Quantized Topological Response in Trapped Quantum Gases

TL;DR

This paper predicts a universal, quantized topological response in trapped 1D quantum gases, which can be experimentally observed through optical pulses and is robust under various conditions, with potential extensions to higher dimensions.

Contribution

It introduces a universal quantized topological response in 1D quantum gases and demonstrates its robustness and experimental observability, extending to nonlinear responses in higher dimensions.

Findings

Linear response is quantized and invariant under deformations.

Numerical results agree with analytical predictions.

Finite pulse duration causes minor deviations near transition times.

Abstract

In this letter, we propose a quantized topological response in trapped 1D quantum gases. The experimental protocol for the response requires the application of an instant optical pulse to a half-infinite region in an asymptotically harmonic trap and measuring the density distribution. We show that the corresponding linear response is described by a universal quantized formula in the thermal dynamical limit, which is invariant under local continuous deformations of the trapping potential $V$, atom distribution $f_\Lambda$, the spatial envelope of the optical pulse $\Theta_p$, and the measurement region $\Theta_m$. We test the statement by various numerical analysis, the result of which is consistent with the analytical prediction to high accuracy. We further show that a short but finite optical pulse duration only results in a violation of the quantization near the transition time, which suggests that quantized response could be observed in realistic experiments. We also generalize our results to non-linear quantized topological responses for atoms in higher dimensional harmonic traps.