Characterization and Control of Spatial Correlations in Entangled Twin Beams

Abstract

Our understanding and ability to manipulate quantum correlations in non-classical states of light will be a determining factor in realizing the next generation of quantum technologies. Over the last several decades, we witnessed the wide-scale use of sensing and communication technologies, such as RADAR/LiDAR, radio, and fiber-optics telecommunications, that were based on classical conceptions of electromagnetic fields. Harnessing the power of the counter-intuitive phenomenon of quantum superposition and entanglement, quantum theory promises a transformative leap in capabilities that lies beyond such classical approaches. The early success of quantum secure communication, quantum computers, advanced gravitational-wave detectors, and quantum random number generators offer a glimpse into the immense potential offered by quantum mechanics. This dissertation investigates the manipulation of quantum correlations in light, particularly focusing on the spatial degrees of freedom, to propel the development of next-generation quantum technologies.

Quantum states of light, known as twin beams, intrinsically linked through quantum correlations, form the cornerstone of this exploration. These bipartite entangled beams of light are at the heart of several quantum sensing applications and are natural candidates to encode and exchange quantum information. Their generation via the nonlinear parametric process of four-wave mixing leads to temporal (energy conservation) and spatial (momentum conservation) correlations in the quantum regime. Notably, the conservation of transverse momentum in the fields during the process implies that the spatial properties of the input photons determine the distribution of spatial correlations in the generated entangled photons, thus providing a practical way to engineer the correlated spatial modes. After characterizing the entanglement within the spatial as well as spatio-temporal degrees of freedom of the twin beams via a direct imaging technique, this dissertation delves into the extensive engineering of spatial correlations of the fields generated through four-wave mixing.

Our approach of using a deliberately phase-structured input field to drive the four-wave mixing leads to the creation of spatially structured quantum states. The degree of control demonstrated via the phase manipulation implies that this approach can be tailored to the specific requirements of quantum sensing and imaging applications. The abundance of spatial modes in the multimode twin beams that utilize the vastness of the Hilbert space associated with spatial modes, coupled with precise control over their correlations, unlocks possibilities for high-dimensional quantum communication protocols, leading to ultra-secure and high-capacity quantum teleportation and communication.