We theoretically investigate dynamics of two dark solitons in a polariton condensate under nonresonant pumping, based on driven dissipative Gross–Pitaevskii equations coupled to the rate equation. The equation of motion of the relative center position of two-dark soliton is obtained analytically by using the Lagrangian approach. In particular, the analytical expression of the effective potential between two dark solitons is given. The resulting equation of motion captures how the open-dissipative character of a polariton Bose–Einstein condensate affects properties of dynamics of two-dark soliton, i.e., two-dark soliton relax by blending with the background at a finite time. We further simulate the relative motion of two dark solitons numerically with the emphasis on how two-soliton motion is manipulated by the initial velocity, in excellent agreement with the analytical results. The prediction of this work is sufficient for the experimental observations within current facilities.
A quantum system in complex potentials obeying parity-time ( P T ) symmetry could exhibit all real spectra, starting out in non-Hermitian quantum mechanics. The key physics behind a P T -symmetric system consists of the balanced gain and loss of the complex potential. We plan to include the nonequilibrium nature (i.e., the intrinsic kinds of gain and loss of a system) to a P T -symmetric many-body quantum system, with an emphasis on the combined effects of non-Hermitian due to nonequilibrium nature and P T symmetry in determining the properties of a system. To this end, we investigate the static and dynamical properties of a dark soliton of a polariton Bose–Einstein condensate under the P T -symmetric non-resonant pumping by solving the driven-dissipative Gross–Pitaevskii equation both analytically and numerically. We derive the equation of motion for the center of mass of the dark soliton’s center analytically with the help of the Hamiltonian approach. The resulting equation captures how the combination of the open-dissipative character and P T -symmetry affects the properties of the dark soliton; i.e., the soliton relaxes by blending with the background at a finite time. Further numerical solutions are in excellent agreement with the analytical results.
Magnetic soliton is an intriguing nonlinear topological excitation that carries magnetic charges while featuring a constant total density. So far, it has only been studied in the ultracold atomic gases with the framework of the equilibrium physics, where its stable existence crucially relies on a nearly spin-isotropic, antiferromagnetic, interaction. Here, we demonstrate that magnetic soliton can appear as the exact solutions of dissipative Gross–Pitaevskii equations in a linearly polarized spinor polariton condensate with the framework of the non-equilibrium physics, even though polariton interactions are strongly spin anisotropic. This is possibly due to a dissipation-enabled mechanism, where spin excitation decouples from other excitation channels as a result of gain-and-loss balance. Such unconventional magnetic soliton transcends constraints of equilibrium counterpart and provides a novel kind of spin-polarized polariton soliton for potential application in opto-spintronics.
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