Feasibility of step-response experiment to directly measure the quantum metric

Determine whether the proposed step electric-field relaxation protocol, in which an insulator is driven by an external electric field E(t)=E0·Θ(−t) and the bulk dipole moment’s relaxation function is measured to extract the symmetric part of the time-dependent quantum geometric tensor (yielding the quantum metric at t=0), can be implemented in a realistic experimental setup, including the constraints of the high-temperature classical limit required for direct extraction and the inversion kernel needed at general temperatures.

Background

The paper proposes a method to directly access the symmetric part of the time-dependent quantum geometric tensor (tQGT) and thereby the quantum metric via a step-response protocol. Specifically, the authors show that the relaxation of the bulk dipole moment following an electric field step E(t)∝Θ(−t) yields a relaxation function related to the symmetric tQGT and, in the classical high-temperature limit, directly proportional to it, enabling extraction of the quantum metric at t=0.

They derive an expression connecting the relaxation function to the symmetric tQGT through a generalized fluctuation-dissipation relation and provide an inversion kernel to recover the symmetric tQGT at general temperatures. The authors note practical challenges, including the need for very high temperatures for the classical limit and potential error amplification due to the non-linear inversion kernel, leading to an explicit uncertainty regarding the experimental feasibility of the protocol.