Spontaneous four-wave mixing in a thin layer with second-order nonlinearity

TL;DR

This work demonstrates that spontaneous four-wave mixing (SFWM) can dominate photon-pair generation in a thin, second-order nonlinear layer such as a $10\,\mu$m lithium niobate film, due to a smaller wavevector mismatch $\Delta k$ compared with cascaded SHG-SPDC. By pumping LN at $1030$ nm, the experiment shows a quadratic dependence of coincidences on pump power and a $g^{(2)}(0)$ above the thermal limit, confirming correlated SFWM photon pairs in the visible and infrared channels, while SPDC contributes a predominantly linear signal in the IR. A complementary SPDC measurement pumped at $515$ nm and SHG efficiency assessment quantify cascaded contributions as about $5\%$ of the total, consistent with a phase-matching argument where $F(L)$ for SFWM outperforms the cascaded pathways at this thickness. The findings highlight the potential of thin-film, flat nonlinear platforms to serve as versatile, high-damage-threshold sources of entangled photons, enabling simultaneous or engineered quantum states via both $χ^{(2)}$ and $χ^{(3)}$ processes.

Abstract

Pairs of entangled photons are crucial for photonic quantum technologies. The demand for integrability and multi-functionality suggests 'flat' platforms - ultrathin layers and metasurfaces - as sources of photon pairs. With the success in demonstrating spontaneous parametric down-conversion (SPDC) from such sources, an alternative process to generate photon pairs, spontaneous four-wave mixing (SFWM), also starts to attract interest. In materials with nonzero second-order nonlinear susceptibility $χ^{(2)}$, SFWM can generate photon pairs both directly, through the third-order nonlinear susceptibility $χ^{(3)}$, and in a cascaded way, through second harmonic generation (SHG) followed by SPDC. Usually, the cascaded process is more efficient. Here, we show that in a thin layer, direct SFWM dominates, because the wavevector mismatch for SFWM is much smaller than for SHG or SPDC. To demonstrate it, we implement the photon pair generation via SFWM in a second-order nonlinear material - a thin layer of lithium niobate (LN). The existence of both second- and third-order nonlinear processes offers broader opportunities for quantum state engineering.

Figures (4)

• Figure 1: Experimental setup: lens L1 focuses the pump on the LN sample; signal (visible, shown in blue) and idler (IR, shown in orange) photons are collimated by lens L2, separated by dichroic mirror DM, and coupled into detectors D1, D2 by lenses L3, L4, respectively. Their polarization is analyzed by an HWP and a PBS in each arm. Filter F1 eliminates unwanted wavelengths in the pump beam, and bandpass filters F2, F3 select the signal and idler photon detection bands. Photon detection events are registered by a time tagger triggered by pulses from the laser.
• Figure 2: SFWM in LN. (a) Mean photon number per pulse for visible (blue circles) and IR (red triangles) photons. (b) The polarization dependences of the photon detection rates in the visible (blue circles) and IR (red triangles) arms. The $0$ angle corresponds to the pump polarization direction. (c) The number of coincidence counts per pulse as a function of the pump power, with a quadratic fitting curve. (d) Corresponding $g^{(2)}$ as a function of the pump power, with a fitting curve.
• Figure 3: SPDC in LN pumped at $515$ nm. (a) The mean number of coincidence counts per pulse as a function of the pump power, with a linear fit. (b) Corresponding $g^{(2)}$ as a function of the pump power, with the fitting curve.
• Figure 4: (a) $[F(L)]^2$ calculated for SFWM generating $770$ nm / $1550$ nm photon pairs from $1030$ nm pump (green solid line), SHG from $1030$ nm (blue dot-dashed line), and SPDC generating $770$ nm / $1550$ nm photon pairs from $515$ nm pump (red dashed line) as functions of the crystal length. (b) Calculated rates of photon pair generation through the direct (green) and cascaded (blue dashed line) processes vs the crystal length.