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constant. If, when they are combined, they exhibit perfect constructive interference, perfect destructive interference, or something in-between but with constant phase difference, then it follows that they are perfectly coherent. As will be discussed below, the second wave need not be a separate entity. It could be the first wave at a different time or position. In this case, the measure of correlation is the
2057:, has large spatial coherence because antennas at opposite ends of the array emit with a fixed phase-relationship. Light waves produced by a laser often have high temporal and spatial coherence (though the degree of coherence depends strongly on the exact properties of the laser). Spatial coherence of laser beams also manifests itself as speckle patterns and diffraction fringes seen at the edges of shadow.
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1146:, at any pair of times. Temporal coherence tells us how monochromatic a source is. In other words, it characterizes how well a wave can interfere with itself at a different time. The delay over which the phase or amplitude wanders by a significant amount (and hence the correlation decreases by significant amount) is defined as the
1516:. At any particular time the red and green waves are uncorrelated; one oscillates while the other is constant and so there will be no interference at this delay. Another way of looking at this is the wavepackets are not overlapped in time and so at any particular time there is only one nonzero field so no interference can occur.
2300:, which is the direction in which the electric or magnetic field oscillates. Unpolarized light is composed of incoherent light waves with random polarization angles. The electric field of the unpolarized light wanders in every direction and changes in phase over the coherence time of the two light waves. An absorbing
1686:
in the extent of a wave to interfere when averaged over time. More precisely, the spatial coherence is the cross-correlation between two points in a wave for all times. If a wave has only 1 value of amplitude over an infinite length, it is perfectly spatially coherent. The range of separation between
900:
function. Cross-correlation quantifies the ability to predict the phase of the second wave by knowing the phase of the first. As an example, consider two waves perfectly correlated for all times (by using a monochromatic light source). At any time, the phase difference between the two waves will be
2401:
are examples of highly coherent quantum systems whose effects are evident at the macroscopic scale. The macroscopic quantum coherence (off-diagonal long-range order, ODLRO) for superfluidity, and laser light, is related to first-order (1-body) coherence/ODLRO, while superconductivity is related to
1524:
Figure 4: The time-averaged intensity (blue) detected at the output of an interferometer plotted as a function of delay Ï for the example waves in
Figures 2 and 3. As the delay is changed by half a period, the interference switches between constructive and destructive. The black lines indicate the
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with atoms in place of light waves, a sufficiently collimated atomic beam creates a coherent atomic wave-function illuminating both slits. Each slit acts as a separate but in-phase beam contributing to the intensity pattern on a screen. These two contributions give rise to an intensity pattern of
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If the electric field wanders by a smaller amount the light will be partially polarized so that at some angle, the polarizer will transmit more than half the intensity. If a wave is combined with an orthogonally polarized copy of itself delayed by less than the coherence time, partially polarized
993:
of the light. Most of the concepts involving coherence which will be introduced below were developed in the field of optics and then used in other fields. Therefore, many of the standard measurements of coherence are indirect measurements, even in fields where the wave can be measured directly.
2353:
As with light, transverse coherence (across the direction of propagation) of matter waves is controlled by collimation. Because light, at all frequencies, travels the same velocity, longitudinal and temporal coherence are linked; in matter waves these are independent. In matter waves, velocity
607:
signals, respectively. For instance, if the signals are functions of time, the cross-correlation is a measure of the similarity of the two signals as a function of the time lag relative to each other and the autocorrelation is a measure of the similarity of each signal with itself in different
90:
Two slits illuminated by one source show an interference pattern. The source is far to the left in the diagram, behind collimators that create a parallel beam. This combination ensures that a wave from the source strikes both slits at the same part of the wave cycle: the wave will have
1998:
Consider a tungsten light-bulb filament. Different points in the filament emit light independently and have no fixed phase-relationship. In detail, at any point in time the profile of the emitted light is going to be distorted. The profile will change randomly over the coherence time
1983:
Figure 9: A wave with infinite coherence area is combined with a spatially shifted copy of itself. Some sections in the wave interfere constructively and some will interfere destructively. Averaging over these sections, a detector with length D will measure reduced
666:
are functions of space, the cross-correlation measures the similarity of two signals in different points in space and the autocorrelations the similarity of the signal relative to itself for a certain separation distance. In that case, coherence is a function of
134:, if the space between the two slits is increased, the coherence dies gradually and finally the fringes disappear, showing spatial coherence. In both cases, the fringe amplitude slowly disappears, as the path difference increases past the coherence length.
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state, can be made to flow and behave as a coherent beam as occurs in a laser. Moreover, the coherence properties of the output light from multimode nonlinear optical structures were found to obey the optical thermodynamic theory.
2425:
and co-workers constructed an operational formulation of quantum coherence as a resource theory. They introduced coherence monotones analogous to the entanglement monotones. Quantum coherence has been shown to be equivalent to
1585:. Since for most natural light sources, the coherence time is much shorter than the time resolution of any detector, the detector itself does the time averaging. Consider the example shown in Figure 3. At a fixed delay, here
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Finally, white light, which has a very broad range of frequencies, is a wave which varies quickly in both amplitude and phase. Since it consequently has a very short coherence time (just 10 periods or so), it is often called
407:
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130:, when one of the mirrors is moved away gradually from the beam-splitter, the time for the beam to travel increases and the fringes become dull and finally disappear, showing temporal coherence. Similarly, in a
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a copy of the red wave; both are monochromatic waves with slightly different frequencies. A proper figure would be a combination of a chirp wave and its delayed copy to match the figure and the current figure
2315:. For polarized light the end of the vector lies on the surface of the sphere, whereas the vector has zero length for unpolarized light. The vector for partially polarized light lies within the sphere.
78:
is given by means of correlation functions. More generally, coherence describes the statistical similarity of a field (electromagnetic field, quantum wave packet etc.) at two points in space or time.
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creation of uniquely quantum coherence analysis. Classical optical coherence becomes a classical limit for first-order quantum coherence; higher degree of coherence leads to many phenomena in
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bright bands due to constructive interference, interlaced with dark bands due to destructive interference, on a downstream screen. Many variations of this experiment have been demonstrated.
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Coherence is used to check the quality of the transfer functions (FRFs) being measured. Low coherence can be caused by poor signal to noise ratio, and/or inadequate frequency resolution.
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In system with macroscopic waves, one can measure the wave directly. Consequently, its correlation with another wave can simply be calculated. However, in optics one cannot measure the
2333:, wave interference, relies on coherence. While initially patterned after optical coherence, the theory and experimental understanding of quantum coherence greatly expanded the topic.
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is the relevant type of coherence for the Young's double-slit interferometer. It is also used in optical imaging systems and particularly in various types of astronomy telescopes.
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LEDs are characterized by Îλ â 50 nm, and tungsten filament lights exhibit Îλ â 600 nm, so these sources have shorter coherence times than the most monochromatic lasers.
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the output, the coherence function will be unitary all over the spectrum. However, if non-linearities are present in the system the coherence will vary in the limit given above.
3039:
Hodgman, S. S.; Dall, R. G.; Manning, A. G.; Baldwin, K. G. H.; Truscott, A. G. (2011). "Direct
Measurement of Long-Range Third-Order Coherence in Bose-Einstein Condensates".
