Quantum droplets in dipolar quasi-one-dimensional Bose-Einstein condensates in optical lattices

Abstract

We consider quantum droplets in dipolar Bose-Einstein condensates (BECs) embedded in optical lattices within the framework of Gross-Pitaevskii equations. In dipolar BECs, the long-range and anistropic dipole-dipole interaction provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find effective potential for the width and show that the optimum width for formation of quantum droplet increases as the dipole-dipole interaction increases. We study dynamics of the stable droplets and see that its width oscillates periodically, and the amplitude of oscillation increases with the increase of dipole-dipole interaction. In presence of optical lattices, width of a stable droplet changes quasi-periodically while the density profile oscillating periodically in space. The frequency of oscillation are found to depend sensitively on the lattice parameters.

Figures (6)

• Figure 1: Left panel: Variation of effective potential with width for different values of dipole-dipole interaction in absence of optical lattice. The blue curve is drawn for $C_{0}=0.0007$ and red curve is drawn $C_{0}=0.05$. For each curve, we have taken $N=10,\,\, g=4.75,\,\, g_{1}=0.75,\,\, V_{0}=0$ and $k=1.5$. Right panel: Variation of chemical potential with number of particle corresponding effective potential.
• Figure 2: Left panel: Variation of width with time for different values of dipole-dipole interaction in absence of optical lattice. The red curve is drawn for $C_{0}=0.005$, blue curve is drawn for $C_{0}=0.004$, and black curve is drawn $C_{0}=0.003$. For each curve, we have taken $N=10,\,\, g=4.75,\,\, g_{1}=0.75,\,\, V_{0}=0,\,\, k=1.5$ and $x_{0}=0$. Right panel: Density profile corresponding to red curve.
• Figure 3: Left panel: Variation of effective optical lattice potential with the change of center of mass. Right panel: Variation of effective optical lattice potential with width and center of mass. In both the panel we take $V_{0}=1.8,\,\, \eta=0.5$ and $w=1.7$.
• Figure 4: Left panel: Variation of effective potential with width for different values of strength of optical lattice in presence of dipole-dipole interaction. The blue curve is drawn for $V_{0}=0$, black curve is drawn for $V_{0}=1$, and red curve is drawn $V_{0}=1.8$. For each curve, we have taken $N=10,\,\, g=4.75,\,\, g_{1}=0.75,\,\, C_{0}=0.0007,\,\, k=1.5,\,\,\,x_{0}=0.5$ and $\eta=3.5$. Right panel: Variation of chemical potential with number of particle corresponding to effective potential.
• Figure 5: Left panel: Variation of width with time in presence of both optical lattice and dipole-dipole interaction. The curve is drawn for $N=10,\,\, g=4.75,\,\, g_{1}=0.75,\,\, C_{0}=0.0007,\,\, k=1.5,\,\,\,V_{0}=1.8,\,\,\, k=1.5$ and $\eta=0.5$. Right panel: Density profile corresponding width verse time curve.