Bulk nonlinear metamaterials for generation of quantum light

Quantum states of light, such as fixed photon number (Fock) states, entangled states, and squeezed states, offer important advantages with respect to classical states of light, such as coherent states and thermal states, in different areas: they enable secure communication and distribution of encryption keys, enable realization of sensors with higher sensitivity and resolution, and are considered candidates for quantum computing and simulation applications. To accommodate these applications, suitable methods for generating the quantum states are needed. Today, the quantum states are often produced by a spontaneous nonlinear process in a standard nonlinear material, followed by a series of optical elements necessary for encoding the desired state on the generated photons. In this review, we consider an alternative approach of structuring the nonlinearity of the crystal so that the desired quantum state will be generated directly at the crystal, without the need for additional elements. Our main focus here is on bulk crystals having structured second-order nonlinearity. The rising interest in these nonlinear metamaterials is fueled by advancements in the ability to efficiently simulate and design spontaneous parametric downconversion (SPDC) processes, as well as by new capabilities of structuring the nonlinearity of ferroelectric crystals, either by electric field poling or by laser-induced writing. As a result, nonlinear metamaterials were recently used to directly shape the spatial and spectral correlations of quantum light that is generated in SPDC. The paper covers the theoretical background and the design and fabrication methods of bulk nonlinear metamaterials for generating quantum light, as well as a series of demonstrations of the use of metamaterials in quantum optical applications.