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out of the pinhole. Far from the pinhole the emerging spherical wavefronts are approximately flat. The coherence area is now infinite while the coherence length is unchanged.
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the wave can interfere perfectly with its delayed copy. But, since half the time the red and green waves are in phase and half the time out of phase, when averaged over
2064:, produced successful holograms more than ten years before lasers were invented. To produce coherent light he passed the monochromatic light from an emission line of a
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In some systems, such as water waves or optics, wave-like states can extend over one or two dimensions. Spatial coherence describes the ability for two spatial points
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A wave containing only a single frequency (monochromatic) is perfectly correlated with itself at all time delays, in accordance with the above relation. (See Figure 1)
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67:. Constructive or destructive interference are limit cases, and two waves always interfere, even if the result of the addition is complicated or not remarkable.
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1433:) of waves, which naturally have a broad range of frequencies, also have a short coherence time since the amplitude of the wave changes quickly. (See Figure 3)
74:, which looks at the size of the interference fringes relative to the input waves (as the phase offset is varied); a precise mathematical definition of the
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in the sense that coherence can be faithfully described as entanglement, and conversely that each entanglement measure corresponds to a coherence measure.
2112:). Conversely, if waves of different frequencies are not coherent, then, when combined, they create a wave that is continuous in time (e.g. white light or
2409:
The classical electromagnetic field exhibits macroscopic quantum coherence. The most obvious example is the carrier signal for radio and TV. They satisfy
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Waves of different frequencies (in light these are different colours) can interfere to form a pulse if they have a fixed relative phase-relationship (see
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of the light exiting the interferometer. The resulting visibility of the interference pattern (e.g. see Figure 4) gives the temporal coherence at delay
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Sometimes people also use "spatial coherence" to refer to the visibility when a wave-like state is combined with a spatially shifted copy of itself.
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1745:, often a feature of a source, is usually an industrial term related to the coherence time of the source, not the coherence area in the medium).
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can easily produce light with coherence lengths of 300 m. Not all lasers have a high monochromaticity, however (e.g. for a mode-locked
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describes the correlation (or predictable relationship) between waves at different points in space, either lateral or longitudinal.
63:) or subtract from each other to create a wave of minima which may be zero (destructive interference), depending on their relative
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second-order coherence/ODLRO. (For fermions, such as electrons, only even orders of coherence/ODLRO are possible.) For bosons, a
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2490:(interpretation: density of the probability amplitude). Here the applications concern, among others, the future technologies of
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The larger the bandwidth â range of frequencies Îf a wave contains â the faster the wave decorrelates (and hence the smaller
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The coherence time is not the time duration of the signal; the coherence length differs from the coherence area (see below).
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3642:
3414:
Yang, C.N. (1962). "Concept of Off-Diagonal Long-Range Order and the
Quantum Phases of Liquid He and of Superconductors".
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Selim, Mahmoud A.; Wu, Fan O.; Pyrialakos, Georgios G.; Khajavikhan, Mercedeh; Christodoulides, Demetrios (2023-03-01).
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pattern requires that both slits be illuminated by a coherent wave as illustrated in the figure. Large sources without
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is an example of a system exhibiting macroscopic quantum coherence through a multiple occupied single-particle state.
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Figure 11: Spectrally incoherent light interferes to form continuous light with a randomly varying phase and amplitude
3924:
677:
3125:"Coherence properties of light in highly multimoded nonlinear parabolic fibers under optical equilibrium conditions"
2915:
Peng, J.-L.; Liu, T.-A.; Shu, R.-H. (2008). "Optical frequency counter based on two mode-locked fiber laser combs".
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Two waves with constant relative phase will be coherent. The amount of coherence can readily be measured by the
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Temporal coherence is the measure of the average correlation between the value of a wave and itself delayed by
1030:(blue). The coherence time of the wave is infinite since it is perfectly correlated with itself for all delays
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include holography. Holographic photographs have been used as art and as difficult to forge security labels.
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When interfering, two waves add together to create a wave of greater amplitude than either one (constructive
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2459:. In quantum mechanics for example one considers a probability field, which is related to the wave function
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1529:. Although the waves in Figures 2 and 3 have different time durations, they have the same coherence time.
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2354:(energy) selection controls longitudinal coherence and pulsing or chopping controls temporal coherence.
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the two points over which there is significant interference defines the diameter of the coherence area,
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describes the correlation between waves observed at different moments in time. Both are observed in the
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Coherence controls the visibility or contrast of interference patterns. For example, visibility of the
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2574: â Application of quantum mechanics and theoretical chemistry to biological objects and problems
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Figure 8: A wave with finite coherence area is incident on a pinhole (small aperture). The wave will
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directly as it oscillates much faster than any detector's time resolution. Instead, one measures the
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Figure 10: Waves of different frequencies interfere to form a localized pulse if they are coherent.
1608:, an infinitely fast detector would measure an intensity that fluctuates significantly over a time
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Principles of optics: electromagnetic theory of propagation, interference and diffraction of light
2586: â Fundamental physics principle stating that physical solutions of linear systems are linear
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from a single source always interfere. Wave sources are not strictly monochromatic: they may be
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rotated to any angle will always transmit half the incident intensity when averaged over time.
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have long coherence lengths (up to hundreds of meters). For example, a stabilized and monomode
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Tan, K.C.; Jeong, H. (2018). "Entanglement as the
Symmetric Portion of Correlated Coherence".
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Conversely, a wave whose phase drifts quickly will have a short coherence time. (See Figure 2)
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595:, respectively. The cross-spectral density and the power spectral density are defined as the
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The coherence of two waves expresses how well correlated the waves are as quantified by the
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is small, the filament is considered a spatially incoherent source. In contrast, a radio
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instants of time. In this case the coherence is a function of frequency. Analogously, if
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the degree of coherence is perfect, whereas it drops significantly as the delay passes
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2525: â Distance over which a propagating wave maintains a certain degree of coherence
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Figure 3: The amplitude of a wavepacket whose amplitude changes significantly in time
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1541:. In these devices, a wave is combined with a copy of itself that is delayed by time
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This figure needs to be changed because, in this figure, the green wave is actually
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Figure 6: A wave with a varying profile (wavefront) and infinite coherence length.
3379:
Penrose, O.; Onsager, L. (1956). "Bose-Einstein
Condensation and Liquid Helium".
3215:
2645:
402:{\displaystyle \gamma _{xy}^{2}(f)={\frac {|S_{xy}(f)|^{2}}{S_{xx}(f)S_{yy}(f)}}}
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1966:
1951:
Figure 7: A wave with a varying profile (wavefront) and finite coherence length.
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of the power spectrum (the intensity of each frequency) to its autocorrelation.
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17:
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1889:{\displaystyle A_{\mathrm {c} }={\frac {\lambda ^{2}z^{2}}{A_{\mathrm {s} }}}}
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it means that the signals are perfectly correlated or linearly related and if
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165:. The property of coherence is the basis for commercial applications such as
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Cronin, Alexander D.; Schmiedmayer, Jörg; Pritchard, David E. (2009-07-28).
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Holography requires temporally and spatially coherent light. Its inventor,
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In optics, temporal coherence is measured in an interferometer such as the
1058:
Figure 2: The amplitude of a wave whose phase drifts significantly in time
917:
These states are unified by the fact that their behavior is described by a
107:
or sources that mix many different frequencies will have lower visibility.
