We have developed a robust interrogation system using frequency modulation spectroscopy to measure the quantum state-dependent phase shift incurred on an off-resonant optical probe when transmitted by an atomic medium. Recently, our focus has been on extending this technique for the detection of Feshbach resonances in 87Rb atoms. Feshbach resonance is a mechanism which allows the atomic interaction strength to be precisely tuned via an external magnetic field. To access a Feshbach resonance atoms must be independently prepared in certain internal states, during which we utilize programmable optical tweezers to perform precise spatial micro-manipulation of the ensemble in laser "test-tubes." We use our dispersive probing system to identify the resonant magnetic field value in a sample with a dense "ball" geometry. An important design consideration for such a probing scheme is the three-dimensional mode-matching at the interface between light and the atomic sample when coupled by the dispersive interaction. We discuss challenges which dealing with this new geometry compared to the previously used prolate geometry, and consider the possibility of dipole-dipole interactions in our sample leading to cooperative light scattering processes.