Dark gap solitons in exciton-polariton condensates in a periodic potential

We show that dark spatial gap solitons can occur inside the band gap of an exciton-polariton condensate (EPC) in a one-dimensional periodic potential. The energy dispersions of an EPC loaded into a periodic potential show a band-gap structure. Using the effective-mass model of the complex Gross-Pitaevskii equation with pump and dissipation in an EPC in a periodic potential, dark gap solitons are demonstrated near the minimum energy points of the band center and band edge of the first and second bands, respectively. The excitation energies of dark gap solitons are below these minimum points and fall into the band gap. The spatial width of a dark gap soliton becomes smaller as the pump power is increased.

Figure 1

(a) Energy dispersion versus $V_0$ at $k=\pi /2$ and (b) band diagram at $V_0=1$.

Figure 2

(a) Numerical (red solid lines) and analytic (blue solid lines) density distributions of dark gap solitons for pump power $\alpha =3,5,7$ under $V_0=1$; (b) numerical (red solid lines) and analytic (blue solid lines) density distributions of dark gap solitons for pump power $\alpha =3,5,7$ under $V_0=3$. The periodic potential is shown by black dashed line. The energy detuning is $\delta =-0.25$, which is located below the first band.

Figure 3

(a) Numerical (red solid lines) and analytic (blue solid lines) density distributions of dark gap solitons for pump power $\alpha =3,5,7$ under $V_0=1$; (b) numerical (red solid lines) and analytic (blue solid lines) density distributions of dark gap solitons for pump power $\alpha =3,5,7$ under $V_0=3$. The periodic potential is shown by black dashed line. The energy detuning is $\delta =-0.25$ inside the band gap of first and second band.

Figure 4

Minimum required pump power (${\alpha }_{min}$) as a function of the potential depth at $\delta =-0.05$ and $\delta =-0.25$.