2250:) then the pulse will have the minimum time duration for its bandwidth (a
2204:
which follows from the properties of the
Fourier transform and results in
1456:
3449:
Baumgratz, T.; Cramer, M.; Plenio, M.B. (2014). "Quantifying
Coherence".
2706:(6. ed., reprinted (with corrections) ed.). Oxford: Pergamon Press.
1006:
Figure 1: The amplitude of a single frequency wave as a function of time
975:
3307:
2341:
The simplest extension of optical coherence applies optical concepts to
1054:
3188:
Streltsov, Alexander; Adesso, Gerardo; Plenio, Martin B. (2017-10-30).
86:
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2280:
spectral phase interferometry for direct electric-field reconstruction
2498:. Additionally the problems of the following subchapter are treated.
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they are totally uncorrelated. If a linear system is being measured,
146:
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1448:, in its classical version, uses light with a short coherence time.
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2753:
Fundamentals of signal processing for sound and vibration engineers
2311:
The polarization of a light beam is represented by a vector in the
3463:
2558: â Electromagnetic radiation with a single constant frequency
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Introduction to the theory of coherence and polarization of light
2546: â Interaction of a quantum system with a classical observer
979:
3591:
2531: â Specific quantum state of a quantum harmonic oscillator
2519: â Type of state of an atom-electromagnetic field system
2455:
Further applications concern the coherent superposition of
2894:(4th ed.). United States of America: Addison Wesley.
2731:(3rd ed.). Addison Wesley Longman. pp. 554â574.
2385:
quantum coherence leads to novel phenomena, the so-called
2266:
Measurement of the spectral coherence of light requires a
149:
but is now used in any field that involves waves, such as
909:). Degree of correlation involves correlation functions.
1444:
requires light with a long coherence time. In contrast,
3018:(1st ed.). Wiley-Interscience. pp. 210, 221.
2646:"Article on Coherence in the RP Photonics Encyclopedia"
2588:
Pages displaying short descriptions of redirect targets
2533:
Pages displaying short descriptions of redirect targets
2026:. Since for a white-light source such as a light-bulb
137:
Coherence was originally conceived in connection with
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If the phase depends linearly on the frequency (i.e.
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The relationship between coherence time and bandwidth
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3283:"Optics and interferometry with atoms and molecules"
2366:â correlation of light upon coincidence â triggered
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is defined as the distance the wave travels in time
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3190:"Colloquium : Quantum coherence as a resource"
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2139:is limited by the spectral bandwidth of the light
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2018:
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1632:. In this case, to find the temporal coherence at
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1797:away from an incoherent source with surface area
1664:, one would manually time-average the intensity.
723:{\displaystyle 0\leq \gamma _{xy}^{2}(f)\leq 1}
2765:Rolf G. Winter; Aephraim M. Steinberg (2008).
2552: â Theoretical problem in quantum physics
2540: â The spectral linewidth of a laser beam
2208:(for quantum particles it also results in the
110:Coherence contains several distinct concepts.
3603:
2270:optical interferometer, such as an intensity
1489:(red) and a copy of the same wave delayed by
1091:(red) and a copy of the same wave delayed by
1010:(red) and a copy of the same wave delayed by
8:
3248:Adams, C.S; Sigel, M; Mlynek, J (May 1994).
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52:. Beams from different sources are mutually
1375:{\displaystyle \tau _{c}\Delta f\gtrsim 1.}
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1232:{\displaystyle \tau =\tau _{\mathrm {c} }}
1122:any interference disappears at this delay.
3523:
3462:
3355:
3340:"The Quantum Theory of Optical Coherence"
3306:
3265:
3205:
3140:
2673:. Cambridge: Cambridge University Press.
2472:
2464:
2220:
2170:
2144:
2121:
2037:
2031:
2010:
2004:
1877:
1876:
1865:
1855:
1848:
1838:
1837:
1831:
1809:
1808:
1802:
1782:
1757:
1756:
1750:
1728:
1727:
1721:
1699:
1698:
1692:
1647:
1646:
1637:
1617:
1590:
1570:
1546:
1494:
1472:
1471:
1465:
1354:
1348:
1323:
1322:
1316:
1283:
1282:
1276:
1254:
1253:
1247:
1222:
1221:
1209:
1183:
1161:
1160:
1154:
1131:
1096:
1070:
1069:
1063:
1035:
1015:
864:
835:
799:
791:
785:
749:
741:
735:
699:
691:
679:
642:
613:
571:
542:
505:
499:
466:
460:
423:
417:
378:
356:
344:
339:
320:
311:
308:
290:
282:
276:
244:
215:
40:expresses the potential for two waves to
3243:
3241:
2960:Christopher Gerry; Peter Knight (2005).
2494:and the already available technology of
1919:Figure 5: A plane wave with an infinite
1561:. A detector measures the time-averaged
1419:Examples of temporal coherence include:
1001:
2600:
1905:
1525:interference envelope, which gives the
126:. Once the fringes are obtained in the
3094:"Cool laser makes atoms march in time"
2580: â Quantum measurement phenomenon
2193:{\displaystyle \Delta f\Delta t\geq 1}
2116:). The temporal duration of the pulse
2071:In February 2011 it was reported that
1512:(green) plotted as a function of time
2413:'s quantum description of coherence.
2254:pulse), otherwise it is chirped (see
1657:{\displaystyle 2\tau _{\mathrm {c} }}
823:{\displaystyle \gamma _{xy}^{2}(f)=0}
773:{\displaystyle \gamma _{xy}^{2}(f)=1}
674:The coherence varies in the interval
7:
2856:Elements of Optical Coherence Theory
2827:Optical Coherence and Quantum Optics
1482:{\displaystyle \tau _{\mathrm {c} }}
1333:{\displaystyle \tau _{\mathrm {c} }}
1293:{\displaystyle \tau _{\mathrm {c} }}
1171:{\displaystyle \tau _{\mathrm {c} }}
1080:{\displaystyle \tau _{\mathrm {c} }}
186:Astronomical optical interferometers
27:Potential for two waves to interfere
2483:{\displaystyle \psi (\mathbf {r} )}
2345:. For example, when performing the
2243:{\displaystyle \theta (f)\propto f}
2825:Leonard Mandel; Emil Wolf (1995).
2329:The signature property of quantum
2206:KĂŒpfmĂŒller's uncertainty principle
2178:
2172:
2146:
2123:
2088:Spectral coherence of short pulses
2068:through a pinhole spatial filter.
1878:
1839:
1810:
1758:
1729:
1700:
1648:
1473:
1389:in mathematics, which relates the
1360:
1324:
1284:
1255:
1223:
1162:
1071:
25:
2276:frequency-resolved optical gating
2262:Measurement of spectral coherence
1452:Measurement of temporal coherence
925:Waves in a rope (up and down) or
4379:
4378:
3092:Pincock, S. (25 February 2011).
2544:Measurement in quantum mechanics
2473:
2210:Heisenberg uncertainty principle
1975:
1957:
1943:
1929:
1911:
1819:{\displaystyle A_{\mathrm {s} }}
1767:{\displaystyle A_{\mathrm {c} }}
1738:{\displaystyle l_{\mathrm {c} }}
1709:{\displaystyle A_{\mathrm {c} }}
1408:, Îλ â 2 nm â 70 nm).
