Universal dynamic scaling and Contact dynamics in quenched quantum gases

Abstract

Recently universal dynamic scaling is observed in several systems, which exhibit a spatiotemporal self-similar scaling behavior, analogous to the spatial scaling near phase transition. The latter one arises from the emergent continuous scaling symmetry. Motivated by this, we investigate the possible relation between the scaling dynamics and the continuous scaling symmetry in this paper. We derive a theorem that the scaling invariance of the quenched Hamiltonian and the initial density matrix can lead to the universal dynamic scaling. It is further demonstrated both in a two-body system analytically and in a many-body system numerically. For the latter one, we calculate the dynamics of quantum gases quenched from the zero interaction to a finite interaction via the non-equilibrium high-temperature virial expansion. A dynamic scaling of the momentum distribution appears in certain momentum-time windows at unitarity as well as in the weak interacting limit. Remarkably, this universal scaling dynamics persists approximately with smaller scaling exponents even if the scaling symmetry is fairly broken. Our findings may offer a new perspective to interpret the related experiments. We also study the Contact dynamics in the BEC−BCS crossover. Surprisingly, the half-way time displays a maximum near unitarity while some damping oscillations occur on the BEC side due to the dimer state, which can be used to detect possible two-body bound states in experiments.

Graphical abstract

Keywords

dynamic scaling / Contact dynamics / quantum gases / cold atom / quench dynamics / virial expansion / continuous scaling symmetry

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Declarations

The authors declare that they have no competing interests and there are no conflicts.

Acknowledgements

We thank Zheyu Shi, Pengfei Zhang, Ran Qi, Zhiyuan Yao, Lei Pan, Ren Zhang, and Hui Zhai for inspiring discussion. The project was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 12004049) and the Fund of State Key Laboratory of IPOC (BUPT) (Nos. 600119525 and 505019124).

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