Molecular Entanglement Witness by Absorption Spectroscopy in Polariton Chemistry

Maintaining molecular entanglement at room temperature and detecting multipartite entanglement features of macroscopic molecular systems remain key challenges for understanding the non-trivial quantum effect in chemical quantum dynamics. Here, we study the quantum Fisher information, a central concept in quantum metrology, as a multipartite entanglement witness. We generalize the entanglement witness functional related to quantum Fisher information regarding non-identical local response operators and show that it is a good molecular entanglement witness for ultrastrong light-matter coupling in cavity quantum electrodynamics and even a multi-molecular entanglement witness during the superradiance phase transition. We further connect quantum Fisher information to the dipole correlator, which suggests that molecular entanglement could be detected by linear absorption spectrum at finite temperatures. Our work proposes a general protocol to sufficiently measure molecular entanglement for chemical systems at room temperature in experiments and demonstrate the long-lived multi-molecular entanglement in the polariton chemistry systems.