Fig. 3: Fulfillment of integrability condition.
The s-wave scattering length value is set, followed by a variation of the radial trapping frequency ωr up to the point at which U0 = U13, corresponding to the frequency required for the system to be integrable. The red dashed (solid) and cyan long dashed (solid) depict U0 (U13) for a = 32.5 a0 and a = 30 a0, respectively, for different values of ωr. By setting a = 32.5 a0 (30 a0), we find ωr ≈ 2π × 54.110 kHz (51.759 kHz) as the frequency for integrability, which results in U0/ℏ = U13/ℏ ≈ 244.405 Hz (245.141 Hz). The points where U0 = U13 and the corresponding frequencies ωr are highlighted by the dotted lines. The system is robust for small deviations from the integrable point (see Supplementary Note 5 for more details).
