# Probing topology by "heating": Quantized circular dichroism in ultracold atoms

## TL;DR

This paper demonstrates a novel topological probe using quantized circular dichroism in ultracold atoms, linking depletion rates under circular drive to the Chern number, revealing a universal method to measure topological order.

## Contribution

It introduces a new method to measure topological invariants via depletion rates in driven systems, connecting topological properties to observable dynamical responses.

## Key findings

- Depletion rate difference relates to the Chern number.
- Quantized response depends non-linearly on drive strength.
- Edge states influence the topological depletion phenomenon.

## Abstract

We reveal an intriguing manifestation of topology, which appears in the depletion rate of topological states of matter in response to an external drive. This phenomenon is presented by analyzing the response of a generic 2D Chern insulator subjected to a circular time-periodic perturbation: due to the system's chiral nature, the depletion rate is shown to depend on the orientation of the circular shake. Most importantly, taking the difference between the rates obtained from two opposite orientations of the drive, and integrating over a proper drive-frequency range, provides a direct measure of the topological Chern number of the populated band ($\nu$): this "differential integrated rate" is directly related to the strength of the driving field through the quantized coefficient $\eta_0\!=\!\nu /\hbar^2$. Contrary to the integer quantum Hall effect, this quantized response is found to be non-linear with respect to the strength of the driving field and it explicitly involves inter-band transitions. We investigate the possibility of probing this phenomenon in ultracold gases and highlight the crucial role played by edge states in this effect. We extend our results to 3D lattices, establishing a link between depletion rates and the non-linear photogalvanic effect predicted for Weyl semimetals. The quantized circular dichroism revealed in this work designates depletion-rate measurements as a universal probe for topological order in quantum matter.