1347:Geophysics
1337:Biophysics
1181:Analytical
1134:Approaches
1027:Audio help
1018:2009-08-11
840:052152735X
823:References
792:2015-10-14
771:2015-10-14
750:2015-10-14
537:models of
486:Poissonian
364:Steven Chu
209:ultrashort
177:statistics
112:, and the
106:Niels Bohr
90:Max Planck
52:, such as
3244:NV center
2679:Threshold
2659:No-hiding
2624:Gleason's
2097:Bell test
1952:Equations
1778:Born rule
1490:Particles
1297:Molecular
1198:Acoustics
1191:Continuum
1186:Celestial
1176:Newtonian
1163:Classical
1106:Divisions
860:L. Mandel
562:electrons
490:nonlinear
362:in 1997,
348:in 2001,
334:in 2005,
323:in 2012,
308:in 2022,
295:photonics
140:in 1960.
104:in 1921.
3306:OpenQASM
3282:Transmon
3159:Physical
2959:Quantum
2860:Grover's
2634:Holevo's
2607:Theorems
2557:timeline
2547:NISQ era
2486:Category
2280:Timeline
2032:Ensemble
2012:Bayesian
1974:Majorana
1890:Collapse
1762:Glossary
1745:Timeline
1555:Rotation
1550:Position
1545:Momentum
1056:Quantiki
1029: ·
954:(2014).
596:See also
521:discrete
425:, where
382:Concepts
300:Several
122:hydrogen
114:spectrum
78:momentum
3296:Quantum
3234:Kane QC
3093:Quantum
3021:Quantum
2950:PostBQP
2920:Quantum
2905:Simon's
2698:Quantum
2535:General
2439:Related
2418:History
2157:Science
1989:Rydberg
1740:History
1654:Squeeze
1602:Orbital
1531:Quantum
1457:General
1381:Related
1265:General
1260:Special
1118:Applied
1016: (
987:minutes
864:E. Wolf
566:photons
554:physics
519:with a
429:is the
400:photons
398:called
82:photons
68:History
46:photons
3397:Optics
3314:IBM QX
3310:Qiskit
3249:NMR QC
3227:-based
3131:Steane
3102:Codes
2900:Shor's
2806:SARG04
2614:Bell's
2132:Popper
1632:Optics
1564:Energy
1476:Parity
1292:Atomic
1247:Modern
1097:Major
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654:Optics
406:, the
254:, and
197:Kimble
171:, and
126:matter
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3136:Toric
2579:Qubit
2042:Local
1984:Pauli
1964:Dirac
1597:Total
1050:Qwiki
912:and
681:Notes
582:laser
500:- or
498:super
482:laser
452:maser
448:laser
153:Dirac
120:from
3328:Cirq
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3225:Spin
3121:Shor
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2734:LOCC
1969:Weyl
1607:Spin
1481:Time
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1113:Pure
960:ISBN
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3142:gnu
3106:CSS
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