We investigate the properties of Bose-Einstein condensates (BECs) in a two-dimensional quasiperiodic optical lattice (OL) with eightfold rotational symmetry by numerically solving the Gross-Pitaevskii equation. In a stationary external harmonic trapping potential, we first analyze the evolution of matter-wave interference pattern from periodic to quasi-periodic as the OL is changed continuously from four-fold periodic and eight-fold quasi-periodic. We also investigate the transport properties during this evolution for different interatomic interaction and lattice depth, and find that the BEC crosses over from ballistic diffusion to localization. Finally, we focus on the case of eightfold symmetric lattice and consider a global rotation imposed by the external trapping potential. The BEC shows vortex pattern with eightfold symmetry for slow rotation, becomes unstable for intermediate rotation, and exhibits annular solitons with approximate axial symmetry for fast rotation. These results can be readily demonstrated in experiments using the same configuration as in Phys. Rev. Lett. 122, 110404 (2019).

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The spontaneous formation of lattice structure of quantized vortices is a characteristic feature of superfluidity in closed systems under thermal equilibrium. In exciton-polariton Bose-Einstein condensate, which is a typical example of macroscopic quantum state in open systems, spontaneous vortex lattices have also been proposed by not yet observed. Here, we take into account the finite decay rate of exciton reservoir, and theoretically investigate the vortex structures in circularly pumped polariton Bose-Einstein condensate. Our results show that a decreasing reservoir decay rate can reduce the number of vortices and destabilize the lattice structure, hence is unfavorable to the formation and observation of vortex lattices. These detrimental effects can be prevailed by applying an external angular momentum.

Phase transitions in nonequilibrium dynamics of many body quantum systems, the so-called dynamical phases transition (DPTs), play an important role for understanding various dynamical phenomena observed in different branches of physics. In general, there have two types of DPTs, the first one refers to the phase transition that is characterized by distinct evolution behaviors of a physical observable, while the second one is marked by the nonanalyticities in the rate function of the initial state survival probability. Here, we focus on such DPTs from both quantum and semiclassical perspectives in a spinor Bose-Einstein condensate (BEC), an ideal platform to investigate nonequilibrium dynamics. By using the sudden quench process, we demonstrate that the system exhibits both types of DPTs present as the control parameter quenches through the critical one, referring to as the critical quench. We show analytically how to determine the critical quenches by means of the semiclassical approach and carry out a detailed examination on both semiclassical and quantum signatures of two types of DPTs. Moreover, we further reveal that the occurrence of DPTs is closely connected to the separatrix in the underlying classical system. Our findings provide more insights into the properties of DPTs and verify the usefulness of semiclassical analysis for understanding DPTs in quantum systems with well-defined semiclassical limit.

The tunneling dynamics of dilute boson gases with three-body interactions in a periodically driven double wells are investigated both theoretically and numerically. In our findings, when the system is with only repulsive two-body interactions or only three-body interactions, the tunneling will be suppressed; while in the case of the coupling between two- and three-body interactions, the tunneling can be either suppressed or enhanced. Particularly, when attractive three-body interactions are twice large as repulsive two-body interactions, CDT occurs at isolated points of driving force, which is similar to the linear case. Considering different interaction, the system can experience different transformation from coherent tunneling to coherent destruction of tunneling (CDT). The quasi-energy of the system as the function of the periodically driving force shows a triangular structure, which provides a deep insight into the tunneling dynamics of the system.