Quantized Topological Response in Trapped Quantum Gases

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.

5 pages, 2 figures + supplementary material

References in corpus (8)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Observation of Quantized Conductance in Neutral Matter
• Two-terminal transport measurements with cold atoms
• Quantized Nonlinear Conductance in Ballistic Metals
• Topological Multipartite Entanglement in a Fermi Liquid
• Quantized Nonlinear Transport with Ultracold Atoms

Cited by in corpus (6)

• Topological Andreev Rectification
• Topological Density Correlations in a Fermi Gas
• Non-Adiabatic Effect in Topological and Interacting Charge Pumping
• Euler--Chern Correspondence via Topological Superconductivity
• Generic reduction theory for Fermi sea topology in metallic systems
• Quantized nonlinear transport and its breakdown in Fermi gases with Berry curvature