We propose a scheme to generate and stabilize one- and two-dimensional dark, bright, dark-like, bright-like solitons, and vortices with m = 1 and m = 2 in a nonresonantly incoherent pumped exciton–polariton condensate. A spatially modulating pumping is introduced, which can compensate (counteract) the loss (gain) originated from the nonlinear excitation of the stable homogeneous polariton. The numerical simulations show that the balance between the gain and loss in this scheme can support and stabilize various nonlinear modes, not just stable dark solitons which have been found in the previous studies. Our proposal may provide a way to generate, stabilize, and control nonlinear modes in the nonresonantly pumped exciton–polariton system.
In this work, we study the nonlinear Josephson dynamics of Fermi superfluids in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a molecular Bose-Einstein condensate (BEC) in a double-well potential. Under a two-mode approximation, we derive a full two-mode (fTM) model including all interaction energy terms. By solving the fTM model numerically, we study the zero-phase and [Formula: see text]-phase modes of Josephson oscillations in the BCS–BEC crossover. We find that in the strongly interacting regime the cross interaction terms not appearing in the two-mode model cannot be easily ignored. The cross interactions can alter the behaviors of Josephson dynamics substantially, and interestingly the alterations for the zero-phase and [Formula: see text]-phase modes are just opposite.
We present a study of static and expansion properties of strongly interacting Fermi superfluids containing a vortex initially trapped by cylindrically symmetric potentials. Based on the order-parameter equation in the framework of the Gross–Pitaevskii equation, a unified expression for the energy of a vortex line in the crossover from a Bardeen–Cooper–Schrieffer superfluid to a molecular Bose–Einstein condensate is analytically presented. Numerical simulations show that the combined effects of interactions and trap configurations lead to an interesting property that the free expansion rate of the vortex core radius is smaller than that of the radius of the superfluid in the radial direction, when the strongly interacting Fermi superfluid containing a vortex is released from a cigar-shaped trap. The effects of the trap anisotropy and vortex on the Efimovian expansions of a unitary Fermi superfluid in real experimental setups are also predicted.
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