Recently, Prof. Xiong-Jun Liu’s group at Peking University, together with Prof. Dapeng Yu at Southern University of Science and Technology published a paper in Phys. Rev. Lett. reporting a progress on realization and detection of non-ergodic critical phases [Phys. Rev. Lett. 125, 073204 (2020)]. This work opens a broad avenue with high experimental feasibility to explore critical phases in ultracold atoms.

Disorder and quasi-periodic systems include the extended and Anderson localization (AL) phases in the absence of interactions, and the ergodic and many-body localization (MBL) phases in the presence of interactions. Both AL and MBL have been observed in cold atomic gases. Between the localization and ergodic extended phases, a third type of fundamental phases, called critical phases, can exist without or with interactions, with the latter case leading to the many-body critical (MBC) phase which is an extended but nonthermal quantum many body state [arXiv:1910.12080]. Critical phases are important in understanding the transitions from localization or MBL to extended phases, and exhibit various interesting features, including the critical spectral statistics, multifractal behavior of wave-functions , and dynamical evolutions. However, the critical phases have not been realized in experiment. So far only few theoretical models may host critical phases, but these models are not realistic in experiment. Further, the experimental diagnostic for detecting the critical phases is lacking. In the recent paper published in PRL, Prof. Xiong-Jun Liu at PKU and the collaborators propose a highly feasible 1D spin-orbit coupled model with incommensurate Zeeman potential for realizing critical phases in a broad phase diagram region separating from the extended and localized phases. In the noninteracting regime, they show that the critical phase can be detected by measuring the mean square displacement of the wave packet after a fixed evolution time in real space or measuring the momentum distributions. With interactions, they propose two observables: the return probability of the initial state and the density imbalance, to distinguish the MBC phase from both the ergodic and MBL phases. This work paves the way to observe the novel critical phases. 

Figure: The phase diagram of the critical phase of the proposed model, the realization, and the numerical results showing the existence of the noninteracting and many-body critical phases.

Dr. Yucheng Wang (PKU & SUSTec) and Dr. Long Zhang (PKU) are co-first authors of the paper. This work was supported by NSFC, MOST, and CAS.