Advancing phase space and matrix product state methods for cavity-coupled molecules

Johannes Schachenmayer University of Strasbourg

Theoretically explaining collective cavity-modified physics and chemistry remains to be a challenge for a large number N of coupled molecules. Key mechanism responsible for experimental observations are still lacking a theoretical understanding up to date. In particular, the question about how local chemistry can be modified in a macroscopic limit (with vanishing single-emitter coupling strengths) is important and still open. This talk will first review how we suggested that disorder and semi-localized [1] dark states can lead to a robust modification of nuclear dynamics, also in the large-N limit in a toy-model molecule setup [2]. Answering the question also for realistic molecules will require more advanced numerical methodologies for large-scale quantum many-body dynamics with long- range connectivity and couplings to an environment. This talk focuses on our recent advances with semi-classical phase space methods [3,4] and with new open-sysem matrix product state approaches [5], and explains how they could become important for the young research field of polaritonic chemistry.

[1] T. Botzung, D. Hagenmüller, S. Schütz, J. Dubail, G. Pupillo, and J. Schachenmayer, Phys. Rev. B 102, 144202 (2020)

[2] D. Wellnitz, G. Pupillo, and J. Schachenmayer, Commun Phys 5, 120 (2022)

[3] B. Zhu, A. M. Rey, and J. Schachenmayer, New J. Phys. 21, 082001 (2019)

[4] L. J. Bond, B. Gerritsen, J. Minář, J. T. Young, J. Schachenmayer, A. Safavi-Naini, arXiv:2407.02617 (2024)

[5] R. Daraban, F. Salas-Ramírez and J. Schachenmayer, Non-Unitarity Optimising Unraveling of Open Quantum Dynamics, [upcoming] (2024)