Multipolar orders are key in addressing many outstanding questions in a wealth of quantum materials. Yet, their coupling to conventional linear probes is very weak, prohibiting the comprehensive understanding and efficient controlling of them. As the lowest rank multipolar order, the ferro-rotational order, schematically featured as a head-to-tail loop arrangement of electric dipole moments and mathematically described by the antisymmetric components of the electric quadrupolar tensor, was theoretically suggested to be widely present, but has been experimentally detected only very recently with nonlinear optics. In this talk, we will exploit the electric quadrupolar contribution to the second harmonic generation (SHG) to couple with this spatial-inversion and time-reversal symmetric ferro-rotational order. We will examine its symmetry properties with the rotational anisotropy (RA) measurements scheme of SHG, map its domain structures and domain boundaries with optical diffraction limited scanning SHG microscopy, and finally manipulate it and track its evolution on an ultrafast time scale with time-resolved RA-SHG.

References

[1] "Observation of a ferro-rotational order coupled with second-order nonlinear optical fields" Nature Physics, 16, 42 (2020)

[2] "Ultrafast modulations and detection of a ferro-rotational charge density wave using time-resolved electric quadrupole second harmonic generation" Phys. Rev. Letters 127, 126401 (2021)

[3] "Ferro-rotational domain walls revealed by electric quadrupole second harmonic generation microscopy" Phys. Rev. B, 107, L180102 (2023)

[4] "Ferroaxial density wave from intertwined charge and orbital order in rare-earth tritellurides" Nature Physics 21, 1578 (2025)

[5] "Electrotoroidicity: New Paradigm for Transverse Electromagnetic Responses" Nature Physics in press (2025)

Bio

Dr. Liuyan Zhao is an Associate Professor in the Department of Physics and a Fellow of the Quantum Research Institute at the University of Michigan. She received her Ph.D. in Physics from Columbia University in 2013 and was then a Richard Tolman Prize Fellow at the California Institute of Technology till 2016, before joining the University of Michigan in 2017. Her research focuses on understanding and controlling emergent quantum phases in solid-state materials through the development and application of advanced optical techniques. Her honors include APS Fellow, Presidential Early Career Award for Scientists and Engineers (PECASE), Mildred Dresselhaus Guest Professorship, Sloan Research Fellowship, and Bryan R. Coles Prize from SCES. She also serves on the Editorial Board of Physical Review X and as an Associate Editor of Progress in Quantum Electronics.