Quantum degenerate gases, in the form of Bose-Einstein condensates, are ideal objects for probing fundamental quantum mechanical phenomena. These platforms are highly isolated, and enable coherent control and manipulation of quantum matter with exquisite precision. The work presented in this thesis utilizes quantum degenerate gases of bosonic $^7$Li which have tunable interactions, allowing for studies of both single-particle and many-body physics. By subjecting these gases to periodic driving, a rich and diverse landscape of physical phenomena is unlocked. I will first describe our work realizing a thermodynamic engine with a quantum degenerate working fluid, achieved via slow periodic driving, and the effect of quantum degeneracy on engine performance. In the regime of fast driving, I will then propose a scheme for a noise-tolerant continuously-trapped atom interferometer.