1385:Formally, this follows from the
1264:{\displaystyle L_{\mathrm {c} }}
1114:(green). At any particular time
921:or some generalization thereof.
2417:Quantum coherence as a resource
974:associated with, for examples,
184:and telescope interferometers (
124:Young's interference experiment
4328:Relativistic quantum mechanics
3542:10.1103/PhysRevLett.121.220401
3481:10.1103/physrevlett.113.140401
3338:Glauber, Roy J. (1963-06-15).
2964:. Cambridge University Press.
2755:. John Wiley & Sons, 2008.
2702:Born, Max; Wolf, Emil (1993).
2477:
2469:
2364:Hanbury Brown and Twiss effect
2231:
2225:
1415:Examples of temporal coherence
875:
869:
846:
840:
811:
805:
761:
755:
711:
705:
653:
647:
624:
618:
582:
576:
553:
547:
520:
514:
481:
475:
438:
432:
393:
387:
371:
365:
340:
335:
329:
312:
302:
296:
255:
249:
226:
220:
1:
4306:Quantum statistical mechanics
4083:Quantum differential calculus
4005:Delayed-choice quantum eraser
3773:Symmetry in quantum mechanics
2387:macroscopic quantum phenomena
2378:Macroscopic quantum coherence
3267:10.1016/0370-1573(94)90066-3
3216:10.1103/RevModPhys.89.041003
2567:Optical heterodyne detection
1988:. For example, a misaligned
1446:optical coherence tomography
913:Examples of wave-like states
182:optical coherence tomography
4108:Quantum stochastic calculus
4098:Quantum measurement problem
4020:MachâZehnder interferometer
3575:Dr. SkySkull (2008-09-03).
2962:Introductory Quantum Optics
2798:The Quantum Theory of Light
2443:Coherent superpositions of
1990:MachâZehnder interferometer
1539:MachâZehnder interferometer
929:(compression and expansion)
905:function (sometimes called
120:MichelsonâMorley experiment
4441:
3577:"Optics basics: Coherence"
3299:10.1103/RevModPhys.81.1051
2831:Cambridge University Press
2621:Cambridge University Press
2322:
2289:
2286:Polarization and coherence
199:
29:
4374:
4168:Quantum complexity theory
4146:Quantum cellular automata
3836:Path integral formulation
3436:10.1103/revmodphys.34.694
3287:Reviews of Modern Physics
3194:Reviews of Modern Physics
3001:Fundamentals of Photonics
2939:10.1007/s00340-008-3111-6
2650:RP Photonics Encyclopedia
2562:Mutual coherence function
2046:{\displaystyle \tau _{c}}
2019:{\displaystyle \tau _{c}}
892:Coherence and correlation
526:{\displaystyle S_{yy}(f)}
487:{\displaystyle S_{xx}(f)}
444:{\displaystyle S_{xy}(f)}
4235:Quantum machine learning
4215:Quantum key distribution
4205:Quantum image processing
4195:Quantum error correction
4045:Wheeler's delayed choice
3357:10.1103/PhysRev.130.2529
2854:Arvind Marathay (1982).
2783:10.1036/1097-8542.146900
2613:M.Born; E. Wolf (1999).
2404:BoseâEinstein condensate
2155:{\displaystyle \Delta f}
2132:{\displaystyle \Delta t}
2081:BoseâEinstein condensate
1535:Michelson interferometer
128:Michelson interferometer
4425:Radar signal processing
4151:Quantum finite automata
3401:10.1103/physrev.104.576
3063:10.1126/science.1198481
2802:Oxford University Press
2796:Loudon, Rodney (2000).
2556:Monochromatic radiation
2457:non-optical wave fields
2451:Non-optical wave fields
1986:interference visibility
1197:{\displaystyle \tau =0}
196:Mathematical definition
72:interference visibility
4255:Quantum neural network
2890:Hecht, Eugene (2002).
2484:
2347:double-slit experiment
2244:
2194:
2156:
2133:
2105:
2097:
2075:atoms, cooled to near
2047:
2020:
1890:
1820:
1791:
1768:
1739:
1710:
1658:
1626:
1602:
1601:{\displaystyle 2\tau }
1579:
1555:
1530:
1517:
1506:
1505:{\displaystyle 2\tau }
1483:
1376:
1334:
1294:
1265:
1233:
1198:
1172:
1140:
1123:
1108:
1107:{\displaystyle 2\tau }
1087:as a function of time
1081:
1051:
1044:
1024:
882:
853:
824:
774:
724:
660:
631:
589:
560:
527:
488:
453:cross-spectral density
445:
403:
262:
233:
155:electrical engineering
143:double-slit experiment
132:double-slit experiment
101:double slit experiment
96:
4280:Quantum teleportation
3793:Waveâparticle duality
2860:John Wiley & Sons
2485:
2362:The discovery of the
2337:Matter wave coherence
2323:Further information:
2290:Further information:
2245:
2195:
2157:
2134:
2103:
2095:
2048:
2021:
1891:
1821:
1792:
1769:
1740:
1711:
1659:
1627:
1625:{\displaystyle \tau }
1603:
1580:
1578:{\displaystyle \tau }
1556:
1554:{\displaystyle \tau }
1523:
1507:
1484:
1459:
1377:
1335:
1295:
1266:
1234:
1199:
1173:
1141:
1139:{\displaystyle \tau }
1109:
1082:
1057:
1045:
1043:{\displaystyle \tau }
1025:
1023:{\displaystyle \tau }
1005:
883:
854:
825:
775:
725:
671:(spatial frequency).
661:
632:
590:
561:
528:
489:
446:
404:
263:
234:
200:Further information:
89:
4311:Quantum field theory
4240:Quantum metamaterial
4185:Quantum cryptography
3915:Consistent histories
2751:Shin. K, Hammond. J.
2644:Rudiger, Paschotta.
2616:Principles of Optics
2496:quantum cryptography
2463:
2428:quantum entanglement
2389:. For instance, the
2219:
2169:
2143:
2120:
2030:
2003:
1830:
1801:
1781:
1749:
1720:
1691:
1636:
1616:
1589:
1569:
1545:
1493:
1464:
1347:
1315:
1275:
1246:
1208:
1182:
1153:
1130:
1095:
1062:
1034:
1014:
941:signals (fields) in
881:{\displaystyle y(t)}
863:
859:being the input and
852:{\displaystyle x(t)}
834:
784:
734:
678:
659:{\displaystyle y(t)}
641:
630:{\displaystyle x(t)}
612:
588:{\displaystyle y(t)}
570:
559:{\displaystyle x(t)}
541:
498:
459:
416:
275:
261:{\displaystyle y(t)}
243:
232:{\displaystyle x(t)}
214:
210:between two signals
30:For other uses, see
4405:Concepts in physics
4296:Quantum fluctuation
4265:Quantum programming
4225:Quantum logic gates
4210:Quantum information
4190:Quantum electronics
3650:Classical mechanics
3581:Skulls in the Stars
3534:2018PhRvL.121v0401T
3473:2014PhRvL.113n0401B
3428:1962RvMP...34..694Y
3393:1956PhRv..104..576P
3055:2011Sci...331.1046H
3049:(6020): 1046â1049.
2931:2008ApPhB..92..513P
2669:Wolf, Emil (2007).
