Editing Mach–Zehnder interferometer (section)

== Uses ==

The Mach&ndash;Zehnder interferometer's relatively large and freely accessible working space, and its flexibility in locating the fringes has made it the interferometer of choice for [[Flow visualization|visualizing flow]] in wind tunnels<ref name=Chevalerias1957>{{Cite journal | last1 = Chevalerias | first1 = R. | last2 = Latron | first2 = Y. | last3 = Veret | first3 = C. | doi = 10.1364/JOSA.47.000703 | title = Methods of Interferometry Applied to the Visualization of Flows in Wind Tunnels | journal = Journal of the Optical Society of America | volume = 47 | issue = 8 | pages = 703 | year = 1957 | bibcode = 1957JOSA...47..703C }}</ref><ref name=Ristic>{{cite web |last=Ristić |first=Slavica |title=Flow visualization techniques in wind tunnels – optical methods (Part II) |url=http://www.vti.mod.gov.rs/ntp/rad2007/2-07/rist/rist.pdf |publisher=Military Technical Institute, Serbia |access-date=6 April 2012}}</ref> and for flow visualization studies in general. It is frequently used in the fields of aerodynamics, [[plasma physics]] and [[heat transfer]] to measure pressure, density, and temperature changes in gases.<ref name=HariharanBasics2007/>{{rp|18,93&ndash;95}}

Mach&ndash;Zehnder interferometers are used in [[electro-optic modulator]]s, electronic devices used in various [[fiber-optic communication]] applications. Mach–Zehnder modulators are incorporated in monolithic [[integrated circuit]]s and offer well-behaved, high-bandwidth electro-optic amplitude and phase responses over a multiple-gigahertz frequency range.

Mach&ndash;Zehnder interferometers are also used to study one of the most counterintuitive predictions of quantum mechanics, the phenomenon known as [[quantum entanglement]].<ref name=Paris1999>{{cite journal |last=Paris |first=M. G. A. |title=Entanglement and visibility at the output of a Mach–Zehnder interferometer |journal=Physical Review A |date=1999 |volume=59 |issue=2 |pages=1615&ndash;1621 |url=http://qinf.fisica.unimi.it/~paris/PDF/visent.pdf |access-date=2 April 2012 |arxiv=quant-ph/9811078 |bibcode=1999PhRvA..59.1615P |doi=10.1103/PhysRevA.59.1615 |s2cid=13963928 |archive-url=https://web.archive.org/web/20160910074215/http://qinf.fisica.unimi.it/~paris/PDF/visent.pdf |archive-date=10 September 2016 |url-status=dead }}</ref><ref name=Haack2010>{{Cite journal | last1 = Haack | first1 = G. R. | last2 = Förster | first2 = H. | last3 = Büttiker | first3 = M. | title = Parity detection and entanglement with a Mach-Zehnder interferometer | doi = 10.1103/PhysRevB.82.155303 | journal = Physical Review B | volume = 82 | issue = 15 | pages = 155303 | year = 2010 |arxiv = 1005.3976 |bibcode = 2010PhRvB..82o5303H | s2cid = 119261326 }}</ref>

The possibility to easily control the features of the light in the reference channel without disturbing the light in the object channel popularized the Mach&ndash;Zehnder configuration in [[holographic interferometry]]. In particular, [[optical heterodyne detection]] with an off-axis, frequency-shifted reference beam ensures good experimental conditions for shot-noise limited holography with video-rate cameras,<ref>{{cite journal |author=Michel Gross |author2=Michael Atlan |title=Digital holography with ultimate sensitivity|journal=Optics Letters|volume=32 |issue=8 |pages=909–911 |year=2007 |arxiv = 0803.3076 |bibcode = 2007OptL...32..909G |doi = 10.1364/OL.32.000909 |pmid=17375150 |s2cid=6361448 }}</ref> vibrometry,<ref>{{cite journal |author=Francois Bruno |author2=Jérôme Laurent |author3=Daniel Royer |author4=Michael Atlan |title=Holographic imaging of surface acoustic waves |journal=Applied Physics Letters|volume=104 |issue=1 |pages=083504 |year=2014 |arxiv=1401.5344 |bibcode = 2014ApPhL.104a3504Y |doi = 10.1063/1.4861116 }}</ref> and laser Doppler imaging of blood flow.<ref>{{cite journal |author=Caroline Magnain |author2= Amandine Castel |author3= Tanguy Boucneau |author4= Manuel Simonutti |author5= Isabelle Ferezou |author6= Armelle Rancillac |author7= Tania Vitalis |author8= José-Alain Sahel |author9= Michel Paques |author10=Michael Atlan |title=Holographic laser Doppler imaging of microvascular blood flow |journal=Journal of the Optical Society of America A |volume=31 |issue= 12|pages=2723–2735 |year=2014 |doi = 10.1364/JOSAA.31.002723|pmid= 25606762 |arxiv = 1412.0580 |bibcode = 2014JOSAA..31.2723M |s2cid= 42373720 }}</ref>

In [[optical telecommunications]] it is used as an [[electro-optic modulator]] for phase and amplitude modulation of light.  [[Optical computing]] researchers have proposed using Mach-Zehnder interferometer configurations in optical neural chips for greatly accelerating complex-valued neural network algorithms.<ref name="Zhang Gu Jiang Thompson 2021 p. ">{{cite journal | last1=Zhang | first1=H. | last2=Gu | first2=M. | last3=Jiang | first3=X. D. | last4=Thompson | first4=J. | last5=Cai | first5=H. | last6=Paesani | first6=S. | last7=Santagati | first7=R. | last8=Laing | first8=A. | last9=Zhang | first9=Y. | last10=Yung | first10=M. H. | last11=Shi | first11=Y. Z. | last12=Muhammad | first12=F. K. | last13=Lo | first13=G. Q. | last14=Luo | first14=X. S. | last15=Dong | first15=B. | last16=Kwong | first16=D. L. | last17=Kwek | first17=L. C. | last18=Liu | first18=A. Q. | title=An optical neural chip for implementing complex-valued neural network | journal=Nature Communications | volume=12 | issue=1 | date=January 19, 2021 | issn=2041-1723 | pmid=33469031 | pmc=7815828 | doi=10.1038/s41467-020-20719-7 | page=457}}</ref>

The versatility of the Mach–Zehnder configuration has led to its being used in a wide range of fundamental research topics in quantum mechanics, including studies on [[counterfactual definiteness]], [[quantum entanglement]], [[quantum computation]], [[quantum cryptography]], [[quantum logic]], [[Elitzur–Vaidman bomb tester]], the [[quantum eraser experiment]], the [[quantum Zeno effect]], and [[neutron diffraction]].