Abstract
We study the spatially localized dark state, called dark soliton, in a one-dimensional system of the non-resonantly pumped microcavity-polariton condensate (MPC). From the recent work by Xue and Matuszewski [Phys. Rev. Lett. 112, 216401 (2014)], we know that the dark soliton in the pure MPC system is unstable. But we find that a dark soliton pinned by a defect in the impure MPC becomes a gray soliton and can be stabilized by the presence of a defect. Moreover, the stable regime of the gray soliton is given in terms of the defect strength and pump parameter.
Highlights
In the past two decades, the rapid experimental and theoretical developments in the field of Bose-Einstein condensates (BECs) [1,2,3,4] have led to a surge of interest in the study of the nonlinear matter waves
The stabilization of a dark soliton (DS) is addressed by introducing a defect in a non-resonantly pumped microcavity-polariton condensate (MPC)
We present an analytical model for a DS pinned by a point defect
Summary
In the past two decades, the rapid experimental and theoretical developments in the field of Bose-Einstein condensates (BECs) [1,2,3,4] have led to a surge of interest in the study of the nonlinear matter waves. The dark soliton (DS) characterized by a density dip and an associated phase gradient can occur in BECs with repulsive interactions They have been studied [6] and observed in a variety of systems such as discrete mechanical systems [7], magnetic films [8], fluids [9], and plasmas [10]. The properties of spontaneously formed vortices were studied thoroughly, the formation and behavior of DSs in non-equilibrium MPCs is much less understood [17,18,19,20]. The solution is obtained by solving the complex Gross-Pitaevskii equation (cGPE) with a defect This mean-field model for non-equilibrium MPCs is a generic model of considering effects from pumping, dissipation, potential trap, relaxation and interactions. The stability and Bogoliubov-excitation spectra of gray solitons pinned by finite-size defects are investigated.
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