Bose-Einstein Condensate in a cavity, phase transitions in an open quantum system

Ultra-cold gases interacting with the coherent field of an optical cavity represent a well-controlled example of an open quantum system. A Bose-Einstein condensate strongly coupled to the cavity mode can undergo a phase transition to an organized state where the atoms scatter light collectively. This system can be mapped to the Dicke model, realizing a driven-dissipative version of it. I will present our latest results on the extension of the coupling scheme to spinor BECs, leading to the appearance of magnetic correlations in the phase diagram. We explore the competition between two organization patterns in a spin mixture. A density modulated phase competes with a novel organized phase characterized by spin modulations. We explain our findings in the context of an extended Dicke model, with excellent agreement to the experimental observations. The natural dissipation channel provided by photons leaking out of the cavity leads to intriguing consequences for the system's statistical properties at zero temperature and allows for real-time access on the system's dynamics. In the case of the spin mixture, dissipation has strong consequences on the phase diagram resulting in the presence of exceptional points leading to dynamical instabilities.