Coherent control of photon pairs via quantum interference between second- and third-order quantum nonlinear processes

Abstract

Genuine quantum interference between independent nonlinear processes of different order provides a route to coherent control that cannot be reduced to a classical field interference. Here we present an all-optical analogue of coherent carrier injection by exploiting interference between second- and third-order quantum nonlinear processes in an integrated photonic platform. Photon pairs generated via spontaneous parametric down-conversion and spontaneous four-wave mixing coherently contribute to the same final two-photon state, resulting in a phase-dependent modulation of both the generation rate and the spectral structure of the emitted biphoton state. We illustrate the features of such interference and how it can be used to shape biphoton wavefunctions and their quantum correlations. These results identify interference between nonlinear processes of different order as a distinct form of coherent quantum control within quantum nonlinear optics.

Figures (4)

• Figure 1: (a) Schematic of the proposed setup. BS: beam splitter; DC: dichroic mirror; PS: phase shifter. Inset: simulated TM and TE modes at $776.4$ nm and $1552.8$ nm, respectively. (b) Energy diagram of the nonlinear interactions.
• Figure 2: Plots of (a) $|\phi_\mathrm{SPDC}(\lambda_1,\lambda_2)|^2$[$pm^{-2}$] and (b) $|\phi_\mathrm{SFWM}(\lambda_1,\lambda_2)|^2$[$pm^{-2}$]. In the color, we encode the cosine of the phase. The SPDC pump has a pulse energy of $10.9pJ$ while the SFWM pump has a peak pulse energy of $220pJ$. Both pumps have a Gaussian spectral shape and a pulse duration of 100ps.
• Figure 3: (a) Plots of $R_r|\beta_{\mathrm{TOT}}(\zeta)\phi_{\mathrm{TOT}}(\lambda_1,\lambda_2,\zeta) |^2 [\mathrm{kHz \,\,pm^{-2}}]$ for different relative phases $\zeta$. The parameters for SPDC and SFWM are the same as in Fig. \ref{['fig:2']}. Quantum interference between the two processes modifies both the amplitude and the spectral correlations of the biphoton wavefunction. (b) Total pair generation rate given by Eq. \ref{['betatot']}, for a repetition rate of 10 MHz. The dots correspond to the six cases shown in panel (a).
• Figure 4: Plot of $|\phi_\mathrm{TOT}(\lambda_1,\lambda_2)|^2$ [pm$^{-2}$]. Here $\zeta=1.8\pi$, pulse duration of the SPDC pump is $3ns$ and the one of SFWM is $100ps$.