1798:
1431:
112:
3014:
3038:
Hanbury Brown and Twiss result. But the quantum approach is more than just a fancy way to reproduce the classical result: if the photons are replaced by identical fermions such as electrons, the antisymmetry of wave functions under exchange of particles renders the interference destructive, leading to zero joint detection probability for small detector separations. This effect is referred to as antibunching of fermions. The above treatment also explains
1793:{\displaystyle {\begin{aligned}\langle \Delta i_{1}\Delta i_{2}\rangle &={\big \langle }(i_{1}-\langle i_{1}\rangle )(i_{2}-\langle i_{2}\rangle ){\big \rangle }=\langle i_{1}i_{2}\rangle -{\big \langle }i_{1}\langle i_{2}\rangle {\big \rangle }-{\big \langle }i_{2}\langle i_{1}\rangle {\big \rangle }+\langle i_{1}\rangle \langle i_{2}\rangle \\&=\langle i_{1}i_{2}\rangle -\langle i_{1}\rangle \langle i_{2}\rangle .\end{aligned}}}
2598:
1353:
2564:
1002:
2182:
1084:
2304:
652:
104:, separated by a few meters, were aimed at the star using crude telescopes, and a correlation was observed between the two fluctuating intensities. Just as in the radio studies, the correlation dropped away as they increased the separation (though over meters, instead of kilometers), and they used this information to determine the apparent
1906:
181:, tend to spread apart, leading to FermiāDirac (anti)correlations. BoseāEinstein correlations have been observed between pions, kaons and photons, and FermiāDirac (anti)correlations between protons, neutrons and electrons. For a general introduction in this field, see the textbook on BoseāEinstein correlations by
2609:
The above discussion makes it clear that the
Hanbury Brown and Twiss (or photon bunching) effect can be entirely described by classical optics. The quantum description of the effect is less intuitive: if one supposes that a thermal or chaotic light source such as a star randomly emits photons, then
156:
below) that demonstrated, first, that wave transmission in quantum optics had exactly the same mathematical form as
Maxwell's equations, albeit with an additional noise term due to quantisation at the detector, and second, that according to Maxwell's equations, intensity interferometry should work.
3037:
Fano's explanation nicely illustrates the necessity of considering two-particle amplitudes, which are not as intuitive as the more familiar single-particle amplitudes used to interpret most interference effects. This may help to explain why some physicists in the 1950s had difficulty accepting the
115:
An example of an intensity interferometer that would observe no correlation if the light source is a coherent laser beam, and positive correlation if the light source is a filtered one-mode thermal radiation. The theoretical explanation of the difference between the correlations of photon pairs in
168:
The original experiment used the fact that two bosons tend to arrive at two separate detectors at the same time. Morgan and Mandel used a thermal photon source to create a dim beam of photons and observed the tendency of the photons to arrive at the same time on a single detector. Both of these
1348:{\displaystyle {\begin{aligned}\langle i_{1}i_{2}\rangle (\tau )&=\lim _{T\to \infty }{\frac {1}{T}}\int \limits _{0}^{T}i_{1}(t)i_{2}(t)\,\mathrm {d} t\\&=\lim _{T\to \infty }{\frac {1}{T}}\int \limits _{0}^{T}{\tfrac {1}{4}}E(t)^{2}E(t-\tau )^{2}\,\mathrm {d} t.\end{aligned}}}
2559:{\displaystyle {\begin{aligned}\langle \Delta i_{1}\Delta i_{2}\rangle (\tau )&=\lim _{T\to \infty }{\frac {(E_{0}\delta E)^{2}}{T}}\int \limits _{0}^{T}\sin(\Omega t)\sin(\Omega t-\Phi )\,\mathrm {d} t\\&={\tfrac {1}{2}}(E_{0}\delta E)^{2}\cos(\Omega \tau ),\end{aligned}}}
997:{\displaystyle {\begin{aligned}i_{1}(t)&={\overline {E_{1}(t)^{2}}}={\overline {E(t)^{2}\sin ^{2}(\omega t)}}={\tfrac {1}{2}}E(t)^{2},\\i_{2}(t)&={\overline {E_{2}(t)^{2}}}={\overline {E(t-\tau )^{2}\sin ^{2}(\omega t-\phi )}}={\tfrac {1}{2}}E(t-\tau )^{2},\end{aligned}}}
169:
effects used the wave nature of light to create a correlation in arrival time ā if a single photon beam is split into two beams, then the particle nature of light requires that each photon is only observed at a single detector, and so an anti-correlation was observed in 1977 by
2177:{\displaystyle {\begin{aligned}i_{1}(t)&={\tfrac {1}{2}}E_{0}^{2}+E_{0}\,\delta E\sin(\Omega t)+{\mathcal {O}}(\delta E^{2}),\\i_{2}(t)&={\tfrac {1}{2}}E_{0}^{2}+E_{0}\,\delta E\sin(\Omega t-\Phi )+{\mathcal {O}}(\delta E^{2}),\end{aligned}}}
3042:: if the source consists of a single atom, which can only emit one photon at a time, simultaneous detection in two closely spaced detectors is clearly impossible. Antibunching, whether of bosons or of fermions, has no classical wave analog.
