Quasi-phase-matched up- and down-conversion in periodically poled layered semiconductors

Nonlinear optics lies at the heart of classical and quantum light generation. The invention of periodic poling revolutionized nonlinear optics and its commercial applications by enabling robust quasi-phase-matching in crystals such as lithium niobate. However, reaching useful frequency conversion efficiencies requires macroscopic dimensions, limiting further technology development and integration. Here we realize a periodically poled van der Waals semiconductor (3R-MoS$_2$). Due to its exceptional nonlinearity, we achieve macroscopic frequency conversion efficiency of 0.03% at the relevant telecom wavelength over a microscopic thickness of 3.4${\mu}$m (that is, 3 poling periods), $10-100\times$ thinner than current systems with similar performances. Due to unique intrinsic cavity effects, the thickness-dependent quasi-phase-matched second harmonic signal surpasses the usual quadratic enhancement by $50\%$. Further, we report the broadband generation of photon pairs at telecom wavelengths via quasi-phase-matched spontaneous parametric down-conversion, showing a maximum coincidence-to-accidental-ratio of $638 \pm 75$. This work opens the new and unexplored field of phase-matched nonlinear optics with microscopic van der Waals crystals, unlocking applications that require simple, ultra-compact technologies such as on-chip entangled photon-pair sources for integrated quantum circuitry and sensing.