Continuous and discrete scaling symmetries are interesting emergent phenomena in a strongly interacting quantum gases. In this talk I will present our theoretical predication and experimental observation of a novel type quantum dynamics for harmonic trapped unitary Fermi gas. When the frequency of the harmonic trap decreases as the inverse of time, surprisingly, instead of expanding continuously, the size of the cloud exhibits a sequence of plateaus. More remarkably, the locations of these plateaus obey a discrete geometric scaling law. We shall discuss the strong connection between this dynamical phenomenon of a many-body system and the Efimov effect of a few-body system. We shall also discuss how to realize a dynamic super-Efimov effect where the expansion of cloud size obeys a double exponential scaling behavior with this scheme. Our results hold for all scale invariant quantum gases, including non-interacting gases, Tonks gas in one-dimension, weakly interacting gases in two-dimension and unitary Fermi gas in three-dimension. We will also discuss the manifestation of scaling symmetry breaking in this effect.
Ref. Shujin Deng, Zhe-Yu Shi, Pengpeng Diao, Qianli Yu, Hui Zhai, Ran Qi, Haibin Wu, arXiv: 1512.02044