We present transport measurements of unshunted dc superconducting quantum interference devices (SQUIDs) consisting of 30 nm wide aluminum nanobridges of varying length L contacted with two and three dimensional banks. 3D nanobridge SQUIDs with L $leq$ 150 nm (approximately 3-4 times the superconducting coherence length) exhibit $approx 70%$ critical current modulation with applied magnetic field, approaching the theoretical limit for an ideal short metallic weak link. In contrast, 2D nanobridge SQUIDs exhibit significantly lower critical current modulation. This enhanced nonlinearity makes 3D nanobridge Josephson junctions well suited to optimize sensitivity in weak link SQUID magnetometers as well as realize ultra low-noise amplifiers and qubits.
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