Dissipation-Induced Coherent Structures in Bose-Einstein Condensates

We discuss how to engineer the phase and amplitude of a complex order parameter using localized dissipative perturbations. Our results are applied to generate and control various types of atomic nonlinear matter waves (solitons) by means of localized dissipative defects.

Figure 1

(a) Evolution of the density for different widths of the defect (3) with ${\gamma }_0=0.5$. The dashed red line shows the exponential decay (2). (b) Dynamics of $N(t)$ normalized to its initial value $N_0=2{\rho }_0^{2}L$ for different strengths of the defect. In (c) and (d) surface plots of $n$ for the defect with $\zeta =1<{\zeta }_{\mathrm{cr}}$ and $\zeta =5>{\zeta }_{\mathrm{cr}}$, respectively. In (e) the same as in (d) but for ${\gamma }_0=-0.5i$ (conservative defect). (f) Snapshots of the current density $j=-|\psi {|}^2[\arg (\psi ){]}_x$ at $t=100$ for the defect from (d) (black solid line) and for the conservative defect from (e) (red dashed line). In all panels $\sigma =1$ and ${\rho }_0=0.4$.

Figure 2

Generation of dark solitons for ${\gamma }_0=0.5$, ${\rho }_0=0.4$, and $\sigma =1$. Shown are density plots with (a) $\zeta =0.1$, $t_f=15$; (b) $\zeta =0.5$, $t_f=15$; and (c) $\zeta =0.5$,$t_f=40$. The time range shown is $t\in [0,100]$ and the spatial range $x\in [-50,50]$.

Figure 3

Effect of the dissipative defect on the condensate in a trap for $\sigma =1$, $\nu =0.002$, ${\rho }_0=0.4$, and ${\gamma }_0=0.5$. (a) $n(0,t)$ for different defect widths: $\zeta =0.5$, 2, 5. (b) Pseudocolor plot of the density evolution for $\zeta =2$. (c) Same as in (b) but removing dissipation at $t_f=100$.

Figure 4

Generation of bright solitons for ${\gamma }_0=0.5$, ${\rho }_0=0.4$. (a) $n(0,t)$ for different defect widths ($\zeta =1$, 3, 5). (b) Density profile at $t=50$ (b) and (c) density evolution for $\zeta =3$.

Figure 5

Generation of dark (a) and bright (b) gap solitons after switching off the defect, with ${\gamma }_0=0.5$ and $\zeta =2$, at $t_f=40$ and $t_f=100$, respectively (solid lines). The initial profiles (dashed lines) are Bloch states for $A=-1$ and ${\rho }_0=0.5$. The dashed line indicates the defect profile.

Figure 6

Initial (thin line) and final (thick line) at $t=1000$ profiles of the density with, $\sigma =-1$, (a) and without, $\sigma =0$, (b) the nonlinearity. The parameters are ${\rho }_0=0.4$, $\zeta =0.5$, and $A=-10$. The dashed line illustrates the defect.

Figure 7

Density plots on the region $(x,y)\in [-30,30]\times [-30,30]$ for different times. The parameters are $t_f=10$, ${\gamma }_0=0.5$, $\zeta =2$, ${\rho }_0=0.66$, and $\nu =0.01$.