FW1F.2.pdf CLEO 2017 © OSA 2017 Hyperentangled Photons Generation Using Crossed Quasi-Phase-Matched Superlattice Salem F. Hegazy 1,2,3 , Salah S. A. Obayya 2 , and Bahaa E. A. Saleh 3,∗ 1 National Institute of Laser Enhanced Sciences, Cairo University, 12613 Giza, Egypt 2 Centre for Photonics and Smart Materials, Zewail City of Science and Technology, 12588 Giza, Egypt 3 CREOL, The College of Optics & Photonics, University of Central Florida, Orlando, FL 32816, USA ∗ besaleh@creol.ucf.edu Abstract: A superlattice structure featuring nonlinear layers with alternating orthogonal optic axes interleaved with orthogonal-poling directions, is shown to generate high-quality hyperentangled photons via orthogonal quasi-phase matching that corrects for phase- and group-velocity mismatching concurrently. OCIS codes: (270.0270) Quantum Optics; (190.0190) Nonlinear Optics. A well-designed source of hyperentangled biphotons based on spontaneous parametric downconversion (SPDC) allows for multiple emission possibilities while minimizing indistinguishability in all degrees of freedom (DOFs) over the entire emission cone. Because of anisotropy and dispersion of the medium the emitted photons experience different spatial and spectral effects as they propagate, so that they acquire distinguishing features marked by their spatial or temporal origin. The standard source is based on type-I interaction of a 45 o –polarized beam pumping two abutted thin nonlinear crystals with orthogonal optic axes (called here the cascaded-crystals (CC) source) [1, 2]. Another source uses a single crystal endowed with a nonlinear tensor supporting two nonlinear type-I and type-0 processes (called here the double- nonlinearity (DN) source) [3]. In these sources, certain physical effects limit or destroy the spatial and temporal indistinguishability of the emitted photons. Spatial distinguishability, which is acquired by the transverse walkoff and noncollinear interaction, can be reduced by use of a pump beam of waist much wider than the thickness of the crystal(s), but this comes at the expense of diminishing the strength of the nonlinear interaction. However, a focused pump does not create SPDC cones with full indistinguishability, so that high-quality entanglement is constrained to narrow collection angles. While temporal indistinguishability may be fully compensated, compensation of the spatial labeling becomes inadequate when entanglement is desired over wide spatial and spectral windows [4–7]. We present here a new source of hyperentangled biphotons with significantly enhanced indistinguishability, using a periodic thin-layered structure with alternating orthogonal optic axes, combined with periodic poling along orthogonal directions, as illustrated in Fig. (1a), creating orthogonal quasi-phase matching (QPM). By combining periodic down- conversion of orthogonally polarized photons along with periodic poling that corrects the phase mismatch, the structure self corrects for longitudinal walkoff as it happens and before it accumulates [see Fig. (1b)]. The superimposed SPDC radiation of the superlattice (SL) creates a two-photon entangled state described by the superposition |ψ 〉 =  d ω 1 d ω 2 d q 1 d q 2 {Φ H (ω 1 , ω 2 ; q 1 , q 2 ) |H; ω 1 ; q 1 〉|H; ω 2 ; q 2 〉 + Φ V (ω 1 , ω 2 ; q 1 , q 2 ) | V ; ω 1 ; q 1 〉| V ; ω 2 ; q 2 〉}, (1) over the frequency–transverse-wavevector space (ω 1 , ω 2 ; q 1 , q 2 ), with Φ H,V (ω 1 , ω 2 ; q 1 , q 2 ) ∝ d H,V χ (2) A p (ω 1 + ω 2 ; q 1 + q 2 ) sinc( 1 2 Δκ e H,V d H,V ) S M ( 1 2 Δϕ H,V ) being the two-photon wavefunctions for HH and VV components, χ (2) is the second-order susceptibility of the bulk domain material, A p (ω p , q p ) is the complex amplitude of the pump, d H and d V are the widths of the H and V layers, respectively, and Δκ e H,V = κ e(H, V ) p − κ e(H, V ) 1 − κ e(H, V ) 2 and Δκ o = κ o p − κ o 1 − κ o 2 are the errors in satisfying the longitudinal conservation of momentum within the interacting (H or V) layers and the noninteracting layers, respectively. Here, S M (x) ≡ sin( 1 2 Mx)/sin x is the phased-array function, which has a maxi- mum value of M/2 for x = 0, with M being the number of layers. This corresponds to satisfying the QPM conditions Δϕ H,V = Δκ o d V,H + Δκ e H,V d H,V − μπ = 0 for HH and VV emissions, respectively, where μ is an integer representing the order of QPM. Ideally, the complex superposition weights Φ H and Φ V should be equal for all frequencies and transverse wave vectors. In reality, they are not, and their relative phase ϑ = arg {Φ V /Φ H } = − 1 2 Δκ o (d H + d V ) − 1 4 M (Δϕ V − Δϕ H ) plays a major role in limiting the indistinguishability of the two components of the state in the conjugate space- time domains. Remarkably, similar expressions apply to the CC source [1, 2], albeit with a different QPM condition, Δϕ (CC) H,V = Δκ e H,V d H,V − μπ = 0 and a relative phase ϑ (CC) = − 1 2 Δκ o L − M 4 (Δϕ (CC) V − Δϕ (CC) H ), where L is the structure © 2017 IEEE 978-1-9435-8027-9/17/$31.00 ©2017 IEEE