Quantum Resistance Paradox of Low-Dimensional Superfluids
Resistance in standard conductors decreases with increasing cross-section. Yet, in low-dimensional superconductors and superfluids residual resistance arises from topological fluctuations of the order parameter manifesting as phase slips in one-dimensional (1D) and vortices in two-dimensional (2D) systems. How resistance and dissipation evolve as geometry interpolates between these regimes remains an open question. This evolution is masked in solid-state experiments by disorder, impurities, and geometric imperfections, and poses theoretical challenges due to competing dissipative processes and pronounced finite-size effects. Here, we use a defect-free unitary Fermi gas in a digitally programmable transport geometry to isolate geometric effects on superfluid dissipation and discover a paradox: in the crossover from 1D to 2D, the resistance reaches a minimum. There, widening a channel increases its resistance. Narrower, quasi-1D channels show dissipation described by Langer-Ambegaokar-McCumber-Halperin theory of phase slips. In this regime, varying the channel width yields the predicted exponential scaling of the activation factor over more than ten orders of magnitude. Wider, quasi-2D channels show dissipation consistent with a finite-size vortex model. The minimal dissipation in the dimensional crossover reflects a transition in the dominant dissipative mechanism, with both phase slips and vortices simultaneously suppressed. Our measurements suggest a route to minimizing dissipation in superconducting devices and provide a benchmark for theoretical efforts aimed at describing the dimensional crossover.