Coherence revivals in two-photon frequency combs

We describe and theoretically analyze the self-imaging Talbot effect of entangled photon pairs in the time domain. Rich phenomena are observed in coherence propagation along dispersive media of mode-locked two-photon states with frequency entanglement exhibiting a comblike correlation function. Our results can be used to remotely transfer frequency standards through optical fiber networks with two-photon light, avoiding the requirement of dispersion compensation.

Figure 1

General scheme to study the evolution of a two-photon wave packet when the signal and idler propagate through two different dispersive media. Unless the dispersive properties are properly chosen, the joint probability of two-photon detection gets broadened.

Figure 2

Example of the broadening of the second-order correlation function $G^{\left(2\right)}\left(\tau \right)$ of two-photon light with the effective dispersion parameter ${\Phi }_{2\mathrm{eff}}$. (a) $G^{\left(2\right)}\left(\tau \right)$ corresponding to a two-photon spectrum (in the inset) with 2-THz full-width half-maximum (FWHM) bandwidth for ${\Phi }_{2\mathrm{eff}}=0{\mathrm{ps}}^2$ (blue solid line), $2.5{\mathrm{ps}}^2$ (red long-dashed), and $5.0{\mathrm{ps}}^2$ (green short-dashed line). (b) Plot of $G^{\left(2\right)}\left(\tau \right)$ as a function of ${\Phi }_{2\mathrm{eff}}$.

Figure 3

Second-order correlation function $G^{\left(2\right)}\left(\tau \right)$ corresponding to the two-photon frequency comb filtered by a cavity with the free spectral range of $\Delta \omega =2\pi \times 80$ GHz (in the inset) for ${\Phi }_{2\mathrm{eff}}=0$ ps${}^2$ (blue solid line), $1.2{\mathrm{ps}}^2$ (red long-dashed line), $2.5{\mathrm{ps}}^2$ (green short-dashed line), and ${\Phi }_{2\mathrm{eff}}=T^2/\pi \approx 50{\mathrm{ps}}^2$ (black dots).

Figure 4

Temporal Talbot carpet. (a) Two-dimensional (2D) behavior of second-order coherence with the dispersion parameter. (b) Unit cell.

Figure 5

Second-order correlation function $G^{\left(2\right)}\left(\tau \right)$ for fractional Talbot distances ${\Phi }_{2\mathrm{eff}}=0$ (blue solid thick line), $T^2/2\pi$ (black dashed line), $T^2/4\pi$ (green short-dashed line), $T^2/6\pi$ (red solid line), and $T^2/8\pi$ (magenta dash-dotted line).

Figure 6

Same Talbot carpet as in Fig. 4a, but considering a 3-GHz linewdith two-photon frequency comb.