• Photonics Research
  • Vol. 8, Issue 6, 1023 (2020)
Pablo Yepiz-Graciano1, Alí Michel Angulo Martínez1, Dorilian Lopez-Mago2、3、*, Hector Cruz-Ramirez1, and Alfred B. U’Ren1、4、*
Author Affiliations
  • 1Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, Ciudad de México 04510, Mexico
  • 2Tecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Ave. Eugenio Garza Sada 2501, Monterrey, N.L. 64849, Mexico
  • 3e-mail: dlopezmago@tec.mx
  • 4e-mail: alfred.uren@correo.nucleares.unam.mx
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    DOI: 10.1364/PRJ.388693 Cite this Article Set citation alerts
    Pablo Yepiz-Graciano, Alí Michel Angulo Martínez, Dorilian Lopez-Mago, Hector Cruz-Ramirez, Alfred B. U’Ren. Spectrally resolved Hong–Ou–Mandel interferometry for quantum-optical coherence tomography[J]. Photonics Research, 2020, 8(6): 1023 Copy Citation Text show less

    Abstract

    In this paper, we revisit the well-known Hong–Ou–Mandel (HOM) effect in which two photons, which meet at a beamsplitter, can interfere destructively, leading to null in coincidence counts. In a standard HOM measurement, the coincidence counts across the two output ports of the beamsplitter are monitored as the temporal delay between the two photons prior to the beamsplitter is varied, resulting in the well-known HOM dip. We show, both theoretically and experimentally, that by leaving the delay fixed at a particular value while relying on spectrally resolved coincidence photon counting, we can reconstruct the HOM dip, which would have been obtained through a standard delay-scanning, non-spectrally resolved HOM measurement. We show that our numerical reconstruction procedure exhibits a novel dispersion cancellation effect, to all orders. We discuss how our present work can lead to a drastic reduction in the time required to acquire a HOM interferogram, and specifically discuss how this could be of particular importance for the implementation of efficient quantum-optical coherence tomography devices.
    |ψ=|0s|0i+ηdΩf(Ω)|ω0+Ωs|ω0Ωi,(1)

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    f(Ω)=f0sinc[L2Δk(Ω)]exp[iL2Δk(Ω)]Ff(Ω),(2)

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    Rc(τ)=R02dΩ|f(Ω)f(Ω)eiΩτ|2.(3)

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    rc(τ,Ω)=12|f(Ω)f(Ω)eiΩτ|2,(4)

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    Rc(τ)=R0dΩrc(τ,Ω).(5)

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    rc(τ,Ω)=12[A(Ω)+B(Ω)eiΩτ+B*(Ω)eiΩτ],(6)

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    A(Ω)=|f(Ω)|2+|f(Ω)|2,(7)

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    B(Ω)=f(Ω)f*(Ω).(8)

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    r˜c(τ,T)=12πdΩrc(τ,Ω)eiTΩ,(9)

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    r˜c(τ,T)=12[A˜(T)+B˜(Tτ)+B˜(Tτ)].(10)

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    |τ|<πδω.(11)

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    N=2LnMcΔτ.(12)

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    r˜c(τ,T)=F˜(T)12F˜(Tτ)+cos(ω0Ts)F˜(TTs/2)cos(ω0Ts)F˜[T(τTs/2)]12F˜[T(τTs)]12F˜(T+τ)+cos(ω0Ts)F˜(T+Ts/2)cos(ω0Ts)F˜[T+(τTs/2)]12F˜[T+(τTs)].(13)

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    Rc(τ)=R02dΩ|f(Ω)|2|H(Ω)H(Ω)eiΩτ|2,(14)

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    H(Ω)=j=0N1r(j)ei(ω0+Ω)Ts(j)=r(0)+r(1)ei(ω0+Ω)Ts(1)+,(15)

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    H(Ω)=j=0N1r(j)ei[(ω0+Ω)Ts(j)+Φj(Ω)].(16)

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    Pablo Yepiz-Graciano, Alí Michel Angulo Martínez, Dorilian Lopez-Mago, Hector Cruz-Ramirez, Alfred B. U’Ren. Spectrally resolved Hong–Ou–Mandel interferometry for quantum-optical coherence tomography[J]. Photonics Research, 2020, 8(6): 1023
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