Extended Data Fig. 1: Expansion in the presence of losses: BPM simulations.

(a) In an ideal lossless system, the overall power is conserved, and the total power contained in the fundamental mode steadily grows during the cooling process. (b) The presence of losses introduces a global power decay (dashed red line), but the relative fraction of power contained in the fundamental mode (solid blue line) at a given propagation distance nevertheless increases as nonlinear expansion proceeds. As shown in Fig. 3b, even in the presence of significant propagation losses attenuation 0.3 dB/cm, a value beyond the typical losses of 0.4 dB/cm for laser-written waveguides in fused silica, the efficiency of the JT power transfer to the ground state only decreases by approximately 10%.