• Photonics Research
  • Vol. 9, Issue 11, 2237 (2021)
Erasto Ortiz-Ricardo1, Cesar Bertoni-Ocampo1, Mónica Maldonado-Terrón1, Arturo Garcia Zurita1, Roberto Ramirez-Alarcon2, Hector Cruz Ramirez1, R. Castro-Beltrán3、4, and Alfred B. U’Ren1、*
Author Affiliations
  • 1Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México, D.F., Mexico
  • 2Centro de Investigaciones en Óptica A.C., Loma del Bosque 115, Colonia Lomas del Campestre, 37150 León, Guanajuato, Mexico
  • 3Departamento de Ingeniería Física, Cuerpo Académico de Mécanica Estadística, Divisón de Ciencias e Ingenierías, Universidad de Guanajuato, 37150 León, Guanajuato, Mexico
  • 4e-mail: cbrigoberto@fisica.ugto.mx
  • show less
    DOI: 10.1364/PRJ.435521 Cite this Article Set citation alerts
    Erasto Ortiz-Ricardo, Cesar Bertoni-Ocampo, Mónica Maldonado-Terrón, Arturo Garcia Zurita, Roberto Ramirez-Alarcon, Hector Cruz Ramirez, R. Castro-Beltrán, Alfred B. U’Ren. Submegahertz spectral width photon pair source based on fused silica microspheres[J]. Photonics Research, 2021, 9(11): 2237 Copy Citation Text show less

    Abstract

    High-efficiency submegahertz bandwidth photon pair generators will enable the field of quantum technology to transition from laboratory demonstrations to transformational applications involving information transfer from photons to atoms. While spontaneous parametric processes are able to achieve high-efficiency photon pair generation, the spectral bandwidth tends to be relatively large, as defined by phase-matching constraints. To solve this fundamental limitation, we use an ultrahigh quality factor (Q) fused silica microsphere resonant cavity to form a photon pair generator. We present the full theory for the spontaneous four-wave mixing (SFWM) process in these devices, fully taking into account all relevant source characteristics in our experiments. The exceptionally narrow (down to kilohertz-scale) linewidths of these devices result in a reduction in the bandwidth of the photon pair generation, allowing submegahertz spectral bandwidth to be achieved. Specifically, using a pump source centered around 1550 nm, photon pairs with the signal and idler modes at wavelengths close to 1540 and 1560 nm, respectively, are demonstrated. We herald a single idler-mode photon by detecting the corresponding signal photon, filtered via transmission through a wavelength division multiplexing channel of choice. We demonstrate the extraction of the spectral profile of a single peak in the single-photon frequency comb from a measurement of the signal–idler time of emission distribution. These improvements in device design and experimental methods enabled the narrowest spectral width (Δν=366 kHz) to date in a heralded single-photon source based on SFWM.
    H^(t)=34ϵ0χ(3)02πdϕ0πdθ0Rdρρ2sinθE1(+)(r,t)E2(+)(r,t)×E^s()(r,t)E^i()(r,t)+H.C.,

    View in Article

    Eν(+)(r,t)=lνAlνflν(ρ,θ)dωαlν(ω)ei[ωtklν(ω)Rϕ],

    View in Article

    E^ν(+)(r,t)=lνflν(ρ,θ)dω(ω)ei[ωtklν(ω)Rϕ]b^lν(kω),

    View in Article

    1λ=12πRns(λ){ν+213αqν13P(λ)[ns(λ)21]12+310223αq2ν13213P(λ)[ns(λ)223P(λ)2][ns2(λ)1]32αqν23},

    View in Article

    |Ψ|0+1i0tdtH^(t)|0.

    View in Article

    |Ψ2=1i0tdtH^(t)|0=l1,l2,ls,liAl1Al2Θl1l2lslidωsdωi{l(ωs)l(ωi)×dω1[αl1(ω1)αl2(ωs+ωiω1)Gl1l2lsli(ω1,ωs,ωi)×b^ls(ωs)b^li(ωi)|0]}.

    View in Article

    Θl1l2lsli=dρdθρ2sinθf1(ρ,θ)f2(ρ,θ)fs*(ρ,θ)fi*(ρ,θ),

    View in Article

    Gl1l2lsli(ω1,ωs,ωi)=sinc[LΔkl1l2lsli(ω1,ωs,ωi)2]exp[iLΔkl1l2lsli(ω1,ωs,ωi)2],

    View in Article

    Δkl1l2lsli(ω1,ωs,ωi)=kl1(ω1)+kl2(ωs+ωiω1)kls(ωs)kli(ωi).

    View in Article

    αlp(ω)αl1(ω)=αl2(ω)=δ(ωωp).

