Route to chaos in an atom-cavity system
Dr. Hans Keßler (Universität Hamburg)

In driven non-linear systems, various kinds of bifurcations can be observed on their route to chaos. From the evolution of Floquet multipliers one can extract information which serves as a precursor for phase transitions and dynamical instabilities. This method is applied in classical non-linear physics, for example, to obtain early warning signals.
Utilising our impressive control over an atom-cavity platform, we are able to prepare our system in various dynamical regimes and study the bifurcation experimentally in a quantum gas to obtain insights that could potentially be applied to more complex systems.
We prepare a Bose-Einstein condensate inside the centre of a cavity and pumping it perpendicular to the cavity axis with a standing wave light field. Upon crossing a critical pump strength, we observe a pitchfork phase transition from a normal to a steady state self-organized phase [1]. Employing an open three- level Dicke model, this transition can be understood as a transition between two fixpoints, indicating a pitchfork bifurcation. If the pump strength is increased further, the system undergoes a Hopf bifurcation. This causes limit cycles, which have time crystalline properties, to emerge [2]. In this regime, our model no longer shows fixpoints but stable attractive periodic orbits [3]. For strong pumping, we observe a second bifurcation, in our case a Neimark-Sacker bifurcation. Its main characteristics is an oscillation with two incommensurate frequencies, this may indicate the formation of a continuous time quasicrystal [4]. Finally, in the regime of very strong pumping, we observe chaotic dynamics with many contributing frequencies.

References:
[1] J. Klinder, et al., PNAS 112, 11 (2015)
[2] P. Kongkhambut, et al., Science 307 (2022)
[3] J. Skulte, et al., arXiv:2401.05332 (2023)
[4] P. Kongkhambut, et al., manuscript in preparation