Self-organisation of cold atoms in optical cavities

Abstract

The realisation of self-organisation of ultracold atoms in optical cavities, where the light field can couple strongly to the atomic field, paves the way for the observation of phase transitions in which the spatial order is entirely emergent, such as glassiness or supersolidity. This fact, and the flexibility of cavity environment, makes these light-matter systems ideal candidates for quantum simulation. A wide range of physics has already been demonstrated in cavities coupled to ultracold atoms.

In this work, we seek to contribute two additions to the growing toolbox of phase transitions in optical cavities. First, we consider a transversely pumped, single mode cavity containing a Bose-condensed atomic cloud – a system that is well studied, and which undergoes spatial self-organisation. We treat this in an open system formalism, without the two-level approximation or linearised treatment which are common assumptions in literature. Within this complete treatment, we observe a first order phase transition, with associated bistability leading to hysteresis. We also demonstrate that in some parameter range, the system displays chaotic behaviour due to a strange attractor of the dynamics. Both of these observations explain features of experimental data from previous literature.

We then consider the case of a multimode, longitudinally pumped cavity in the confocal geometry, i.e. supporting a degenerate mode family. This is motivated both by the rich physics observed in a multimode confocal cavity in the transversely pumped regime, and by the self-patterning observed in single-mirror experiments. We find that the behaviour of the system is too complex for characterisation, and that the analytic understanding we can gain from weak coupling approximations never holds. We conclude that there is no simple self-organisation in our model.