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Digital signal processing is supporting novel in-field applications of optical interferometry, such as in laser ranging and distributed acoustic sensing. While the highest performances are achieved with field-programmable gated arrays, their complexity and cost are often too high for many tasks. Here, we describe an alternative solution for processing optical signals in real-time, based on a dual-core 32-bit microcontroller. We implemented in-phase and quadrature demodulation of optical beat-notes resulting from the interference of independent laser sources, phase noise analysis of deployed optical fibers covering intercity distances, and synchronization of remote acquisitions via optical trigger signals. The embedded architecture can efficiently accomplish a large variety of tasks in the context of optical signal processing, being also easily configurable, compact and upgradable. These features make it attractive for applications that require long-term, remotely-operated, and field-deployed instrumentation.

When a second-order phase transition is crossed at finite speed, domains with independent order parameters can appear in the system, with the consequent formation of defects at the domain boundaries. The Kibble-Zurek theory provides a description for this universal phenomenon, which applies to many different systems in nature, and it predicts a power-law dependence of the defect density on the quench rate. This thesis reports on the results of the experimental study of the Kibble-Zurek mechanism in elongated Bose-Einstein condensates of atomic sodium gases, following the observations on the spontaneous formation of defects after temperature quenches across the BEC transition. The power-law scaling of the defect number with the quench speed was observed and characterized for the first time in ultracold gases. The characterization of the density and phase profiles of the defects allowed their identification as solitonic vortices, representing the first direct experimental evidence for this kind of long living excitation, which sets a link between solitons and vortices. The measurements reported in this thesis provide a novel approach to the study of the critical phenomena happening at phase transitions, and introduce to the possibility of exploring the turbulent dynamics of quenched systems through the spontaneous production of solitonic vortices.