2578:Quantum Zeno effect
2550:Measurement problem
2445:optical wave fields
2325:Quantum decoherence
1527:degree of coherence
1429:Similarly, pulses (
1387:convolution theorem
804:
754:
704:
295:
202:Degree of coherence
82:Qualitative concept
76:degree of coherence
46:monochromatic beams
4349:in popular culture
4131:Quantum algorithms
3979:Von NeumannâWigner
3959:Objective collapse
3655:Old quantum theory
3016:Statistical Optics
2584:Wave superposition
2480:
2308:light is created.
2272:optical correlator
2240:
2190:
2152:
2129:
2106:
2098:
2066:mercury-vapor lamp
2043:
2016:
1886:
1816:
1787:
1764:
1735:
1716:(Coherence length
1706:
1654:
1622:
1598:
1575:
1551:
1531:
1518:
1502:
1479:
1372:
1330:
1290:
1261:
1229:
1194:
1168:
1136:
1124:
1104:
1077:
1052:
1040:
1020:
998:Temporal coherence
943:transmission lines
878:
849:
820:
787:
770:
737:
720:
687:
656:
627:
597:Fourier transforms
585:
556:
523:
484:
455:of the signal and
441:
399:
278:
258:
229:
208:coherence function
116:Temporal coherence
97:
4420:Quantum mechanics
4392:
4391:
4366:Quantum mysticism
4344:Schrödinger's cat
4275:Quantum simulator
4245:Quantum metrology
4173:Quantum computing
4136:Quantum amplifier
4113:Quantum spacetime
4078:Quantum cosmology
4068:Quantum chemistry
3768:Scattering theory
3716:Zero-point energy
3711:Degenerate levels
3619:Quantum mechanics
3151:10.1364/OL.483282
3025:978-0-471-01502-4
2971:978-0-521-52735-4
2918:Applied Physics B
2901:978-0-8053-8566-3
2869:978-0-471-56789-9
2840:978-0-521-41711-2
2811:978-0-19-850177-0
2738:978-0-201-83887-9
2713:978-0-08-026481-3
2680:978-0-521-82211-4
2630:978-0-521-64222-4
2492:quantum computing
2395:superconductivity
2383:Macroscopic scale
2319:Quantum coherence
2296:Light also has a
2292:Unpolarized light
2252:transform-limited
2110:Fourier transform
1993:
1970:
1952:
1938:
1924:
1907:Spatial coherence
1884:
1790:{\displaystyle z}
1668:Spatial coherence
1406:Ti-sapphire laser
1402:heliumâneon laser
1396:Narrow bandwidth
1391:Fourier transform
898:cross-correlation
601:cross-correlation
397:
163:quantum mechanics
112:Spatial coherence
16:(Redirected from
4432:
4382:
4381:
4093:Quantum geometry
4088:Quantum dynamics
3945:Superdeterminism
3877:RaritaâSchwinger
3826:Matrix mechanics
3681:Braâket notation
3612:
3605:
3598:
3589:
3584:
3562:
3561:
3527:
3507:
3501:
3500:
3466:
3446:
3440:
3439:
3411:
3405:
3404:
3376:
3370:
3369:
3359:
3350:(6): 2529â2539.
3335:
3329:
3328:
3310:
3293:(3): 1051â1129.
3278:
3272:
3271:
3269:
3245:
3236:
3235:
3209:
3185:
3179:
3178:
3144:
3135:(5): 1208â1211.
3120:
3114:
3113:
3111:
3110:
3089:
3083:
3082:
3036:
3030:
3029:
3014:Goodman (1985).
3011:
3005:
3004:
2996:
2990:
2982:
2976:
2975:
2957:
2951:
2950:
2912:
2906:
2905:
2887:
2874:
2873:
2851:
2845:
2844:
2822:
2816:
2815:
2793:
2787:
2786:
2762:
2756:
2749:
2743:
2742:
2724:
2718:
2717:
2699:
2693:
2692:
2666:
2660:
2659:
2657:
2656:
2641:
2635:
2634:
2619:(7th ed.).
2610:
2589:
2534:
2523:Coherence length
2517:Atomic coherence
2489:
2487:
2486:
2481:
2476:
2249:
2247:
2246:
2241:
2199:
2197:
2196:
2191:
2161:
2159:
2158:
2153:
2138:
2136:
2135:
2130:
2052:
2050:
2049:
2044:
2042:
2041:
2025:
2023:
2022:
2017:
2015:
2014:
1982:
1979:
1964:
1961:
1950:
1947:
1936:
1933:
1921:coherence length
1918:
1915:
1895:
1893:
1892:
1887:
1885:
1883:
1882:
1881:
1871:
1870:
1869:
1860:
1859:
1849:
1844:
1843:
1842:
1825:
1823:
1822:
1817:
1815:
1814:
1813:
1796:
1794:
1793:
1788:
1773:
1771:
1770:
1765:
1763:
1762:
1761:
1744:
1742:
1741:
1736:
1734:
1733:
1732:
1715:
1713:
1712:
1707:
1705:
1704:
1703:
1663:
1661:
1660:
1655:
1653:
1652:
1651:
1631:
1629:
1628:
1623:
1607:
1605:
1604:
1599:
1584:
1582:
1581:
1576:
1560:
1558:
1557:
1552:
1511:
1509:
1508:
1503:
1488:
1486:
1485:
1480:
1478:
1477:
1476:
1381:
1379:
1378:
1373:
1359:
1358:
1339:
1337:
1336:
1331:
1329:
1328:
1327:
1299:
1297:
1296:
1291:
1289:
1288:
1287:
1270:
1268:
1267:
1262:
1260:
1259:
1258:
1241:coherence length
1238:
1236:
1235:
1230:
1228:
1227:
1226:
1203:
1201:
1200:
1195:
1178:. At a delay of
1177:
1175:
1174:
1169:
1167:
1166:
1165:
1145:
1143:
1142:
1137:
1113:
1111:
1110:
1105:
1086:
1084:
1083:
1078:
1076:
1075:
1074:
1049:
1047:
1046:
1041:
1029:
1027:
1026:
1021:
887:
885:
884:
879:
858:
856:
855:
850:
829:
827:
826:
821:
803:
798:
779:
777:
776:
771:
753:
748:
729:
727:
726:
721:
703:
698:
665:
663:
662:
657:
