Hybrid model reduction techniques for semiclassical dynamics with strong quantum features

While quantum models for many-body dynamical systems quickly become intractable to numerically analyze, turning to naive semiclassicalization also precludes key features such as entanglement or non-Gaussianity. Often however, these features only manifest in a handful of degrees of freedom (e.g., strongly coupled atoms), while the remainder of the state remains close to some simple, low-dimensional manifold. We demonstrate a model reduction technique based on the formalism of [1], where a dynamic basis transformation using manifold coordinates can be used to reduce the complexity of the state, while retaining a full quantum description up to truncation. For concreteness, we apply this technique to a multi-atom cavity QED system, where a handful of atoms strongly couple to the cavity field amidst a background of many weakly coupled atoms. We show that the manifold coordinate evolution corresponds to Maxwell-Bloch dynamics, while the residual quantum state features Jaynes-Cummings physics.

[1] N. Tezak, N. H. Amini, and H. Mabuchi, arXiv:1704.05369 [Physical Review A (to be published)].