Interference
and Interferometry |

**In General** > s.a. atom interferometry; photons; wave phenomena.

* __For light__: 1801,
Young's double slit experiment; 1909, Seen by G I Taylor with weak light,
one photon going through at a time.

* __Interference in time__:
A plot of electron energies shows an interference pattern when the electrons
could have been emitted in one of two "slits" in time; In the Paulus
et al experiment, laser pulses with two maxima passed through a gas of Ar atoms.

@ __For light__: Sanz et al AP(10) [in terms of photon trajectories]; Padgett et al PRS(11) [knotted and tangled threads of darkness in interfering beams].

@ __For matter__: Gustavsson et al NJP(10) [interacting matter waves]; Steane PLA(17)-a1710 [coherence limit from cosmic gravitational wave background]; > s.a. wave-function collapse.

@ __Interference in time__: news pw(05)mar
[experiment];
Horwitz PLA(06)qp/05 [significance], FP(07); Campagne-Ibarcq et al PRL(14)-a1311 [between past and future quantum states, in resonance fluorescence].

> __And gravity__: see gravitational
radiation; photon
phenomenology
in quantum gravity.

> __Related topics__: see astronomy [interferometry]; number theory [use for factoring numbers]; temperature [interferometric thermometer].

**In Quantum Mechanics** > s.a. classical
limit; decoherence and models [gravitational]; quantum
information; Superposition Principle.

* __With electrons__: Experiment first performed in 1961 by Claus Jönsson at the University of Tübingen.

* __Non-classical paths__: The three scenarios with one or two slits open at a time represent different sets of boundary conditions, so the superposition principle is not exactly applicable; In a path-integral approach the difference arises from non-classical paths, and can be testes in triple-slit experiments.

@ __With electrons__:
Rodgers pw(02)sep
[double slit]; Beau EJP(12) [path-integral approach]; Bach et al NJP(13) + news pw(13)mar [Feynman's version]; Marzlin & Lee PRA(14) [influence of Lorentz contraction].

@ __General references__: Schulman AJP(69)dec;
Braun & Georgeot PRA(06)
[quantitative measure]; Sanz & Miret-Artés JPA(08)-a0806 [in
terms of trajectories]; Silverman 08; Camacho & Camacho-Galván RPP(07)-a0811 [testing fundamental
physics]; Rave FP(08)
[interpretation in terms of a phaselike quantity]; Chou et al PRL(09)
[hydrodynamic
view]; Sancho JPB(10)-a1003 [of
indistinguishable particles]; Štefaňák PhD(10)-a1009 [in quantum information]; Grössing et al AP(12)-a1106 [classical trajectories plus zero-point fluctuations];
Davidović & Sanz EPN(14)-a1403 [complementarity and quantum foundations];
Tavernelli a1710 [self-interference and interpretations]; > s.a. experiments in quantum theory; many-worlds interpretation.

@ __Welcher-Weg (which-way) experiment__: Ferrari &
Braunecker AJP(10)aug;
Sen a1201.

@ __Single particle__: Frisch CP(65),
reprint CP(09);
Grangier et al EPL(86)
[single photon]; Scarani & Suarez AJP(98)aug
[rev]; Ferrari & Braunecker AJP(10)aug [and quantum erasure];
Rasel Phy(12) [free-space single-particle matter-wave interference];
news pw(13)mar [single-electron double-slit diffraction]; Rueckner & Peidle AJP(13)dec [single photon interferometer with which-path marker and quantum eraser]; Aspden et al AJP(16)sep-a1602 [video recording]; Blasiak a1701 [single-particle interference can be understood classically].

@ __Two-particle interference__: Horne et al PRL(89), Nat(90)oct;
Sancho EPJD(14)-a1403 [two-particle, two-slit experiment].

@ __Afshar's version__: Afshar in(05); Drezet qp/05,
Steuernagel FP(07),
Kastner FP(09)-a0801 [and
complementarity]; Flores SPIE(09)-a0803 [modified
version], FP(08)-a0802 [reply to comments];
Qureshi a1002 and
Kastner a1002;
Flores & De Tata FP(10);
> s.a. Complementarity.

@ __Non-local interferometer__: Kirby & Franson PRA(14)-a1310 [with entangled macroscopic coherent states]; Williams et al PRA(14)-a1408 [for entanglement detection].

@ __Other versions__: Gooding & Unruh PRD(14)-a1407 [self-gravitating interferometer, and intrinsic gravitational decoherence]; Garner et al a1412 [other quantum theories and relativity of simultaneity]; Orlando et al a1610-in [interference patterns and free fall].

@ __Related topics__: Nitta & Kudo PRA(08)
[time of arrival in double slit]; Sen a1201 [proposed experiment with atoms of noble gases]; Malvimat et al MNRAS(13)-a1304 [higher-order HBT correlations and intensity interferometry with more than two detectors];
Schmidt et al PRL(13) [momentum transfer to a double slit, realization of Einstein-Bohr thought experiment]; Brodutch et al PRD(14)-a1412 [post-Newtonian gravitational effects]; news forbes(15)dec [solar-systems size "double-slit" experiment]; Bromley et al PRA(17)-a1610 [more than entanglement]; > s.a. particle statistics [many-particle interference]; pilot-wave phenomenology; quantum measurements [weak measurements].

**Multi-Path or Higher-Order Interference**

* __Idea__:
Born's rule predicts that quantum interference, as shown by a double-slit diffraction
experiment, occurs from pairs of paths; A generalized version of quantum mechanics
might allow multi-path, i.e., higher-order interference; Sorkin has defined a hierarchy of possible interference behaviours, where classical theory is at the first level and quantum theory at the second level; Informally, the order in the hierarchy corresponds to the number of paths that have an irreducible interaction in a multi-slit experiment; 2010, The generalized types of interference are currently under experimental investigation.

@ __General references__: Henson PRL(15)-a1406 [and non-locality and contextuality]; Bolotin a1611.

@ __Triple-slit__: Ududec et al FP(11)-a0909 [and
structure of quantum theory];
Kobayashi et al PRA(10)-a0911 [and
geometric phase for photon]; Niestegge AMP(12)-a0912 [Sorkin's
third-order interference term]; Sinha et al Sci(10)jul-a1007 +
news pw(10)jul [experiment,
ruling out third and higher-order interference]; Niestegge FP(13)-a1104 [and Tsirelson's bound];
De Raedt et al PRA(12)-a1112 [analysis of multipath interference];
Siddiqui & Qureshi PTEP(15)-a1405 [duality relation];
Sawant et al PRL(14)-a1408 + focus Phy(14) + news pw(14)sep [role of non-classical paths];
Sewell Phy(17), news pw(17)apr [demonstration by two independent groups]; Cotter et al SciAdv(17)aug + news sa(17)aug [with large molecules]; > s.a. pilot-wave interpretation.

@ __ N-fold interference__: Sbitnev a1001 [and Bohmian trajectories]; Kauten et al NJP(17)-a1508 [five-path interferometer]; Bagan et al PRL(16)-a1509 [coherence and path-information]; Lee & Selby NJP(16)-a1604 [no computational speed-up over quantum theory]; Agne et al PRL(17)-a1609 [observation of genuine three-photon interference].

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