Quantized topological response in trapped quantum gases

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_Λ, the spatial envelope of the optical pulse Θₚ, and the measurement region Θₘ. 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.