Qudits, with their state space of dimension d > 2, open fascinating experimental prospects. The quantum properties of their states provide new potentialities for quantum information, quantum contextuality, expressions of geometric phases, facets of quantum entanglement and many other foundational aspects of the quantum world, which are unapproachable with qubits. We here experimentally investigate the quantum dynamics of a qudit (d = 4) that consists of a single 3/2 nuclear spin embedded in a molecular magnet transistor geometry, coherently driven by a microwave electric field. We propose and implement three protocols based on a generalization of the Ramsey interferometry to a multilevel system. First, the standard Ramsey interference is used to measure the accumulation of geometric phases. Then, two distinct transitions of the nuclear spin are addressed to measure the phase of an iSWAP quantum gate. Finally, through a succession of two Hadamard gates, the coherence time of a 3-state superposition is measured.
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