We study the quantized topological response of trapped one-dimensional quantum gases, which involves applying an optical pulse to a half-infinite region in an asymptotically harmonic trap and measuring the resulting density distribution. We prove that the corresponding linear response is described by a universal quantized formula in the thermodynamic limit, which is invariant under local continuous deformations of the trapping potential $V$, atom distribution $f_{\mathrm{\Lambda }}$, the spatial envelope of the optical pulse ${\mathrm{\Theta }}_p$, and the measurement region ${\mathrm{\Theta }}_m$. Our numerical analysis confirms this prediction with high accuracy, and we show that a short but finite optical pulse duration only causes a violation of quantization near the transition time. Our work presents an exciting avenue for exploring quantized topological phenomena in trapped quantum gases.

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• Atomic & molecular processes in external fields
• Fermi gases
• Trapped atoms
• Topology