Nonequilibrium metastability of the attractive one-dimensional Bose gas

Many-body quantum systems out-of-equilibrium host phases of matter that simply do not exist in equilibrium scenarios: the one-dimensional Bose Gas (1dBG) with contact attractive interactions is an outstanding example of this dichotomy. The 1dBG is a ubiquitous effective description of many cold atoms experiments, where the presence of Feshbach resonances allows for a dynamical exploration of the whole interactions' range. On the theory side, a hallmark of the 1dBG is its integrability, which hinders thermalization and allows for analytical and exact insight. Within the attractive phase, the 1dBG forms bound states with arbitrary large negative binding energy, critically harming the stability of the gas at equilibrium. On the other hand, integrability prevents thermalization and enhances the stability of the gas.

In this talk, I discuss how, by slowly changing the interactions from positive to negative, it is possible to engineer a stable nonequilibrium phase. I build on new developments in the hydrodynamic theory of integrable models and provide an exact analytical solution of the protocol directly at the many-body level, showing the controlled formation of bound states and creating a far-richer scenario than the well-known Super Tonks-Girardeau phase. Experimental signatures in realistic settings of this new nonequilibrium phase are discussed.