Nonlinear interactions using neutral atomic gases

Abstract

Nonlinearities in quantum systems provide some of the most intriguing physics to be exploited for quantum technologies and for quantum simulations. In this thesis, we explore quantum nonlinearities in two different contexts: The first is an experimental demonstration of coherent microwave-to-optical conversion using a warm $^{87}$Rb atomic vapor located inside a cylindrical microwave cavity. Frequency conversion is essential for transferring quantum information generated in the microwave domain to optical frequencies, where it can be transmitted and networked with minimal propagation loss. A hybrid, second-order nonlinear susceptibility in the vapor enables coherent frequency conversion of single- and multi-channel microwave signals. This conversion is tunable over a large 550(30) MHz range of output optical frequencies due to the thermal Doppler broadening of the excited atomic state. This system also permits phase-correlated amplitude control of select frequency channels, providing an analog to a frequency domain beam splitter across five orders of magnitude in frequency. The second context is a computational approach for accelerating computational solutions of the nonlinear Schr\"odinger equation. We employ open-source code and readily available graphics processing unit hardware. This allows us to simulate a quasi-2D version of the Gross-Pitaevskii equation, a specific type of the nonlinear Schr\"odinger model, where the nonlinearity arises from density-dependent scattering interactions. The equation describes a trapped, interacting, two-component Bose-Einstein condensate (BEC) subject to a spatially dependent interspin coupling. This computational approach lets us probe high-resolution spatial features—revealing an interaction-dependent phase transition—all in a reasonable amount of time.