Bose-Einstein Condensate Analogue of a Density Bounce: Healing Length at Peak Compression

This paper examines how far a rubidium condensate can be compressed before the healing length reaches the cloud size, as a laboratory analogue of a density turnaround. The system considered is a rubidium-87 condensate with scattering length 5.3 nm compressed through four decades of density, and the observable is healing length, chemical potential and the compression endpoint. Evaluating the ordinary behaviour of the system and the spin-torsion contribution under explicit assumptions about polarisation and uniformity, and inverting the comparison at the stated laboratory precision, gives a quantitative bound rather than a qualitative assertion of smallness. The computed record is: rows contains 4 evaluated points; point 1 n_per_m3 = 1.000e+19; point 1 healing_m = 8.664e-07; point 1 mu_J = 5.127e-32; point 1 mu_over_kB_nK = 3.714; point 2 n_per_m3 = 1.000e+20; point 2 healing_m = 2.740e-07; point 2 mu_J = 5.127e-31; point 2 mu_over_kB_nK = 37.14; point 3 n_per_m3 = 1.000e+21; point 3 healing_m = 8.664e-08; point 3 mu_J = 5.127e-30; point 3 mu_over_kB_nK = 371.4; g_SI = 5.127e-51; mass_kg = 1.445e-25; healing_at_1e20_m = 2.740e-07. The torsion-related contribution is far below the level that would alter the ordinary behaviour of the system at current precision, and the value that would have produced a visible residual is stated so that future improvements can be assessed against it directly. No new measurement is reported. This study is simulated and computed from stated assumptions, not measured.