• Photonics Research
  • Vol. 11, Issue 11, 1820 (2023)
Jong-Moo Lee1,*, Alessio Baldazzi2, Matteo Sanna2, Stefano Azzini2..., Joon Tae Ahn1, Myung-Lae Lee1, Youngik Sohn3 and Lorenzo Pavesi2|Show fewer author(s)
Author Affiliations
  • 1Electronics and Telecommunications Research Institute (ETRI), Daejeon 34129, Republic of Korea
  • 2Department of Physics, University of Trento, 38123 Trento, Italy
  • 3Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea
  • show less
    DOI: 10.1364/PRJ.489869 Cite this Article Set citation alerts
    Jong-Moo Lee, Alessio Baldazzi, Matteo Sanna, Stefano Azzini, Joon Tae Ahn, Myung-Lae Lee, Youngik Sohn, Lorenzo Pavesi, "Do different kinds of photon-pair sources have the same indistinguishability in quantum silicon photonics?," Photonics Res. 11, 1820 (2023) Copy Citation Text show less

    Abstract

    In the same silicon photonic integrated circuit, we compare two types of integrated degenerate photon-pair sources (microring resonators and waveguides) using Hong–Ou–Mandel (HOM) interference experiments. Two nominally identical microring resonators are coupled to two nominally identical waveguides, which form the arms of a Mach–Zehnder interferometer. This is pumped by two lasers at two different wavelengths to generate, by spontaneous four-wave mixing, degenerate photon pairs. In particular, the microring resonators can be thermally tuned in or out of resonance with the pump wavelengths, thus choosing either the microring resonators or the waveguides as photon-pair sources, respectively. In this way, an on-chip HOM visibility of 94% with microring resonators and 99% with straight waveguides is measured upon filtering. We compare our experimental results with theoretical simulations of the joint spectral intensity and the purity of the degenerate photon pairs. We verify that the visibility is connected to the sources’ indistinguishability, which can be quantified by the overlap between the joint spectral amplitudes (JSA) of the photon pairs generated by the two sources. We estimate a JSA overlap of 98% with waveguides and 89% with microring resonators.
    |ΨIIdωidωs[F1(ωi,ωs)a^1(ωi)a^1(ωs)+F2(ωi,ωs)a^2(ωi)a^2(ωs)]|vac,

    View in Article

    V=2dωidωsF1(ωi,ωs)F¯2(ωi,ωs)1+dωidωsF1(ωi,ωs)F¯2(ωi,ωs),

    View in Article

    |Ψ=dω1dω2F(ω1,ω2)a^(ω1)a^(ω2)|vac,(A1)

    View in Article

    F(ω1,ω2)=λrλuλ(1)(ω1)uλ(2)(ω2),(A2)

    View in Article

    |Ψ=λrλ[dω1uλ(1)(ω1)a^(ω1)][dω2uλ(2)(ω2)a^(ω2)]|vac.(A3)

    View in Article

    P=dω1dω2dω1dω2F(ω1,ω2)F¯(ω1,ω2)F(ω1,ω2)F¯(ω1,ω2)=λrλ2.(A4)

    View in Article

    ρ^2Tr1|ΨΨ|=dω2dω2[dω1F(ω1,ω2)F¯(ω1,ω2)]a^(ω2)|vacvac|a^(ω2)=λrλ[dω2uλ(2)(ω2)a^(ω2)]|vacvac|[dω2u¯λ(2)(ω2)a^(ω2)].(A5)

    View in Article

    HFWM=γSIP1P22ωSIP1P24π2dxdω1dω2dω3dω4ei(ω1+ω2ω3ω4)tei[kS(ω1)+kI(ω2)kP1(ω3)kP2(ω4)]xas(ω1)ai(ω2)aP1(ω3)aP2(ω4)+h.c.,(A6)

    View in Article

    ωSIP1P2=(ωsωiωP1ωP2)1/4,γSIP1P2=n2ωSIP1P2cASIP1P2eff.(A7)

    View in Article

    |Ψ=U^|vac,whereU^=exp[12ξdωsdωiF(ωs,ωi)a^(ωs)a^(ωi)h.c.],(A8)

    View in Article

    F(ωs,ωi)=dωα(ω)β(ωs+ωiω)ϕ(ωs,ωi,ω),(A9)

    View in Article

    ϕ(ωs,ωi,ω)=exp[iΔk(ωs,ωi,ω)L2]sinc[Δk(ωs,ωi,ω)L2],(A10)

    View in Article

    F(ωs,ωi)=ls(ωs)li(ωi)dωα(ω)lp1(ω)β(ωs+ωiω)lp2(ωs+ωiω),(A11)

    View in Article

    |Ψ=exp(12λξλA^λ2h.c.)|vac=λ[1coshξλn=0(tanhξλ)n(2n)!2nn!|2nλ],(A12)

    View in Article

    ξλξrλ,|nλ1n!(A^λ)n|vacandA^λdωuλ(ω)a^(ω).(A13)

    View in Article

    n^=λ(sinhξλ)2,(A14)

    View in Article

    ptrig=1λsechξλ,(A15)

    View in Article

    A^ληλA^λ+1ηλ2e^λ,(A16)

