Shock wave occurrence and soliton propagation in polariton condensates

Abstract

We study the effects of the gain and the loss of polaritons on the wave propagation in polariton condensates. This system is described by a modified Gross–Pitaevskii equation. In the case of small damping, we use the reductive perturbation method to transform this equation; we get a modified Burgers equation in the dispersionless limit and a damped Korteweg – de Vries equation in a more general case. We demonstrate that the shock wave occurrence depends on the gain and the loss of polaritons in the dispersionless polariton condensate. The resolution of the damped Korteweg – de Vries equation shows that the soliton behaves like a damped wave in the case of a constant damping. Based on an asymptotic solution, the survival time and the distance traveled by this soliton are evaluated. We solve the damped Korteweg – de Vries equation and the modified Gross–Pitaevskii numerically to validate the analytical calculations and discuss especially the soliton propagation in the system.

Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form

“…Certain generalized versions of Eq. ( 1) have been also applied to the study of BE condensate of polaritons [24][25][26][27][28][29][30][31][32].…”

Generation and Control of Shock Waves in Exciton-Polariton Condensates

“…[1][2][3][4][5][6][7][8][9][10][11][12] The polariton BEC is a non-thermodynamic equilibrium system. [13] At the same time, the system has the characteristics [14] of short lifetime, small effective mass, [15,16] strong interaction, coexistence of gain and loss, [17] and so on. Bright solitons, [18,19] gap solitons, [20] multipolar solitons, [21] vortex lattices, [22] spatial patterns, [23] and spinor dark soliton trains [24] were discovered in previous studies by introducing different pumps and external potentials.…”

“…[26,27] Shock waves have been found in different fields of physics, such as plasmas, [28] optics, [29] water waves, [30] and polariton BECs. [13,31] Under weak dispersion approximation conditions, through the discussion of the Riemann problem [32][33][34][35][36] of the defocusing nonlinear Schrödinger equation (NLSE), the wave structure of the solution is composed of two kinds of rarefaction waves and two kinds of shock waves, and the parameter ranges of various shock waves are shown. [26,[37][38][39] However, there is no report about the effects of saturated nonlinearity and normal dispersion on shock waves.…”

“…Exciton polariton condensates can provide an ideal platform to study the shock waves controlled by the gain and loss, the dispersion, and the Kerr and saturated nonlinearity. One kind of shock waves has been obtained by theoretical research, [13] in which the dispersion term and the cross interaction are neglected, and an approximation perturbation method is adopted. A type of shock waves can also be acquired when an obstacle potential is introduced, and the cross interaction is also not considered.…”

“…( 6) will be reduced to the simple model given in Ref. [13]. Equation ( 5) permits the following plane wave solution, and its amplitude can be derived from the balance between gain and loss,…”