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The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while 'the half-quantum vortex street' is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately 0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system. [ABSTRACT FROM AUTHOR]

The use of Rydberg dressing technology to achieve long-range soft-core interaction in Bose–Einstein condensates (BECs) opens up new avenues for exploration of supersolid and its related phenomenon. We investigate the ground state of a two-component spin–orbit-coupled BECs with both long-range soft-core and contact interactions in radially periodic potentials. Our results show that the ground-state structures of the system are strongly influenced by spin–orbit coupling, contact interactions, long-range soft-core interactions, and the amplitude of the external potential. We find that such parameters can been used to induce desired ground-states structures, such as necklace structure of lump, striped standing wave, and especially ring dark soliton. Furthermore, we observe that the long-range soft-core interactions are used to manipulate the transition between miscible-immiscible phases like contact interactions. Our research provides another degree of freedom for manipulating supersolids in spin–orbit-coupled BECs. [ABSTRACT FROM AUTHOR]

The equation of state (EOS) of mixture of Li 1. 2 Mn 0. 5 4 Co 0. 1 3 Ni 0. 1 3 O2 and LiNi 0. 8 7 Co 0. 0 9 Mn 0. 0 3 Al 0. 0 1 O2 was studied by synchrotron radiation X-ray diffraction (XRD) at room-temperature in a diamond anvil cell (DAC). The results showed that the hexagonal structure is maintained to the highest pressure of 23.1 GPa. The bulk modulus and its first derivative obtained from XRD data are K 0 = 1 4 7. 4 (3. 1)  GPa and K 0 ′ = 2. 2 1 (0. 3 3) , respectively. In addition, we have investigated the high-pressure electrical conductivity of the mixture of Li 1. 2 Mn 0. 5 4 Co 0. 1 3 Ni 0. 1 3 O2 and LiNi 0. 8 7 Co 0. 0 9 Mn 0. 0 3 Al 0. 0 1 O2 to 22.9 GPa in a DAC. It is found that the resistance decreases with the increase of pressure and changes exponentially. [ABSTRACT FROM AUTHOR]