| Summary: | <p> Over the last two decades, the emergence of quantum information science has uncovered many practical applications in areas such as communications, imaging, and sensing where harnessing quantum features of Nature provides tremendous benefits over existing methods exploiting classical physical phenomena. In this effort, one of the frontiers of research has been to identify and utilize quantum phenomena that are not susceptible to environmental and parasitic noise processes. Quantum photonics has been at the forefront of these studies because it allows room-temperature access to its inherently quantum-mechanical features, and allows leveraging the mature telecommunication industry. Accompanying the weak environmental influence, however, are also weak optical nonlinearities. Efficient nonlinear optical interactions are indispensible for many of the existing protocols for quantum optical computation and communication, e.g. high-fidelity entangling quantum logic gates rely on large nonlinear responses at the one- or few-photon-level. </p><p> While this has been addressed to a great extent by interfacing photons with single quantum emitters and cold atomic gases, scalability has remained elusive. In this work, we identify the macroscopic second-order nonlinear polarization as a robust platform to address this challenge, and utilize the recent advances in the burgeoning field of optical microcavities to enhance this nonlinear response. In particular, we show theoretically that by using the quantum Zeno effect, low-noise, single-photon-level optical nonlinearities can be realized in lithium niobate whispering-gallery-mode microcavities, and present experimental progress toward this goal. Using the measured strength of the second-order nonlinear response in lithium niobate, we modeled the nonlinear system in the strong coupling regime using the Schrödinger picture framework and theoretically demonstrated that the single-photon-level operation can be observed for cavity lifetimes in excess of 500 ns for all the three waves in the interaction, provided a cavity of radius <i>R </i> < 10 μm is fabricated. </p><p> Experimentally, we showed that the absorption-limited quality (<i> Q</i>) factors for lithium niobate, <i>Q<sub>intrinsic</sub></i> ≈ 10<sup>8</sup>, can be achieved using diamond-turning methods for disk radii, <i>R</i> > 100 μm, whereas for the smaller disks, additional rigorous polishing may be required. We also fabricated resonators as small as <i>R</i> ∼ 40 μm via this method. In a millimeter-sized resonator, we experimentally demonstrated triply resonant sum-frequency generation, which allowed for an observation of the classical manifestation of the quantum Zeno effect, wherein line-splitting occurs due to the high efficiency intracavity frequency conversion. For the sub-100 μm resonators, we present phase-matching calculations and dispersion-management techniques using analytical approximations and rigorous finite-element-method simulations. Experimentally, <i>Q </i>-factor measurements are shown, and we identify the specific short-comings of the fabrication procedure that may have led to the lower, surface-roughness-limited <i> Q</i>-factors. Finally, we identify pathways toward achieving the single-photon-level nonlinear optics using off-resonant nonlinear optics, which requires the simultaneous realization of phase-matching, large cavity lifetimes, and small mode volumes. We believe this would be feasible in the near future as more advanced fabrication and processing methods are developed for crystalline materials and novel nonlinear crystals are synthesized.</p>
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