We report the experimental observation of the full phase diagram across a transition where the spatial parity symmetry is broken. Our system consists of an ultra-cold gas of 39K with tunable interactions trapped in a double-well potential. At a critical value of the interaction strength, we observe a continuous quantum phase transition where the gas localizes in one well or the other, thus breaking the underlying symmetry of the system. Furthermore, we show the robustness of the asymmetric state against controlled energy mismatch between the two wells. This is the result of hysteresis associated with an additional discontinuous quantum phase transition that we fully characterize. Our results pave the way to the production of a broad class of quantum entangled states including Schroedinger cat states with macroscopic atom number.
A. Trenkwalder et al.,