Double transverse wave-vector correlations in photon pairs generated by spontaneous parametric down-conversion pumped by Bessel-Gauss beams

Abstract

We present an experimental and theoretical study of type I, frequency-degenerate spontaneous parametric downconversion (SPDC) with a Bessel-Gauss pump in which we include, both, paraxial and non-paraxial pump beam configurations. We present measurements of the SPDC angular spectrum (AS), of the conditional angular spectrum (CAS) of signal-mode single photons as heralded by the detection of an idler photon, and of the transverse wavevector signal-idler correlations (TWC). We show that as the pump is made increasingly non-paraxial the AS acquires a non-concentric double-cone structure, with the CAS shape depending on the azimuthal location of the heralding detector, while the signal-idler wavevector correlation region splits into characteristic doublet stripes, representing as yet unexplored non-trivial, non-local quantum correlations between the signal and idler photons. Our work provides further understanding of SPDC with a particular class of structured pump beams, and we believe that the controlled presence of double wavevector correlations represents an interesting new resource for photon-pair quantum state engineering.

Optimal Pump Shaping for Entanglement Control in Any Countable Basis

“…A potential further investigation of this protocol would be to consider whether this formalism could be adapted to include bases which are indexed by continuous parameters, such as the Bessel–Gaussian basis. [ 30 ] This would be a challenging, but worthwhile endeavor, and would most likely entail instead restricting to a subset of a continuous basis. Further improvements might consider alternative phase‐matching [ 49 ] and SPDC [ 50–52 ] conditions, and a generalization to time‐domain shaping [ 53,54 ] and boson sampling.…”

“…This was first done in the seminal work on orbital angular momentum (OAM) entanglement, [ 23 ] where the conservation of OAM was confirmed down to the single photon level using different OAM pumps. Since then, various works have studied the OAM spectrum of downconverted light from a crystal pumped by a conventional Gaussian, [ 24 ] phase‐flipped Gaussian, [ 25 ] inverted Gaussian, [ 26 ] Ince–Gaussian, [ 27 ] Laguerre–Gaussian (LG), [ 28 ] Hermite–Gaussian (HG), [ 29 ] Bessel–Gaussian, [ 30 ] and vector‐vortex beams. [ 31 ] For the special case when the basis is OAM and the pump is a pure LG mode, the coefficients of the spectrum can be determined analytically.…”

Spatial control of spontaneous parametric down-conversion photon pairs through the use of apertured Bessel-Gauss pump beams

“…where g is an effective coupling constant that incorporates the χ (2) nonlinearity of the crystal, and α p is the coherent-state amplitude of the pump beam [22]. In this equation the joint amplitude F (k s ⊥ , ω s , k i ⊥ , ω p − ω s ) depends on the structure of the incident pump beam through its angular spectrum ψ(k p ⊥ ), and can be expressed as…”

“…One cone contains the other in such a manner that the two meet tangentially [17]. In [22] we explored how this dual cone structure leads to double transverse wavevector correlations.…”

Engineering Entangled Photons for Transmission in Ring-Core Optical Fibers

“…A beautiful and useful characteristic of SPDC is that the two photon spatial state can be engineered by manipulating the pump beam [29][30][31][32][33][34][35]. This has led to the production of quantum states with interesting properties [36][37][38][39][40]. The entanglement properties of these states are determined by the mode decomposition of the two-photon state, in which one has the freedom to choose between quite a few families of transverse modes.…”