91:
for measuring the tiny angular size of stars, suggesting that it might work with visible light as well. Soon after they successfully tested that suggestion: in 1956 they published an in-lab experimental mockup using blue light from a
2960:
respectively. If the photons are indistinguishable, the two amplitudes interfere constructively to give a joint detection probability greater than that for two independent events. The sum over all possible pairs
581:
1358:
Most modern schemes actually measure the correlation in intensity fluctuations at the two detectors, but it is not too difficult to see that if the intensities are correlated, then the fluctuations
2958:
2907:
2309:
1911:
1436:
1089:
657:
1076:
260:
2257:
1397:
494:
2601:
Photon detections as a function of time for a) antibunching (e.g. light emitted from a single atom), b) random (e.g. a coherent state, laser beam), and c) bunching (chaotic light). Ļ
1898:
2214:
419:
266:
to determine the spaceātime dimensions of the particle emission source for heavy-ion collisions. For developments in this field up to 2005, see for example this review article.
3591:
R. Hanbury Brown; R. Q. Twiss (1957). "Interferometry of the intensity fluctuations in light. I. Basic theory: the correlation between photons in coherent beams of radiation".
1423:
2293:
615:
360:
300:
3763:
P. Grangier; G. Roger; A. Aspect (1986). "Experimental
Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences".
3631:
R. Hanbury Brown; R. Q. Twiss (1958). "Interferometry of the intensity fluctuations in light. II. An experimental test of the theory for partially coherent light".
2587:
1857:
387:
1830:
644:
329:
3665:
3053:) to apply quantum electrodynamics to new situations, many of which had never been experimentally studied, and in which classical and quantum predictions differ.
2985:
3625:
3008:
2856:
2836:
2816:
2796:
2772:
2752:
2732:
2712:
2692:
2672:
2652:
2632:
136:, but there were concerns that the effect should break down at optical wavelengths, since the light would be quantised into a relatively small number of
3072:
586:
The intensity recorded by each detector is the square of the wave amplitude, averaged over a timescale that is long compared to the wave period
2610:
it is not obvious how the photons "know" that they should arrive at a detector in a correlated (bunched) way. A simple argument suggested by
161:
immediately supported the technique, pointing out that the clumping of bosons was simply a manifestation of an effect already known in
3759:ā the cavity-QED equivalent for Kimble & Mandel's free-space demonstration of photon antibunching in resonance fluorescence
148:
worried that the correlation was inconsistent with the laws of thermodynamics. Some even claimed that the effect violated the
502:
3861:
3842:
3819:
2912:
2861:
3916:
3871:
Y. Bromberg; Y. Lahini; E. Small; Y. Silberberg (2010). "Hanbury Brown and Twiss
Interferometry with Interacting Photons".
1029:
201:
3045:
From the point of view of the field of quantum optics, the HBT effect was important to lead physicists (among them
215:
2219:
1361:
427:
3353:
Fano, U. (1961). "Quantum theory of interference effects in the mixing of light from phase independent sources".
3062:
174:
132:
This result was met with much skepticism in the physics community. The radio astronomy result was justified by
3921:
3264:
Richard M. Weiner, Introduction to BoseāEinstein
Correlations and Subatomic Interferometry, John Wiley, 2000.
1862:
186:
2858:(green arrows). The quantum mechanical probability amplitudes for these two possibilities are denoted by
263:
2190:
395:
165:. After a number of experiments, the whole physics community agreed that the observed effect was real.
3478:
E. Brannen; H. Ferguson (1956). "The question of correlation between photons in coherent light beams".
1402:
3926:
3133:
Hanbury Brown, R.; Twiss, R. Q. (1956). "Correlation between
Photons in two Coherent Beams of Light".
275:
178:
44:
3906:
3785:
3693:
2262:
43:
received by two detectors from a beam of particles. HBT effects can generally be attributed to the
589:
334:
84:
56:
3516:
R. Hanbury Brown; R. Q. Twiss (1956). "A Test of a New Type of
Stellar Interferometer on Sirius".
