# The wave of a photon/Other experiments

## Hong–Ou–Mandel Interferometer ^{[1]}

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The Hong-Ou-Mandel interferometer is a variant of the Mach-Zehnder interferometer in which two simultaneous photons are compared. A 351 nm laser radiates a KDP crystal, which because of SPDC emits now and then two entangled photons of about 702 nm. The KDP is propably a type I, in which both photons have the same polarization and the same phase. Both waves are mixed in a 50% reflecting mirror, filtered by a bandpass interference filter IF and detected with a coincidence of 7.2 ns.

It is supposed that this beam splitter is a glass plate with reflector on one side, causing (only) the reflection from the normal input having a phase shift of π. All other have no phase shift. At the detectors the waves are: I_{u} = 0.5sin(π+ωt+φ/2) + 0.5sinαsin(ωt-φ/2) and I_{l} = 0.5sin(ωt+φ/2) + 0.5sinαsin(ωt-φ/2). With an ideal bandwidth filter d = Δω/ω, the probability is calculated:

P_{u} = 0.5 - 0.5cos(4πΔx/λ) sin(πd(2k+2Δx/λ)) / πd(2k+2Δx/λ) and P_{l} = 0.5 + 0.5cos(4πΔx/λ) sin(πd(2k+2Δx/λ)) / πd(2k+2Δx/λ)

These formula predicts the result of the measurement if the cosine term is ignored and k = 0. Then the formula will be:

P_{u} = 0.5 - 0.5sin(πd2Δx/λ) / πd2Δx/λ

P_{l} = 0.5 + 0.5sin(πd2Δx/λ) / πd2Δx/λ

coincident: P = P_{u} * P_{l}

In the experiment ω = 2πc/702nm = 2.7 10^{15}. The bandwidth filter is 3 10^{13}, d = 3 10^{13} / 2.7 10^{15} = 0.011. Then FWHM = 113 μm.

## References

edit- ↑ Hong, C. K.; Ou, Z. Y.; Mandel, L. (1987). "Measurement of subpicosecond time intervals between two photons by interference".
*Phys. Rev. Lett.***59**(18): 2044–2046. Bibcode:1987PhRvL..59.2044H. doi:10.1103/PhysRevLett.59.2044. PMID 10035403.`{{cite journal}}`

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