Probing quantum geometry with two-dimensional nonlinear optical spectroscopy

Paul Froese; Mark R. Hirsbrunner; Yong Baek Kim

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arXiv · 2506.05462

Probing quantum geometry with two-dimensional nonlinear optical spectroscopy

Paul Froese·Mark R. Hirsbrunner·Yong Baek Kim

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Abstract

Recent studies have shown that the nonlinear optical response of crystalline systems is fundamentally a quantum geometric property. In this work, we propose two-dimensional coherent spectroscopy (2DCS), which measures the nonlinear conductivity as a function of two independent frequencies using two time-delayed light pulses, as a probe of quantum geometry. We show how the two-frequency second-order nonlinear conductivity, which is naturally measured by 2DCS, decomposes into distinct quantum geometric contributions. We identify a term arising from the multi-band quantum connection that does not appear in linear response, and show that it can be measured in isolation by considering specific polarizations and enforcing time-reversal symmetry. We explore this finding via model calculations for transition metal dichalcogenides and Sr$_2$RuO$_4$. Through these examples, we demonstrate how 2DCS enables study of the quantum connection, providing a way to compare the quantum geometry of different materials. We also show that one can gain rough momentum-resolved knowledge of the quantum geometry by varying the chemical potential.

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Paul Froese, Mark R. Hirsbrunner, Yong Baek Kim. 2025-07-04. Probing quantum geometry with two-dimensional nonlinear optical spectroscopy. https://arxiv.org/abs/2506.05462

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