3286:
G. Goldhaber; W. B. Fowler; S. Goldhaber; T. F. Hoang; T. E. Kalogeropoulos; W. M. Powell (1959).
3096:
Hanbury Brown, R.; Twiss, R.Q. (1954). "A new type of interferometer for use in radio astronomy".
3942:
3780:
3688:
3098:
133:
121:
3812:
BOFFIN : A Personal Story of the Early Days of Radar, Radio
Astronomy and Quantum Optics
369:
Since the detectors are separated, say the second detector gets the signal delayed by a time
285:
162:
149:
47:
of the beam, and the results of a given experiment depend on whether the beam is composed of
3711:
3880:
3772:
3726:
3680:
3640:
3600:
3563:
3525:
3487:
3454:
3404:
3362:
3299:
3239:
3189:
2572:
1835:
1020:
372:
158:
101:
76:
3671:
B. L. Morgan; L. Mandel (1966). "Measurement of Photon
Bunching in a Thermal Light Beam".
3439:
3224:
1806:
620:
305:
8:
3554:
E. Purcell (1956). "The
Question of Correlation Between Photons in Coherent Light Rays".
3067:
3039:
2964:
1008:
125:
40:
3917:
https://web.archive.org/web/20070609114114/http://www.du.edu/~jcalvert/astro/starsiz.htm
3884:
3776:
3730:
3710:
Dayan, B.; Parkins, A. S.; Aoki, T.; Ostby, E. P.; Vahala, K. J.; Kimble, H. J. (2008).
3684:
3644:
3604:
3567:
3529:
3512:ā paper which (incorrectly) disputed the existence of the Hanbury Brown and Twiss effect
3491:
3458:
3408:
3366:
3303:
3243:
3193:
2990:
3831:
3798:
3750:
3656:
3616:
3579:
3541:
3503:
3389:
3315:
3205:
3158:
2841:
2821:
2801:
2781:
2757:
2737:
2717:
2697:
2677:
2657:
2637:
2617:
93:
3857:
3838:
3815:
3802:
3742:
3660:
3420:
3150:
3115:
182:
3794:
3754:
3620:
3545:
3319:
3209:
3888:
3790:
3734:
3698:
3648:
3608:
3583:
3571:
3533:
3507:
3495:
3462:
3412:
3370:
3307:
3247:
3197:
3162:
3142:
3107:
1007:
where the overline indicates this time averaging. For wave frequencies above a few
197:
193:
96:, and later in the same year, they applied this technique to measuring the size of
80:
3911:
3416:
152:. Hanbury Brown and Twiss resolved the dispute in a neat series of articles (see
88:
3702:
3466:
3287:
3285:
3251:
3050:
3046:
170:
117:
64:
3311:
3111:
3936:
3892:
3154:
3119:
2614:
in 1961 captures the essence of the quantum explanation. Consider two points
390:
141:
111:
3738:
3177:
2694:
as in the diagram. A joint detection takes place when the photon emitted by
3922:
http://www.2physics.com/2010/11/hanbury-brown-and-twiss-interferometry.html
3746:
3652:
3612:
3424:
2605:
is the coherence time (the time scale of photon or intensity fluctuations).
363:
105:
274:
The HBT effect can, in fact, be predicted solely by treating the incident
189:
in the "trap-and-free fall" analogy of the HBT effect affects comparison.
3870:
3273:
36:
3340:
3013:
1016:
1012:
145:
3575:
3537:
3374:
3201:
3499:
3146:
209:
173:. Finally, bosons have a tendency to clump together, giving rise to
60:
3274:
Comparison of the Hanbury Brown-Twiss effect for bosons and fermions
3033:. The two colors represent two different ways to detect two photons.
2611:
2597:
3907:
http://adsabs.harvard.edu//full/seri/JApA./0015//0000015.000.html
1023:
cannot produce photocurrents that vary on such short timescales.