636:
634:
633:
628:
594:
592:
591:
586:
565:
563:
562:
557:
535:spectral density
532:
530:
529:
524:
513:
512:
493:
491:
490:
485:
474:
473:
450:
448:
447:
442:
431:
430:
408:
406:
405:
400:
398:
396:
386:
385:
364:
363:
350:
349:
348:
343:
328:
327:
315:
309:
294:
289:
267:
265:
264:
259:
238:
236:
235:
230:
190:radio telescopes
21:
18:Incoherent light
4440:
4439:
4435:
4434:
4433:
4431:
4430:
4429:
4395:
4394:
4393:
4388:
4370:
4356:Wigner's friend
4332:
4323:Quantum gravity
4284:
4270:Quantum sensing
4250:Quantum network
4230:Quantum machine
4200:Quantum imaging
4163:Quantum circuit
4158:Quantum channel
4117:
4063:Quantum biology
4049:
4025:ElitzurâVaidman
4000:DavissonâGermer
3983:
3935:Hidden-variable
3925:de BroglieâBohm
3902:Interpretations
3896:
3845:
3799:
3686:Complementarity
3664:
3621:
3616:
3574:
3571:
3566:
3565:
3512:Phys. Rev. Lett
3509:
3508:
3504:
3451:Phys. Rev. Lett
3448:
3447:
3443:
3413:
3412:
3408:
3378:
3377:
3373:
3344:Physical Review
3337:
3336:
3332:
3280:
3279:
3275:
3254:Physics Reports
3247:
3246:
3239:
3187:
3186:
3182:
3122:
3121:
3117:
3108:
3106:
3104:ABC News Online
3091:
3090:
3086:
3038:
3037:
3033:
3026:
3013:
3012:
3008:
2998:
2997:
2993:
2983:
2979:
2972:
2959:
2958:
2954:
2914:
2913:
2909:
2902:
2889:
2888:
2877:
2870:
2853:
2852:
2848:
2841:
2824:
2823:
2819:
2812:
2795:
2794:
2790:
2764:
2763:
2759:
2750:
2746:
2739:
2726:
2725:
2721:
2714:
2701:
2700:
2696:
2681:
2668:
2667:
2663:
2654:
2652:
2643:
2642:
2638:
2631:
2612:
2611:
2602:
2597:
2592:
2587:
2572:Quantum biology
2538:Laser linewidth
2532:
2529:Coherent states
2512:
2504:
2461:
2460:
2453:
2441:
2436:
2419:
2380:
2360:
2339:
2327:
2321:
2313:Poincaré sphere
2294:
2288:
2264:
2217:
2216:
2167:
2166:
2141:
2140:
2118:
2117:
2090:
2033:
2028:
2027:
2006:
2001:
2000:
1994:
1980:
1971:
1962:
1953:
1948:
1939:
1934:
1925:
1916:
1904:
1872:
1861:
1851:
1850:
1833:
1828:
1827:
1804:
1799:
1798:
1779:
1778:
1752:
1747:
1746:
1723:
1718:
1717:
1694:
1689:
1688:
1684:
1677:
1670:
1642:
1634:
1633:
1614:
1613:
1587:
1586:
1567:
1566:
1543:
1542:
1491:
1490:
1467:
1462:
1461:
1454:
1417:
1350:
1345:
1344:
1318:
1313:
1312:
1309:
1278:
1273:
1272:
1249:
1244:
1243:
1217:
1206:
1205:
1180:
1179:
1156:
1151:
1150:
1128:
1127:
1093:
1092:
1065:
1060:
1059:
1032:
1031:
1012:
1011:
1000:
939:Electromagnetic
915:
903:autocorrelation
894:
861:
860:
832:
831:
782:
781:
732:
731:
676:
675:
639:
638:
610:
609:
605:autocorrelation
568:
567:
539:
538:
501:
496:
495:
462:
457:
456:
419:
414:
413:
374:
352:
351:
338:
316:
310:
273:
272:
241:
240:
212:
211:
204:
198:
84:
50:partly coherent
35:
28:
23:
22:
15:
12:
11:
5:
4438:
4436:
4428:
4427:
4422:
4417:
4415:Wave mechanics
4412:
4407:
4397:
4396:
4390:
4389:
4387:
4386:
4375:
4372:
4371:
4369:
4368:
4363:
4358:
4353:
4352:
4351:
4340:
4338:
4334:
4333:
4331:
4330:
4325:
4320:
4319:
4318:
4308:
4303:
4301:Casimir effect
4298:
4292:
4290:
4286:
4285:
4283:
4282:
4277:
4272:
4267:
4262:
4260:Quantum optics
4257:
4252:
4247:
4242:
4237:
4232:
4227:
4222:
4217:
4212:
4207:
4202:
4197:
4192:
4187:
4182:
4181:
4180:
4170:
4165:
4160:
4155:
4154:
4153:
4143:
4138:
4133:
4127:
4125:
4119:
4118:
4116:
4115:
4110:
4105:
4100:
4095:
4090:
4085:
4080:
4075:
4070:
4065:
4059:
4057:
4051:
4050:
4048:
4047:
4042:
4037:
4035:Quantum eraser
4032:
4027:
4022:
4017:
4012:
4007:
4002:
3997:
3991:
3989:
3985:
3984:
3982:
3981:
3976:
3971:
3966:
3961:
3956:
3951:
3950:
3949:
3948:
3947:
3932:
3927:
3922:
3917:
3912:
3906:
3904:
3898:
3897:
3895:
3894:
3889:
3884:
3879:
3874:
3869:
3864:
3859:
3853:
3851:
3847:
3846:
3844:
3843:
3838:
3833:
3828:
3823:
3818:
3813:
3807:
3805:
3801:
3800:
3798:
3797:
3796:
3795:
3790:
3780:
3775:
3770:
3765:
3760:
3755:
3750:
3745:
3740:
3735:
3730:
3725:
3720:
3719:
3718:
3713:
3708:
3703:
3693:
3691:Density matrix
3688:
3683:
3678:
3672:
3670:
3666:
3665:
3663:
3662:
3657:
3652:
3647:
3646:
3645:
3635:
3629:
3627:
3623:
3622:
3617:
3615:
3614:
3607:
3600:
3592:
3586:
3585:
3570:
3569:External links
3567:
3564:
3563:
3518:(22): 220401.
3502:
3457:(14): 140401.
3441:
3422:(4): 694â704.
3416:Rev. Mod. Phys
3406:
3387:(3): 576â584.
3371:
3330:
3273:
3260:(3): 143â210.
3237:
3180:
3129:Optics Letters
3115:
3084:
3031:
3024:
3006:
2999:Saleh, Teich.
2991:
2977:
2970:
2952:
2907:
2900:
2875:
2868:
2846:
2839:
2817:
2810:
2788:
2757:
2744:
2737:
2727:Hecht (1998).
