A universal time-of-arrival signature of Bose--Einstein condensation

We show that Bose–Einstein condensation produces a cusp in the time-of-arrival (TOA) statistics of a harmonically trapped gas released into free fall. In the semiclassical long time-of-flight regime, with $\epsilon ={\sigma }_V\mathrm{/}\sqrt{2gH}\ll 1$, both the mean and standard deviation of the arrival time distribution, which are governed by the longitudinal velocity variance, remain continuous, but acquire a cusp whose one-sided slope ratio is universal within the ideal-gas far-field limit, ${\mathcal{R}}_{\mathrm{\infty }}=2.5556\dots$, and equals the trapped-gas specific-heat ratio $C(T{c}^{-})\mathrm{/}C(T{c}^{+})$. Finite atom number rounds the cusp and weak interactions perturb it only weakly, leaving a measurable time-domain signature of condensation.