Fig. 1. (a) Scheme of generation of photon pairs through the spontaneous parametric down-conversion in a nonlinear PT-symmetric coupler with linear absorption in the second waveguide. (b) Graphical representation of biphoton correlation function |ϕns,ni|2.

Fig. 2. Evolution of spatial signal and idler photon correlations between the two waveguide modes along the propagation direction (z) depending on the phase mismatch (Δβ) for different losses in the second waveguide γs=γi=γ. (a)–(c) γ=0.5 below the PT-symmetry breaking threshold. (d)–(f) γ=3 corresponding to PT-broken regime. For all plots, the coupling coefficients are Cs=Ci=1, Cp=0, and pump is coupled to the first waveguide, A1(z=0)=1, A2(z=0)=0, and γp=0.

Fig. 3. Normalized photon correlations, |ϕns,ni|2/∑ns′,ni′|ϕns′,ni′|2, versus the phase mismatch and loss in the second waveguide at the fixed propagation distance z=10. The pump is input to the (a)–(c) first [A1(z=0)=1, A2(z=0)=0] or (d)–(f) second waveguide [A1(z=0)=0, A2(z=0)=1]. Dashed lines indicate the linear PT-breaking threshold at γPT=2C. Other parameters correspond to Fig. 2.

Fig. 4. (a) Scheme of SFG in passive PT-symmetric nonlinear coupler with linear absorption in one waveguide. (b) Mismatch F between the SPDC and SFG depending on the input power P for |uns(z=0)|2=|vni(z=0)|2=P/2, plotted on a logarithmic scale. The propagation distance is z=10, signal and idler losses are equal γs=γi=0.5, there is no loss in the pump mode γp=0, and the coupling coefficients are Cs=Ci=1, Cp=0.