    View in Article

    |Ψ2=lp,ls,liAlp2ΘlplplslidΩ(ωp+Ω)(ωpΩ)×glplsli(Ω)b^ls(ωp+Ω)b^ls(ωpΩ)|0,

    View in Article

    glplsli(ωp,Ω)=sinc[LΔκlplsli(ωp,Ω)2]exp[iLΔκlplsli(ωp,Ω)2]

    View in Article

    Δκlplsli(ωp,Ω)=2klp(ωp)kls(ωp+Ω)kli(ωpΩ)2γP.

    View in Article

    2γP=PinQn2πnRAeff.

    View in Article

    |Ψ2=dΩglplsli(Ω)b^ls(ωp+Ω)b^ls(ωpΩ)|vac.

    View in Article

    b^lv(ω)rvn+1+einklv(ω)La^v(ω)+[1rvn+1ei(n+1)klv(ω)L1rveiklv(ω)L]tva^v(ω).

    View in Article

    limnb^lν(ω)|0ν=Aν(ω)a^ν(ω)|0ν,

    View in Article

    Aν(ω)=tν1rνeiklν(ω)L.

    View in Article

    |Ψ2=dΩglplsli(Ω)As(ωp+Ω)Ai(ωpΩ)×a^s(ωp+Ω)a^i(ωpΩ)|0.

    View in Article

    |Ψ2=tp|Ψ2+tprp2eiklp(ωp)L|Ψ2+tprp4ei2klp(ωp)L|Ψ2+...+tprp2nei2nklp(ωp)L|Ψ2=tp[1rp2(n+1)eiklp(ωp)L(n+1)]1rp2eiklp(ωp)L|Ψ2.

    View in Article

    limn|Ψ=Ap(ωp)|Ψ

    View in Article

    Ap(ω)=tp1rp2eiklp(ω)L.

    View in Article

    |Ψ(ωp)=|vac+ηAp(ωp)×dΩf(Ω;ωp)a^s(ωp+Ω)a^i(ωpΩ)|vac|vac+ηAp(ωp)|φ(ωp),

    View in Article

    f(Ω;ωp)=glplsli(Ω;ωp)As(ωp+Ω)Ai(ωpΩ).

    View in Article

    |Ψ(ωp)=|vac+ηAp(ωp)dωsdωif2(ωs,ωi;ωp)a^s(ωs)a^i(ωi)|vac

    View in Article

    f2(ωs,ωi;ωp)=δ(ωs+ωi2ωp)Glplplsli(ωp,ωs,ωi)As(ωs)Ai(ωi).

    View in Article

    f2(ω+,Ω;ωp)=δ(ω+ωp)×Glplplsli(ωp,ω++Ω,ω+Ω)As(ω++Ω)Ai(ω+Ω).

    View in Article

    ρ^=dωp|Ap(ωp)|2|φ(ωp)φ(ωp)|.

    View in Article

    Ri(Ω)=dωsn^(ωs)n^(ωpΩ)=Tr[a^(ωs)a^(ωpΩ)a^(ωpΩ)a^(ωs)ρ^]

    View in Article

    =dωp|A(ωp)f(Ω;ωp)|2.

    View in Article

    Ri(Ω)=dωp|glplsli(Ω)|2Ap(ωp)As(ωp+Ω)Ai(ωpΩ)dωpAp(ωp)As(ωp+Ω)Ai(ωpΩ)

    View in Article

    a^t(t)=12πdωa^(ω)eiωt.

    View in Article

    R˜(ts,ti)=n^t(ts)nt(ti)=Tr[a^t(ts)a^t(ti)a^t(ti)a^t(ts)ρ^]=dωpAp(ωp)dΩ|f(Ω;ωp)|2ei(tsti)Ω=dΩdωpAp(ωp)|f(Ω;ωp)|2ei(tsti)Ω=dΩRi(Ω)ei(tsti)Ω.

    View in Article

    Ri(Ω)=H(Ω)·h(Ω)*combδΩ(Ω),

    View in Article

    combΔ(x)=j=δ(xjΔ).

    View in Article

    R˜(T)=h˜(T)·H˜(T)*comb1/δΩ(T).

    View in Article

    Erasto Ortiz-Ricardo, Cesar Bertoni-Ocampo, Mónica Maldonado-Terrón, Arturo Garcia Zurita, Roberto Ramirez-Alarcon, Hector Cruz Ramirez, R. Castro-Beltrán, Alfred B. U’Ren. Submegahertz spectral width photon pair source based on fused silica microspheres[J]. Photonics Research, 2021, 9(11): 2237
    Download Citation