Non-Markovian atom-only dynamics in multimode cavity QED

Ultracold atoms in multimode cavity QED provide an ideal platform to study quantum many-body physics out of equilibrium, as the cavity modes mediate tunable-range interactions between atoms allowing for the exploration of a wide range of models [1]. In such systems, it is desirable to derive open quantum system descriptions of the atoms in order to significantly shrink the Hilbert space, which otherwise becomes quickly intractable. However, we will show that the most standard approximations used to derive such atom-only descriptions can lead to wrong predictions, even in the simple case of the driven-dissipative Dicke model in a single-mode cavity. In this context, we will show that a Redfield master equation for the atoms (which goes beyond the secular approximation and the large detuning limit) is needed to predict the existence of the superradiant phase transition [2]. Then, we will present how an exact non-Markovian stochastic method [3] can be used to overcome the problem of choosing the right atom-only model, allowing for an accurate numerical description of the atomic dynamics in single- and multimode cavities.

[1] V. D. Vaidya, Y. Guo, R. M. Kroeze, K. E. Ballantine, A. J. Kollár, J. Keeling, and B. L. Lev, Phys. Rev. X 8, 011002 (2018).

[2] F. Damanet, A. J. Daley, and J. Keeling, Phys. Rev. A 99, 033845 (2019).

[3] D. Suess, A. Eisfeld, and W. T. Strunz, Phys. Rev. Lett. 113, 150403 (2014).