2719:
2712:
2694:
2679:
2661:
2636:
2629:
2599:
2598:
2596:
2593:
2591:
2590:
2581:
2575:
2569:
2564:
2559:
2553:
2547:
2541:
2535:
2526:
2520:
2513:
2511:
2508:
2503:
2502:Modal analysis
2500:
2479:
2475:
2471:
2468:
2452:
2449:
2440:
2437:
2435:
2432:
2418:
2415:
2379:
2376:
2372:quantum optics
2359:
2358:Quantum optics
2356:
2338:
2335:
2320:
2317:
2287:
2284:
2263:
2260:
2239:
2236:
2233:
2230:
2227:
2224:
2202:
2201:
2189:
2186:
2183:
2180:
2177:
2174:
2162:according to:
2151:
2148:
2128:
2125:
2089:
2086:
2040:
2036:
2013:
2009:
1996:
1995:
1981:
1974:
1972:
1963:
1956:
1954:
1949:
1942:
1940:
1935:
1928:
1926:
1917:
1910:
1908:
1903:
1900:
1880:
1875:
1868:
1864:
1858:
1854:
1847:
1841:
1836:
1812:
1807:
1786:
1760:
1755:
1731:
1726:
1702:
1697:
1682:
1675:
1669:
1666:
1650:
1645:
1641:
1621:
1597:
1594:
1574:
1550:
1501:
1498:
1475:
1470:
1453:
1450:
1439:
1438:
1434:
1427:
1424:
1416:
1413:
1383:
1382:
1371:
1368:
1365:
1362:
1357:
1353:
1326:
1321:
1308:
1305:
1286:
1281:
1257:
1252:
1225:
1220:
1216:
1213:
1193:
1190:
1187:
1164:
1159:
1148:coherence time
1135:
1103:
1100:
1073:
1068:
1039:
1019:
999:
996:
987:electric field
983:
982:
969:
959:
950:
945:
936:
930:
914:
911:
907:self-coherence
893:
890:
877:
874:
871:
868:
848:
845:
842:
839:
819:
816:
813:
810:
807:
802:
797:
794:
790:
769:
766:
763:
760:
757:
752:
747:
744:
740:
719:
716:
713:
710:
707:
702:
697:
694:
690:
686:
683:
655:
652:
649:
646:
626:
623:
620:
617:
584:
581:
578:
575:
555:
552:
549:
546:
533:are the power
522:
519:
516:
511:
508:
504:
483:
480:
477:
472:
469:
465:
440:
437:
434:
429:
426:
422:
410:
409:
395:
392:
389:
384:
381:
377:
373:
370:
367:
362:
359:
355:
347:
342:
337:
334:
331:
326:
323:
319:
314:
307:
304:
301:
298:
293:
288:
285:
281:
268:is defined as
257:
254:
251:
248:
228:
225:
222:
219:
197:
194:
178:antenna arrays
83:
80:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4437:
4426:
4423:
4421:
4418:
4416:
4413:
4411:
4408:
4406:
4403:
4402:
4400:
4385:
4377:
4376:
4373:
4367:
4364:
4362:
4359:
4357:
4354:
4350:
4347:
4346:
4345:
4342:
4341:
4339:
4335:
4329:
4326:
4324:
4321:
4317:
4314:
4313:
4312:
4309:
4307:
4304:
4302:
4299:
4297:
4294:
4293:
4291:
4287:
4281:
4278:
4276:
4273:
4271:
4268:
4266:
4263:
4261:
4258:
4256:
4253:
4251:
4248:
4246:
4243:
4241:
4238:
4236:
4233:
4231:
4228:
4226:
4223:
4221:
4220:Quantum logic
4218:
4216:
4213:
4211:
4208:
4206:
4203:
4201:
4198:
4196:
4193:
4191:
4188:
4186:
4183:
4179:
4176:
4175:
4174:
4171:
4169:
4166:
4164:
4161:
4159:
4156:
4152:
4149:
4148:
4147:
4144:
4142:
4139:
4137:
4134:
4132:
4129:
4128:
4126:
4124:
4120:
4114:
4111:
4109:
4106:
4104:
4101:
4099:
4096:
4094:
4091:
4089:
4086:
4084:
4081:
4079:
4076:
4074:
4073:Quantum chaos
4071:
4069:
4066:
4064:
4061:
4060:
4058:
4056:
4052:
4046:
4043:
4041:
4040:SternâGerlach
4038:
4036:
4033:
4031:
4028:
4026:
4023:
4021:
4018:
4016:
4013:
4011:
4008:
4006:
4003:
4001:
3998:
3996:
3993:
3992:
3990:
3986:
3980:
3977:
3975:
3974:Transactional
3972:
3970:
3967:
3965:
3964:Quantum logic
3962:
3960:
3957:
3955:
3952:
3946:
3943:
3942:
3941:
3938:
3937:
3936:
3933:
3931:
3928:
3926:
3923:
3921:
3918:
3916:
3913:
3911:
3908:
3907:
3905:
3903:
3899:
3893:
3890:
3888:
3885:
3883:
3880:
3878:
3875:
3873:
3870:
3868:
3865:
3863:
3860:
3858:
3855:
3854:
3852:
3848:
3842:
3839:
3837:
3834:
3832:
3829:
3827:
3824:
3822:
3819:
3817:
3814:
3812:
3809:
3808:
3806:
3802:
3794:
3791:
3789:
3786:
3785:
3784:
3783:Wave function
3781:
3779:
3776:
3774:
3771:
3769:
3766:
3764:
3761:
3759:
3758:Superposition
3756:
3754:
3753:Quantum state
3751:
3749:
3746:
3744:
3741:
3739:
3736:
3734:
3731:
3729:
3726:
3724:
3721:
3717:
3714:
3712:
3709:
3707:
3706:Excited state
3704:
3702:
3699:
3698:
3697:
3694:
3692:
3689:
3687:
3684:
3682:
3679:
3677:
3674:
3673:
3671:
3667:
3661:
3658:
3656:
3653:
3651:
3648:
3644:
3641:
3640:
3639:
3636:
3634:
3631:
3630:
3628:
3624:
3620:
3613:
3608:
3606:
3601:
3599:
3594:
3593:
3590:
3582:
3578:
3573:
3572:
3568:
3559:
3555:
3551:
3547:
3543:
3539:
3535:
3531:
3526:
3521:
3517:
3513:
3506:
3503:
3498:
3494:
3490:
3486:
3482:
3478:
3474:
3470:
3465:
3460:
3456:
3452:
3445:
3442:
3437:
3433:
3429:
3425:
3421:
3417:
3410:
3407:
3402:
3398:
3394:
3390:
3386:
3382:
3375:
3372:
3367:
3363:
3358:
3353:
3349:
3345:
3341:
3334:
3331:
3326:
3322:
3318:
3314:
3309:
3304:
3300:
3296:
3292:
3288:
3284:
3277:
3274:
3268:
3263:
3259:
3255:
3251:
3250:"Atom optics"
3244:
3242:
3238:
3233:
3229:
3225:
3221:
3217:
3213:
3208:
3203:
3200:(4): 041003.
3199:
3195:
3191:
3184:
3181:
3176:
3172:
3168:
3164:
3160:
3156:
3152:
3148:
3143:
3138:
3134:
3130:
3126:
3119:
3116:
3105:
3101:
3100:
3095:
3088:
3085:
3080:
3076:
3072:
3068:
3064:
3060:
3056:
3052:
3048:
3044:
3043:
3035:
3032:
3027:
3021:
3017:
3010:
3007:
3002:
2995:
2992:
2987:
2981:
2978:
2973:
2967:
2963:
2956:
2953:
2948:
2944:
2940:
2936:
2932:
2928:
2924:
2920:
2919:
2911:
2908:
2903:
2897:
2893:
2886:
2884:
2882:
2880:
2876:
2871:
2865:
2861:
2857:
2850:
2847:
2842:
2836:
2832:
2828:
2821:
2818:
2813:
2807:
2803:
2799:
2792:
2789:
2784:
2780:
2776:
2772:
2771:AccessScience
2768:
2761:
2758:
2754:
2748:
2745:
2740:
2734:
2730:
2723:
2720:
2715:
2709:
2705:
2698:
2695:
2690:
2686:
2682:
2676:
2672:
2665:
2662:
2651:
2647:
2640:
2637:
2632:
2626:
2622:
2618:
2617:
2609:
2607:
2605:
2601:
2594:
2585:
2582:
2579:
2576:
2573:
2570:
2568:
2565:
2563:
2560:
2557:
2554:
2551:
2548:
2545:
2542:
2539:
2536:
2530:
2527:
2524:
2521:
2518:
2515:
2514:
2509:
2507:
2501:
2499:
2497:
2493:
2466:
2458:
2450:
2448:
2446:
2438:
2433:
2431:
2429:
2424:
2416:
2414:
2412:
2407:
2405:
2400:
2399:superfluidity
2396:
2392:
2388:
2384:
2377:
2375:
2373:
2369:
2365:
2357:
2355:
2351:
2348:
2344:
2336:
2334:
2332:
2326:
2318:
2316:
2314:
2309:
2305:
2303:
2299:
2293:
2285:
2283:
2281:
2277:
2273:
2269:
2261:
2259:
2257:
2253:
2237:
2234:
2228:
2222:
2213:
2211:
2207:
2187:
2184:
2181:
2175:
2165:
2164:
2163:
2149:
2126:
2115:
2111:
2102:
2094:
2087:
2085:
2082:
2078:
2077:absolute zero
2074:
2069:
2067:
2063:
2058:
2056:
2055:antenna array
2038:
2034:
2011:
2007:
1992:will do this.
