Dynamics of Two Dark Solitons in a Polariton Condensate

Abstract

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.

Nonautonomous Breather and Rogue Wave in Spinor Bose–Einstein Condensates with Space-Time Modulated Potentials

“…Spinor Bose-Einstein condensates (BECs) have attracted great interests of researchers since their experimental realization on the optically trapped 23 Na Bose condensate. [1][2][3][4][5][6][7] Spinor BECs with freedom of internal spin degrees possess abundant phenomena including magnetic crystallization, spin texture, and fractional vortices, which have no counterpart in magnetically trapped condensates with the spin degree being frozen. [7] Many experimental and theoretical studies on spinor BECs have revealed a variety of interesting phenomena, such as polarto-ferromagnetic phase transitions, quantum knots, condensation of magnon excitations, and various kinds of nonlinear excitations consisting of dark/bright solitons, soliton complexes, rogue waves, and vortices, etc.…”

“….) be the complex matrix solutions of Lax pair (2) with 𝑄 = 𝑄[0] and 𝜆(𝑡) = 𝜆𝑗(𝑡), we obtain the following 𝑁 th-step DT for system (1): [30] 𝛹…”

Interaction between an impurity and nonlinear excitations in a polariton condensate

“…The time evolution of the parameters in Eq. ( 7) can be then obtained via the Euler-Lagrangian equations for the dissipative system [43][44][45][46][47]…”

Interaction between an Impurity and Nonlinear Excitations in a Polariton Condensate

“…The key assumption underlying the ansatz ( 7 ) is that the functional forms of the soliton and the impurity-induced function are preserved in the presence of perturbation, whereas the corresponding parameters become slowly time-dependent. The time evolution of the parameters in Equation ( 7 ) can be obtained via the Euler-Lagrangian equations for the dissipative system [ 47 , 48 , 49 , 50 , 51 ] with and , and labels the real part of the expression. In Equation ( 8 ), the Lagrangian is referred to as the average Lagrangian of Equation ( 6 ) with , where the Lagrangian density is given by …”