Fast Entanglement Generation via Collective Three-Body Interactions in an Optical Cavity*

Cavity QED provides a powerful platform for quantum metrology and simulation, traditionally relying on pairwise spin-spin interactions. Our recent experimental demonstration of mean-field dynamics in novel three-body interactions [1] challenges this paradigm and motivates new studies about the nature of the generated states and their advantages in quantum sensing. In this talk, we first show that collective three-body interactions can generate high-fidelity GHZ states with an O(N) speedup over the One-Axis Twisting (OAT) model under realistic conditions. For more general evolution times,  the generated states exhibit Heisenberg scaling and possess discrete rotational symmetry, which can be probed by measuring standard collective spin observables after a time-reversal protocol and further characterized through measurements of multiple-quantum coherences. We analyze the effects of intrinsic dissipation in the cavity QED system, and demonstrate that three-body interactions can be more robust than OAT in certain parameter regimes. Our protocols naturally extend to other systems coupled by bosonic mediated interactions, such as trapped ions and superconducting circuits, paving the way for fast entanglement generation and highly non-Gaussian quantum states with exotic symmetries.

[1] Luo, C., Zhang, H., Maruko, C., Bohr, E. A., Chu, A., Rey, A. M., & Thompson, J. K. (2024). Realization of three and four-body interactions between momentum states in a cavity through optical dressing. arXiv preprint arXiv:2410.12132.