Quantum critical states and phase transitions in the presence of non equilibrium noise

Quantum critical points are characterized by scale invariant correlations and correspondingly long ranged entanglement. As such, they present fascinating examples of quantum states of matter, the study of which has been an important theme in modern physics. Nevertheless very little is known about the fate of quantum criticality under non equilibrium conditions. In this paper we investigate the effect of external noise sources on quantum critical points. It is natural to expect that noise will have a similar effect to finite temperature, destroying the subtle correlations underlying the quantum critical behavior. Surprisingly we find that in many interesting situations the ubiquitous 1/f noise preserves the critical correlations. The emergent states show intriguing interplay of intrinsic quantum critical and external noise driven fluctuations. We demonstrate this general phenomenon with specific examples in solid state and ultracold atomic systems. Moreover our approach shows that genuine quantum phase transitions can exist even under non equilibrium conditions.