Two-dimensional dipolar gap solitons in free space with spin-orbit coupling

Abstract

We present gap solitons (GSs) that can be created in free nearly two-dimensional (2D) space in dipolar spinor Bose-Einstein condensates with the spin-orbit coupling (SOC), subject to tight confinement, with size a ⊥ , in the third direction. For quasi-2D patterns, with lateral sizes l ≫ a ⊥ , the kinetic-energy terms in the respective spinor Gross-Pitaevskii equations may be neglected in comparison with SOC. This gives rise to a bandgap in the system's spectrum, in the presence of the Zeeman splitting between the spinor components. While the present system with contact interactions does not produce 2D solitons, stable gap solitons (GSs), with vorticities 0 and 1 in the two components, are found, in quasi-analytical and numerical forms, under the action of dipoledipole interaction (DDI). Namely, isotropic and anisotropic 2D GSs are obtained when the dipoles are polarized, respectively, perpendicular or parallel to the 2D plane. The GS families extend, as embedded solitons (ESs), into spectral bands, a part of the ES branch being stable for isotropic solitons. The GSs remain stable if the competing contact interaction, with the sign opposite to that of the DDI, is included, while the addition of the contact term with the same sign destabilizes the GSs, at first replacing them by breathers, and eventually leading to destruction of the solitons. Mobility and collision of the GSs are studied too, revealing negative and positive effective masses of the isotropic and anisotropic solitons, respectively.

Two-dimensional solitons and quantum droplets supported by competing self- and cross-interactions in spin-orbit-coupled condensates

“…If the SOC is too strong, figure 6 in [51] suggests that the LHY correction may qualitatively change its form. In fact, the mean-field part of the model may also undergo a dramatic change in the case of strong SOC, replacing the regular solitons by gap solitons, as shown in [22]. Thus, both the mean-field and LHYparts of the model adopted in the present work are relevant (the LHY part is displayed below), provided that the SOC does not grow too strong.…”

“…Recently, we have found that SOC can also support stable 2D gap solitons in the free-space spinor BEC with dipole-dipole interactions (possibly combined with contact interactions, which cannot create such solitons by themselves) in the presence of the Zeeman splitting between the components [22]. In that case, the bandgap in the systemʼs spectrum, which is populated by the gap solitons, is a result of the interplay of the SOC and Zeeman splitting.…”

Gap and embedded solitons in microwave-coupled binary condensates

“…[57], while families of gap solitons obtained in the model with the dipole-dipole interaction, considered in Ref. [30], extend into the bands (however, gaps were never empty in that system). Fig.…”

Two-dimensional composite solitons in Bose-Einstein condensates with spatially confined spin-orbit coupling

“…Similar settings can be implemented in optics, predicting the creation of spatiotemporal solitons ("light bullets") in planar dual-core waveguides and twisted cylinder waveguide with the self-focusing Kerr nonlinearity, respectively [39][40][41]. Further, the interplay between the SO coupling and anisotropic dipole-dipole interactions in 2D free space can create stripe solitons [42], solitary vortices [43][44][45][46], and gap solitons [47] (2D free-space gap solitons can also be created in SO-coupled BECs with contact interactions, at appropriate values of parameters [48]). Recently, it was also found that the combination of LHY and SO-coupling terms in 2D creates anisotropic "quantum droplets" in spinor BECs [12].…”