1015:), such a time averaging is unavoidable, since detectors such as
262:
decay. From then on, the HBT technique started to be used by the
48:
20:
137:
97:
2987:
in the source washes out the interference unless the distance
52:
3762:
204:
and found an unexpected angular correlation among identical
3833:
More Than One Mystery: Explorations in Quantum Interference
3630:
3590:
3515:
279:
205:
3854:
The intensity interferometer; its application to astronomy
3288:"Pion-pion correlations in antiproton annihilation events"
3178:"A Test Of A New Type Of Stellar Interferometer On Sirius"
2298:
The correlation function of these two intensities is then
1078:
of these time-averaged intensities can then be computed:
2654:
in a source that emit photons detected by two detectors
1425:
is the average intensity, ought to be correlated, since
576:{\displaystyle E_{2}(t)=E(t-\tau )\sin(\omega t-\phi ).}
282:. Suppose we have a monochromatic wave with frequency
3712:"A Photon Turnstile Dynamically Regulated by One Atom"
2953:{\displaystyle \langle B|a\rangle \langle A|b\rangle }
2902:{\displaystyle \langle A|a\rangle \langle B|b\rangle }
2491:
2068:
1941:
1274:
951:
781:
331:
that varies on timescales slower than the wave period
63:, although they are also heavily used in the field of
3709:
3670:
3477:
2993:
2967:
2915:
2864:
2844:
2824:
2804:
2784:
2760:
2740:
2720:
2700:
2680:
2660:
2640:
2620:
2575:
2307:
2265:
2222:
2193:
1909:
1865:
1838:
1809:
1434:
1405:
1364:
1087:
1032:
655:
623:
592:
505:
430:
398:
375:
362:. (Such a wave might be produced from a very distant
337:
308:
288:
218:
16:
Quantum correlations related to wave-particle duality
3437:
3222:
55:. Devices which use the effect are commonly called
3830:
3390:"The Fermionic Hanbury Brown and Twiss Experiment"
3175:
3132:
3095:
3002:
2979:
2952:
2901:
2850:
2830:
2810:
2790:
2766:
2746:
2726:
2706:
2686:
2666:
2646:
2626:
2581:
2558:
2287:
2251:
2208:
2176:
1892:
1851:
1824:
1792:
1417:
1391:
1347:
1070:
996:
638:
609:
575:
488:
413:
381:
354:
323:
294:
254:
3828:
3073:Timeline of electromagnetism and classical optics
1071:{\displaystyle \langle i_{1}i_{2}\rangle (\tau )}
3934:
3438:Kimble, H. J.; Dagenais, M.; Mandel, L. (1977).
3223:Kimble, H. J.; Dagenais, M.; Mandel, L. (1977).
2361:
1233:
1135:
3851:
3809:
3440:"Photon antibunching in resonance fluorescence"
3225:"Photon Antibunching in Resonance Fluorescence"
124:"for his contribution to the quantum theory of
3912:http://physicsweb.org/articles/world/15/10/6/1
116:thermal and in laser beams was first given by
3126:
3089:
2569:showing a sinusoidal dependence on the delay
1672:
1639:
1629:
1596:
1557:
1480:
255:{\displaystyle \rho ^{0}\to \pi ^{-}\pi ^{+}}
2947:
2933:
2930:
2916:
2896:
2882:
2879:
2865:
2341:
2312:
2252:{\displaystyle {\mathcal {O}}(\delta E^{2})}
1859:with a small sinusoidally varying component
1780:
1767:
1764:
1751:
1745:
1722:
1709:
1696:
1693:
1680:
1667:
1654:
1624:
1611:
1588:
1565:
1549:
1536:
1514:
1501:
1468:
1439:
1412:
1406:
1392:{\displaystyle \Delta i=i-\langle i\rangle }
1386:
1380:
1115:
1092:
1056:
1033:
489:{\displaystyle E_{1}(t)=E(t)\sin(\omega t),}
3553:
3550:ā experimental demonstration of the effect
3176:Hanbury Brown, R.; Twiss, Dr R.Q. (1956).
617:but short compared to the fluctuations in
200:et al. performed an experiment in 1959 in
3784:
3692:
2592:
2471:
2107:
1980:
1329:
1213:
3387:
3012:
2596:
110:
3935:
2295:, which are small and may be ignored.
1893:{\displaystyle \delta E\sin(\Omega t)}
3352:
1900:, the time-averaged intensities are
302:on two detectors, with an amplitude
39:and anti-correlation effects in the
3929:(Becker & Hickl GmbH, web page)
3025:emit photons detected by detectors
13:
3633:Proceedings of the Royal Society A
3593:Proceedings of the Royal Society A
2540:
2473:
2465:
2456:
2438:
2371:
2328:
2315:
2225:
2209:{\displaystyle \Phi =\Omega \tau }
2200:
2194:
2143:
2132:
2123:
2010:
1996:
1881:
1832:consists mainly of a steady field
1455:
1442:
1365:
1331:
1243:
1215:
1145:
414:{\displaystyle \phi =\omega \tau }
14:
3954:
3900:
1418:{\displaystyle \langle i\rangle }
269:
2259:indicates terms proportional to
100:. In the latter experiment, two
3431:
3381:
366:with a fluctuating intensity.)
185:. A difference in repulsion of
153:
3927:Hanbury-Brown-Twiss Experiment
3388:M. Henny; et al. (1999).