1991:
1987:
1978:
1973:
1968:
1960:
1955:
1946:
1941:
1932:
1927:
1922:
1914:
1909:
1906:
1901:
1899:
1896:
1873:
1866:
1862:
1856:
1852:
1845:
1834:
1805:
1784:
1775:
1753:
1724:
1695:
1685:
1678:
1667:
1665:
1643:
1639:
1619:
1611:
1595:
1592:
1572:
1564:
1548:
1540:
1536:
1528:
1522:
1515:
1499:
1496:
1468:
1458:
1451:
1449:
1447:
1443:
1435:
1432:
1428:
1425:
1422:
1421:
1420:
1414:
1412:
1409:
1407:
1403:
1399:
1394:
1392:
1388:
1369:
1366:
1363:
1355:
1351:
1343:
1342:
1341:
1319:
1306:
1304:
1301:
1279:
1250:
1242:
1218:
1214:
1211:
1191:
1188:
1185:
1157:
1149:
1133:
1121:
1117:
1101:
1098:
1090:
1066:
1056:
1037:
1017:
1009:
1004:
997:
995:
992:
988:
981:
977:
973:
970:
967:
963:
960:
958:
954:
951:
949:
946:
944:
940:
937:
934:
933:Surface waves
931:
928:
924:
923:
922:
920:
919:wave equation
912:
910:
908:
904:
899:
891:
889:
872:
866:
843:
837:
817:
814:
808:
800:
795:
792:
788:
767:
764:
758:
750:
745:
742:
738:
717:
714:
708:
700:
695:
692:
688:
684:
681:
672:
670:
650:
644:
621:
615:
606:
602:
598:
579:
573:
550:
544:
537:functions of
536:
517:
509:
506:
502:
478:
470:
467:
463:
454:
435:
427:
424:
420:
390:
382:
379:
375:
368:
360:
357:
353:
345:
332:
324:
321:
317:
305:
299:
291:
286:
283:
279:
271:
270:
269:
252:
246:
223:
217:
209:
203:
195:
193:
191:
187:
183:
179:
175:
172:
168:
164:
160:
156:
152:
148:
144:
140:
135:
133:
129:
125:
121:
117:
113:
108:
106:
102:
94:
88:
81:
79:
77:
73:
68:
66:
62:
57:
55:
51:
47:
43:
39:
33:
19:
4103:Quantum mind
4015:FranckâHertz
3857:KleinâGordon
3811:Formulations
3804:Formulations
3733:Interference
3723:Entanglement
3701:Ground state
3696:Energy level
3669:Fundamentals
3633:Introduction
3580:
3515:
3511:
3505:
3454:
3450:
3444:
3419:
3415:
3409:
3384:
3380:
3374:
3347:
3343:
3333:
3308:1721.1/52372
3290:
3286:
3276:
3257:
3253:
3197:
3193:
3183:
3132:
3128:
3118:
3107:. Retrieved
3097:
3087:
3046:
3040:
3034:
3015:
3009:
3000:
2994:
2989:description.
2985:
2980:
2961:
2955:
2922:
2916:
2910:
2891:
2855:
2849:
2826:
2820:
2797:
2791:
2770:
2760:
2752:
2747:
2728:
2722:
2703:
2697:
2670:
2664:
2653:. Retrieved
2649:
2639:
2614:
2505:
2456:
2454:
2444:
2442:
2434:Applications
2423:M. B. Plenio
2420:
2408:
2381:
2361:
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2343:matter waves
2340:
2331:matter waves
2328:
2310:
2306:
2298:polarization
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2251:
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2203:
2107:
2070:
2062:Dennis Gabor
2059:
1997:
1897:
1776:
1680:
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1532:
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1440:
1431:wave packets
1418:
1410:
1395:
1384:
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1125:
1119:
1115:
1088:
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972:Matter waves
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159:neuroscience
139:Thomas Young
136:
115:
111:
109:
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4361:EPR paradox
4141:Quantum bus
4010:Double-slit
3988:Experiments
3954:Many-worlds
3892:Schrödinger
3841:Phase space
3831:Schrödinger
3821:Interaction
3778:Uncertainty
3748:Nonlocality
3743:Measurement
3738:Decoherence
3728:Hamiltonian
3099:ABC Science
2775:McGraw-Hill
2767:"Coherence"
2278:(FROG), or
2114:white noise
1777:A distance
1437:incoherent.
962:Light waves
953:Radio waves
935:in a liquid
105:collimation
4399:Categories
4289:Extensions
4123:Technology
3969:Relational
3920:Copenhagen
3816:Heisenberg
3763:Tunnelling
3626:Background
3525:1805.10750
3207:1609.02439
3142:2212.10063
3109:2011-03-02
2925:(4): 513.
2655:2023-06-07
2595:References
2439:Holography
2282:(SPIDER).
2256:dispersion
1442:Holography
957:microwaves
669:wavenumber
167:holography
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3995:Bell test
3850:Equations
3676:Born rule
3464:1311.0275
3381:Phys. Rev
3366:0031-899X
3317:0034-6861
3224:0034-6861
3175:254877557
3159:1539-4794
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2368:Glauber's
2302:polarizer
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2185:≥
2179:Δ
2173:Δ
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2124:Δ
2035:τ
2008:τ
1853:λ
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1620:τ
1612:equal to
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1563:intensity
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1500:τ
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1367:≳
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1320:τ
1280:τ
1219:τ
1212:τ
1186:τ
1158:τ
1134:τ
1102:τ
1067:τ
1038:τ
1018:τ
991:intensity
976:electrons
789:γ
739:γ
715:≤
689:γ
685:≤
280:γ
174:gyroscope
151:acoustics
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38:Coherence
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3872:Majorana
3788:Collapse
3660:Glossary
3643:Timeline
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2510:See also
1967:diffract
1902:Examples
603:and the
176:, radio
4337:Related
4316:History
4055:Science
3887:Rydberg
3638:History
3530:Bibcode
3469:Bibcode
3424:Bibcode
3389:Bibcode
3079:5336898
3051:Bibcode
3042:Science
2927:Bibcode
2411:Glauber
599:of the
451:is the
4410:Optics
4030:Popper
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1398:lasers
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3862:Dirac
3554:S2CID
3520:arXiv
3493:S2CID
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3321:S2CID
3228:S2CID
3202:arXiv
3171:S2CID
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3067:PMID
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