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

Mathieu Beau; Timothey Szczepanski

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arXiv · 2607.00184

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

Mathieu Beau·Timothey Szczepanski

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Abstract

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 $\epsilon=\sigma_V/\sqrt{2gH}\ll1$, 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, $\mathcal{R}_\infty=2.5556\ldots$, and equals the trapped-gas specific-heat ratio $C(Tc^-)/C(Tc^+)$. Finite atom number rounds the cusp and weak interactions perturb it only weakly, leaving a measurable time-domain signature of condensation.

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Mathieu Beau, Timothey Szczepanski. 2026-06-30. A universal time-of-arrival signature of Bose--Einstein condensation. https://arxiv.org/abs/2607.00184

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