3346:
3326:
3279:
3267:
3258:
3216:
3169:
2940:
2923:
2889:
2872:
2546:
2537:
2522:
2502:
2468:
2453:
2444:
2435:
2399:
2379:
2368:
2350:
2344:
2288:{\displaystyle (\delta E)^{2}}
2276:
2266:
2246:
2230:
2164:
2148:
2135:
2120:
2057:
2051:
2031:
2015:
2002:
1993:
1930:
1924:
1887:
1878:
1819:
1813:
1552:
1520:
1517:
1485:
1320:
1307:
1295:
1288:
1240:
1210:
1204:
1191:
1185:
1142:
1124:
1118:
1065:
1059:
978:
965:
938:
923:
901:
888:
864:
857:
834:
828:
802:
795:
768:
759:
737:
730:
706:
699:
676:
670:
633:
627:
567:
552:
543:
531:
522:
516:
480:
471:
462:
456:
447:
441:
318:
312:
229:
1:
3083:
610:{\displaystyle 2\pi /\omega }
355:{\displaystyle 2\pi /\omega }
3417:10.1126/science.284.5412.296
3078:
1803:In the particular case that
942:
874:
772:
716:
177:, while fermions due to the
59:and were originally used in
7:
3703:10.1103/PhysRevLett.16.1012
3355:American Journal of Physics
3334:Annu. Rev. Nucl. Part. Sci.
3056:
2589:between the two detectors.
120:, who was awarded the 2005
10:
3959:
3829:Mark P. Silverman (1995).
3467:10.1103/PhysRevLett.39.691
3252:10.1103/PhysRevLett.39.691
3063:BoseāEinstein correlations
2734:and the photon emitted by
1011:(wave periods less than a
175:BoseāEinstein correlations
70:
3795:10.1209/0295-5075/1/4/004
3312:10.1103/PhysRevLett.3.181
3112:10.1080/14786440708520475
3010:is sufficiently small.
2798:'s photon is detected by
1026:The correlation function
276:electromagnetic radiation
179:Pauli exclusion principle
57:intensity interferometers
3893:10.1038/nphoton.2010.195
3852:R Hanbury Brown (1974).
3810:R Hanbury Brown (1991).
187:BoseāEinstein condensate
85:intensity interferometer
3739:10.1126/Science.1152261
3447:Physical Review Letters
3232:Physical Review Letters
295:{\displaystyle \omega }
144:in the detectors. Many
35:is any of a variety of
25:Hanbury Brown and Twiss
3653:10.1098/rspa.1958.0001
3613:10.1098/rspa.1957.0177
3099:Philosophical Magazine
3034:
3004:
2981:
2954:
2903:
2852:
2832:
2812:
2792:
2768:
2748:
2728:
2708:
2688:
2668:
2648:
2628:
2606:
2593:Quantum interpretation
2583:
2560:
2428:
2289:
2253:
2210:
2178:
1894:
1853:
1826:
1794:
1419:
1393:
1349:
1272:
1174:
1072:
998:
640:
611:
577:
490:
415:
383:
356:
325:
296:
256:
192:Also, in the field of
129:
122:Nobel Prize in Physics
3016:
3005:
2982:
2955:
2904:
2853:
2833:
2813:
2793:
2769:
2749:
2729:
2709:
2689:
2669:
2649:
2629:
2600:
2584:
2582:{\displaystyle \tau }
2561:
2414:
2290:
2254:
2211:
2179:
1895:
1854:
1852:{\displaystyle E_{0}}
1827:
1795:
1420:
1394:
1350:
1258:
1160:
1073:
1021:photomultiplier tubes
999:
641:
612:
578:
491:
416:
389:, or equivalently, a
384:
382:{\displaystyle \tau }
357:
326:
297:
257:
163:statistical mechanics
150:uncertainty principle
140:that induce discrete
114:
102:photomultiplier tubes
45:waveāparticle duality
2991:
2965:
2913:
2862:
2842:
2822:
2802:
2782:
2758:
2738:
2718:
2698:
2678:
2658:
2638:
2618:
2573:
2305:
2263:
2220:
2191:
1907:
1863:
1836:
1825:{\displaystyle E(t)}
1807:
1432:
1403:
1362:
1085:
1030:
653:
639:{\displaystyle E(t)}
621:
590:
503:
428:
396:
373:
335:
324:{\displaystyle E(t)}
306:
286:
216:
159:Edward Mills Purcell
77:Robert Hanbury Brown
3885:2010NaPho...4..721B
3777:1986EL......1..173G
3765:Europhysics Letters
3731:2008Sci...319.1062D
3725:(5866): 1062ā1065.
3685:1966PhRvL..16.1012M
3645:1958RSPSA.243..291B
3605:1957RSPSA.242..300B
3568:1956Natur.178.1449P
3562:(4548): 1449ā1450.
3530:1956Natur.178.1046H
3524:(4541): 1046ā1048.