    View in Article

    ρ^=λρ^λ,ρ^λ=1coshξλn=0(tanhξλ)2n[(2n)!2nn!]2k=0nηλ2(2nk)(1ηλ2)kk!(2nk)!|2nkλ2nk|λ.(A17)

    View in Article

    n^=ληλ2(sinhξλ)2,(A18)

    View in Article

    ptrig=1λsech  ξλ1(1ηλ)2(tanhξλ)2.(A19)

    View in Article

    |Ψ0=exp{dω[α(ω)+β(ω)]A^(ω)}|vac,(A20)

    View in Article

    dωα(ω)β¯(ω)=0.(A21)

    View in Article

    |ΨI=exp{dωα(ω)+β(ω)2[a^1(ω)+a^2(ω)]}|vac,(A22)

    View in Article

    |ΨII=exp{ξ2dωidωs[F1(ωi,ωs)a^1(ωi)a^1(ωs)+F2(ωi,ωs)a^2(ωi)a^2(ωs)]}|vac,(A23)

    View in Article

    |ΨIII=exp{ξ2dωidωs[F1(ωi,ωs)e2iϕa^1(ωi)a^1(ωs)+F2(ωi,ωs)a^2(ωi)a^2(ωs)]}|vac.(A24)

    View in Article

    a^112(a^1+ia^2),a^212(a^2+ia^1).(A25)

    View in Article

    |ΨIV=exp{ξ4dωidωs{F1(ωi,ωs)e2iϕ[a^1(ωi)+ia^2(ωi)][a^1(ωs)+ia^2(ωs)]+F2(ωi,ωs)[a^2(ωi)+ia^1(ωi)][a^2(ωs)+ia^1(ωs)]}}|vac=exp{ξ4dωidωs{[F1(ωi,ωs)e2iϕF2(ωi,ωs)][a^1(ωi)a^1(ωs)a^2(ωi)a^2(ωs)]+2i[F1(ωi,ωs)e2iϕ+F2(ωi,ωs)]a^1(ωi)a^2(ωs)}}|vac.(A26)

    View in Article

    P^idωf(ω)n01n![a^i(ω)]n|vacvac|[a^i(ω)]n,(A27)

    View in Article

    p12=Tr{|ψoutψout|P^1P^2}Tr{|ψoutψout|}=ψout|P^1P^2|ψoutψout|ψout14dωidωsf(ωi)f(ωs){|F1(ωi,ωs)|2+|F2(ωi,ωs)|2+2Re[F1(ωi,ωs)F¯2(ωi,ωs)e2iϕ]}=12{1+Re[e2iϕdωidωsf(ωi)f(ωs)F1(ωi,ωs)F¯2(ωi,ωs)]}.(A28)

    View in Article

    V=p12maxp12minp12max.(A29)

    View in Article

    p12(ϕ,δ,N)=12[1+Ncos(2ϕ+δ)],(A30)

    View in Article

    Neiδdωidωsf(ωi)f(ωs)F1(ωi,ωs)F¯2(ωi,ωs).(A31)

    View in Article

    V=2N1+N,(A32)

    View in Article

    N|dωidωsf(ωi)f(ωs)F1(ωi,ωs)F¯2(ωi,ωs)|.(A33)

    View in Article

    p12norm(ϕ,δ,N)=11+N[1+Ncos(2ϕ+δ)].(A34)

    View in Article

    |ΨIV=exp{ξ4dωidωs{F1(ωi,ωs)e2iϕ[a^1(ωi)+ia^2(ωi)][a^1(ωs)+ia^2(ωs)]+F2(ωi,ωs)[a^2(ωi)+ia^1(ωi)][a^2(ωs)+ia^1(ωs)]}}|vac.(A35)

    View in Article

    a^112(a^1+a^3),a^212(a^4+a^2),(A36)

    View in Article

    pij=Tr{|ψoutψout|P^iP^j}Tr{|ψoutψout|}=ψout|P^iP^j|ψoutψout|ψout.(A37)

    View in Article

    p12=18{1+Re[e2iϕ1dωidωsf(ωi)f(ωs)F1(ωi,ωs)F¯2(ωi,ωs)]},(A38)

    View in Article

    p34=18{1+Re[e2i(ϕ1ϕ2)dωidωsf(ωi)f(ωs)F1(ωi,ωs)F¯2(ωi,ωs)]}.(A39)

    View in Article

    V=p34maxp34minp34max,(A40)

    View in Article

    ρtot=c|ψoutψout|+(1c)ρnoise,(A41)

    View in Article

    pij=Tr{ρtotP^iP^j}Tr{ρtot}=cψout|P^iP^j|ψout+(1c)Tr{ρnoiseP^iP^j}Tr{ρtot}.(A42)

    View in Article

    V=2N1+N+D,(A43)

    View in Article

    Jong-Moo Lee, Alessio Baldazzi, Matteo Sanna, Stefano Azzini, Joon Tae Ahn, Myung-Lae Lee, Youngik Sohn, Lorenzo Pavesi, "Do different kinds of photon-pair sources have the same indistinguishability in quantum silicon photonics?," Photonics Res. 11, 1820 (2023)
    Download Citation