3492:1956Natur.178..481B
3459:1977PhRvL..39..691K
3409:1999Sci...284..296H
3367:1961AmJPh..29..539F
3304:1959PhRvL...3..181G
3244:1977PhRvL..39..691K
3194:1956Natur.178.1046H
3188:(4541): 1046ā1048.
3068:Degree of coherence
3040:photon antibunching
2980:{\displaystyle a,b}
2093:
1966:
264:heavy-ion community
134:Maxwell's equations
3866:. ASIN B000LZQD3C.
3035:
3017:Two source points
3003:{\displaystyle AB}
3000:
2977:
2950:
2899:
2848:
2828:
2808:
2788:
2764:
2744:
2724:
2704:
2684:
2664:
2644:
2624:
2607:
2579:
2556:
2554:
2500:
2375:
2285:
2249:
2206:
2174:
2172:
2079:
2077:
1952:
1950:
1890:
1849:
1822:
1790:
1788:
1415:
1389:
1345:
1343:
1283:
1247:
1149:
1068:
994:
992:
960:
790:
636:
607:
573:
486:
411:
379:
352:
321:
292:
252:
208:, discovering the
130:
94:mercury-vapor lamp
3863:978-0-470-10797-3
3844:978-0-387-94376-3
3821:978-0-7503-0130-5
3679:(22): 1012ā1014.
3639:(1234): 291ā319.
3599:(1230): 300ā324.
3576:10.1038/1781449a0
3538:10.1038/1781046a0
3486:(4531): 481ā482.
3403:(5412): 296ā298.
3375:10.1119/1.1937827
3339:, p. 357 (2005),
3332:M. Lisa, et al.,
3202:10.1038/1781046a0
2851:{\displaystyle A}
2831:{\displaystyle b}
2811:{\displaystyle B}
2791:{\displaystyle a}
2767:{\displaystyle B}
2747:{\displaystyle b}
2727:{\displaystyle A}
2707:{\displaystyle a}
2687:{\displaystyle B}
2667:{\displaystyle A}
2647:{\displaystyle b}
2627:{\displaystyle a}
2499:
2412:
2360:
2076:
1949:
1282:
1256:
1232:
1158:
1134:
959:
945:
877:
789:
775:
719:
183:Richard M. Weiner
126:optical coherence
3950:
3896:
3873:Nature Photonics
3867:
3848:
3836:
3825:
3806:
3788:
3758:
3716:
3706:
3696:
3664:
3624:
3587:
3549:
3511:
3500:10.1038/178481a0
3471:
3470:
3444:
3435:
3429:
3428:
3394:
3385:
3379:
3378:
3350:
3344:
3330:
3324:
3323:
3283:
3277:
3271:
3265:
3262:
3256:
3255:
3229:
3220:
3214:
3213:
3173:
3167:
3166:
3147:10.1038/177027a0
3130:
3124:
3123:
3106:(366): 663ā682.
3093:
3009:
3007:
3006:
3001:
2986:
2984:
2983:
2978:
2959:
2957:
2956:
2951:
2943:
2926:
2908:
2906:
2905:
2900:
2892:
2875:
2857:
2855:
2854:
2849:
2837:
2835:
2834:
2829:
2817:
2815:
2814:
2809:
2797:
2795:
2794:
2789:
2773:
2771:
2770:
2765:
2753:
2751:
2750:
2745:
2733:
2731:
2730:
2725:
2713:
2711:
2710:
2705:
2693:
2691:
2690:
2685:
2673:
2671:
2670:
2665:
2653:
2651:
2650:
2645:
2633:
2631:
2630:
2625:
2588:
2586:
2585:
2580:
2565:
2563:
2562:
2557:
2555:
2530:
2529:
2514:
2513:
2501:
2492:
2483:
2476:
2427:
2422:
2413:
2408:
2407:
2406:
2391:
2390:
2377:
2374:
2340:
2339:
2327:
2326:
2294:
2292:
2291:
2286:
2284:
2283:
2258:
2256:
2255:
2250:
2245:
2244:
2229:
2228:
2215:
2213:
2212:
2207:
2183:
2181:
2180:
2175:
2173:
2163:
2162:
2147:
2146:
2106:
2105:
2092:
2087:
2078:
2069:
2050:
2049:
2030:
2029:
2014:
2013:
1979:
1978:
1965:
1960:
1951:
1942:
1923:
1922:
1899:
1897:
1896:
1891:
1858:
1856:
1855:
1850:
1848:
1847:
1831:
1829:
1828:
1823:
1799:
1797:
1796:
1791:
1789:
1779:
1778:
1763:
1762:
1744:
1743:
1734:
1733:
1715:
1708:
1707:
1692:
1691:
1676:
1675:
1666:
1665:
1653:
1652:
1643:
1642:
1633:
1632:
1623:
1622:
1610:
1609:
1600:
1599:
1587:
1586:
1577:
1576:
1561:
1560:
1548:
1547:
1532:
1531:
1513:
1512:
1497:
1496:
1484:
1483:
1467:
1466:
1454:
1453:
1424:
1422:
1421:
1416:
1398:
1396:
1395:
1390:
1354:
1352:
1351:
1346:
1344:
1334:
1328:
1327:
1303:
1302:
1284:
1275:
1271:
1266:
1257:
1249:
1246:
1225:
1218:
1203:
1202:
1184:
1183:
1173:
1168:
1159:
1151:
1148:
1114:
1113:
1104:
1103:
1077:
1075:
1074:
1069:
1055:
1054:
1045:
1044:
1003:
1001:
1000:
995:
993:
986:
985:
961:
952:
946:
941:
919:
918:
909:
908:
883:
878:
873:
872:
871:
856:
855:
845:
827:
826:
810:
809:
791:
782:
776:
771:
755:
754:
745:
744:
725:
720:
715:
714:
713:
698:
697:
687:
669:
668:
645:
643:
642:
637:
616:
614:
613:
608:
603:
582:
580:
579:
574:
515:
514:
495:
493:
492:
487:
440:
439:
420:
418:
417:
412:
388:
386:
385:
380:
361:
359:
358:
353:
348:
330:
328:
327:
322:
301:
299:
298:
293:
261:
259:
258:
253:
251:
250:
241:
240:
228:
227:
198:Gerson Goldhaber
194:particle physics
157:Others, such as
81:Richard Q. Twiss
3958:
3957:
3953:
3952:
3951:
3949:
3948:
3947:
3933:
3932:
3903:
3879:(10): 721ā726.
3864:
3845:
3822:
3814:. Adam Hilger.
3786:10.1.1.178.4356
3714:
3694:10.1.1.713.7239
3673:Phys. Rev. Lett
3666:download as PDF
3626:download as PDF
3474:
3453:(11): 691ā695.
3442:
3436:
3432:
3392:
3386:
3382:
3351:
3347:
3331:
3327:
3292:Phys. Rev. Lett
3284:
3280:
3272:
3268:
3263:
3259:
3238:(11): 691ā695.
3227:
3221:
3217:
3174:
3170:
3141:(4497): 27ā29.
3131:
3127:
3094:
3090:
3086:
3081:
3059:
2992:
2989:
2988:
2966:
2963:
2962:
2939:
2922:
2914:
2911:
2910:
2888:
2871:
2863:
2860:
2859:
2843:
2840:
2839:
2823:
2820:
2819:
2803:
2800:
2799:
2783:
2780:
2779:
2759:
2756:
2755:
2754:is detected by
2739:
2736:
2735:
2719:
2716:
2715:
2714:is detected by
2699:
2696:
2695:
2679:
2676:
2675:
2659:
2656:
2655:
2639:
2636:
2635:
2619:
2616:
2615:
2604:
2595:
2574:
2571:
2570:
2553:
2552:
2525:
2521:
2509:
2505:
2490:
2481:
2480:
2472:
2423:
2418:
2402:
2398:
2386:
2382:
2378:
2376:
2364:
2353:
2335:
2331:
2322:
2318:
2308:
2306:
2303:
2302:
2279:
2275:
2264:
2261:
2260:
2240:
2236:
2224:
2223:
2221:
2218:
2217:
2192:
2189:
2188:
2171:
2170:
2158:
2154:
2142:
2141:
2101:
2097:
2088:
2083:
2067:
2060:
2045:
2041:
2038:
2037:
2025:
2021:
2009:
2008:
1974:
1970:
1961:
1956:
1940:
1933:
1918:
1914:
1910:
1908:
1905:
1904:
1864:
1861:
1860:
1843:
1839:
1837:
1834:
1833:
1808:
1805:
1804:
1787:
1786:
1774:
1770:
1758:
1754:
1739:
1735:
1729:
1725:
1713:
1712:
1703:
1699:
1687:
1683:
1671:
1670:
1661:
1657:
1648:
1644:
1638:
1637:
1628:
1627:
1618:
1614:
1605:
1601:
1595:
1594:
1582:
1578:
1572:
1568:
1556:
1555:
1543:
1539:
1527:
1523:
1508:
1504:
1492:
1488:
1479:
1478:
1471:
1462:
1458:
1449:
1445:
1435:
1433:
1430:
1429:
1404:
1401:
1400:
1363:
1360:
1359:
1342:
1341:
1330:
1323:
1319:
1298:
1294:
1273:
1267:
1262:
1248:
1236:
1223:
1222:
1214:
1198:
1194:
1179:
1175:
1169:
1164:
1150:
1138:
1127:
1109:
1105:
1099:
1095:
1088:
1086:
1083:
1082:
1050:
1046:
1040:
1036:
1031:
1028:
1027:
991:
990:
981:
977:
950:
914:
910:
904:
900:
884:
882:
867:
863:
851:
847:
846:
844:
837:
822:
818:
815:
814:
805:
801:
780:
750:
746:
740:
736:
726:
724:
709:
705:
693:
689:
688:
686:
679:
664:
660:
656:
654:
651:
650:
622:
619:
618:
599:
591:
588:
587:
510:
506:
504:
501:
500:
435:
431:
429:
426:
425:
397:
394:
393:
374:
371:
370:
344:
336:
333:
332:
307:
304:
303:
287:
284:
283:
278:as a classical
272:
246:
242:
236:
232:
223:
219:
217:
214:
213:
89:radio astronomy
83:introduced the
73:
17:
12:
11:
5:
3956:
3946:
3945:
3943:Quantum optics
3931:
3930:
3924:
3919:
3914:
3909:
3902:
3901:External links
3899:
3898:
3897:
3868:
3862:
3849:
3843:
3826:
3820:
3807:
3771:(4): 173ā179.
3760:
3707:
3668:
3628:
3588:
3551:
3513:
3473:
3472:
3430:
3380:
3361:(8): 539ā545.
3345:
3325:
3278:
3266:
3257:
3215:
3168:
3125:
3087:
3085:
3082:
3080:
3077:
3076:
3075:
3070:
3065:
3058:
3055:
3051:Leonard Mandel
3047:Roy J. Glauber
2999:
2996:
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2973:
2970:
2949:
2946:
2942:
2938:
2935:
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2887:
2884:
2881:
2878:
2874:
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2807:
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2743:
2723:
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2567:
2566:
2551:
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2512:
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2199:
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2185:
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2128:
2125:
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2075:
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2001:
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1992:
1989:
1986:
1983:
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1973:
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1695:
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1660:
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1641:
1636:
1631:
1626:
1621:
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1585:
1581:
1575:
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1538:
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1500:
1495:
1491:
1487:
1482:
1477:
1474:
1472:
1470:
1465:
1461:
1457:
1452:
1448:
1444:
1441:
1438:
1437:
1414:
1411:
1408:
1388:
1385:
1382:
1379:
1376:
1373:
1370:
1367:
1356:
1355:
1340:
1337:
1333:
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1322:
1318:
1315:
1312:
1309:
1306:
1301:
1297:
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1265:
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1255:
1252:
1245:
1242:
1239:
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1231:
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1209:
1206:
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1197:
1193:
1190:
1187:
1182:
1178:
1172:
1167:
1163:
1157:
1154:
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1141:
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1126:
1123:
1120:
1117:
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1108:
1102:
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1091:
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1067:
1064:
1061:
1058:
1053:
1049:
1043:
1039:
1035:
1005:
1004:
989:
984:
980:
976:
973:
970:
967:
964:
958:
955:
949:
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937:
934:
931:
928:
925:
922:
917:
913:
907:
903:
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893:
890:
887:
881:
876:
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866:
862:
859:
854:
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833:
830:
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813:
808:
804:
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753:
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560:
557:
554:
551:
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351:
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343:
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317:
314:
311:
291:
271:
270:Wave mechanics
268:
249:
245:
239:
235:
231:
226:
222:
212:, by means of
171:H. Jeff Kimble
142:photoelectrons
118:Roy J. Glauber
72:
69:
65:quantum optics
15:
9:
6:
4:
3:
2:
3955:
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3761:
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106:angular size
74:
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1017:photodiodes
421:; that is,
210:Ļ resonance
108:of Sirius.
87:concept to
41:intensities
37:correlation
3298:(4): 181.
3084:References
1013:picosecond
154:References
146:physicists
3856:. Wiley.
3803:250837011
3781:CiteSeerX
3689:CiteSeerX
3661:121428610
3155:0028-0836
3120:1941-5982
3079:Footnotes
2948:⟩
2934:⟨
2931:⟩
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1997:Ω
1991:
1982:δ
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75:In 1954,
61:astronomy
3937:Category
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3747:18292335
3621:16941860
3546:38235692
3425:10195890
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2612:Ugo Fano
1673:⟩
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1399:, where
202:Berkeley
49:fermions
3881:Bibcode
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3719:Science
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3641:Bibcode
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3163:4224650
138:photons
71:History
21:physics
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